1. A long straddle consists of a long call and a long put on the same stock and profits from dramatic price movement by the stock. A short straddle involves the sale of a call and a put on the same stock and profits from little or no stock price change. Investors going long would anticipate volatility in excess of that discounted by the options’ prices while investors going short would expect volatility below that already discounted. Since volatility enhances option prices, long straddles would tend to pay higher premiums for more volatile options, whereas short straddles must accept lower premiums for less volatile options.

2. A range forward is actually an option strategy that combines a long call and a short put (or vice versa) through a costless transaction. Because the options will not have the same striking price, the combination is classified as a range forward as opposed to an actual forward, created by combining long and short options with the same striking price. It is fair to view actual forwards as a special case (or zero-cost version) of range forwards.

3. CFA Examination II (1993)

Call options give the owner the right, but not the obligation, to purchase SFr’s for a pre-specified amount of domestic currency. Purchasing an at-the-money call option would guarantee the current exchange rate over the life of the option. If the SFr declines in value, the call will not be exercised since francs can be purchased more cheaply in the open market and redeeming the bond issue will be less costly.

Contrasting characteristics: (1) Currency options are traded worldwide and enjoy a liquid market. (2) Exchange-traded currency option contracts have standard amounts, maturities, etc. (3) Over-the-counter options could be tailored to meet Michelle’s needs. (4) The initial cash outflow would be the premium. (5) The use of options preserves the ability to profit. (6) No counterparty credit risk. (7) Must roll to match year obligation.

Currency forward contracts commit the seller to deliver the specified amount of currency to the buyer on a specified future date at a fixed price. A short position in a forward contract requires delivery.

Contrasting characteristics: (1) The market for forward contracts is over-the-counter and sometimes may not be as liquid as option or futures market. (2) Forward contracts may be custom designed for specific applications. (3) Cash does not change hands until a forward contract is settled. (4) Counterparty credit risk. (5) Can best match 5-year obligation.

Currency futures are like forward contracts except the gain or loss on the contract is settled daily under the supervision of an organized exchange. A short position in the futures requires either offset or delivery at expiration.

Contrasting characteristics: (1) Futures are traded in standardized contracts and are highly liquid. (2) Cash is required for daily settlement. (3) A margin account is required. (4) Management and administration costs are higher than with a forward or option contract. (5) No counterparty credit risk. (6) Must roll to match year obligation.

4. CFA Examination III (1991)

The other three factors affecting the value of call options and the ways that changes in them affect value are:

(1). Increases in underlying stock volatility. A call cannot be worth less than zero no matter how far the stock price falls, but rising stock prices can increase the call’s value without limit. Therefore, the wider the range within which a stock’s price can fluctuate (i.e. the greater its volatility), the greater the chance that the option will expire in-the-money, the higher the expected payoff from owning it, and the higher its value. A wider range of probable future prices on the underlying stock increases the probability of higher payoffs in general but because the call’s value cannot decline below zero does not symmetrically increase the probability of lower payoffs.

(2). The risk-free interest rate. Call value increase with increases in interest rates (given constant stock prices) because higher interest rates make the ownership of call options more attractive. The call owner does not pay for the stock until the option is exercised; its owner can, therefore, take advantage of the time value of money by investing free interest rate increases the time value benefit to the call owner, increasing the value of the call option.

(3). The exercise price of the option. Call values decrease with increases in the exercise price. When a call option is exercised, the payoff is the difference between the stock price at the time of exercise and the exercise (or strike) price. A higher exercise price decreases the expected payoff from the call, thus reducing the option’s value.

5. Put-call parity indicates that a long position in a stock combined with being short a call and long a put (with the same strike price) is a risk-free investment. In other words, no matter what the stock price at expiration, the payoff will be the same. Consequently, any investment in this portfolio should earn the risk-free return. The three-step process for valuing options is to

(1). Determine a distribution of future stock prices,

(2). Calculate the cash flows from the option at the future prices, and

(3). Discount these expected cash flows to the present at the risk-free rate.

It is this final step that is relevant. Cash flows can be discounted at the risk-free rate because of the riskless replicating portfolio strategy.

6. The Black-Scholes model is derived by showing how a portfolio of the underlying asset and risk-free bonds can be created that exactly mimics the price of an option. This involves taking a long position in the underlying asset to replicate a call option. For currency options, the underlying asset can be thought of as risk-free deposits (bonds) in the foreign currency. So, just as stocks pay dividends, foreign deposits pay interest. Therefore, we can just substitute the foreign risk-free rate for the dividend yield when pricing options on currency.

7. If there are no transaction costs, it is only rational to exercise a call option early, immediately before a dividend payment. This is because it will always be more profitable to sell the option and buy the stock in the open market rather than exercise the option, unless there is a dividend. When a firm pays a dividend, the price of the stock usually declines by approximately the amount of the dividend. This has two impacts on the option holder. First, the decrease in the stock price decreases the value of his option. Second, the investor does not get the dividend payment unless he actually has exercised the option and owns the stock. Consequently, if the value of the dividend is greater than C+K-S, it will be beneficial to exercise early. Note, this is most likely to happen for every in-the-money options.

For put options, it may be the case that the interest that could be earned on the proceeds from early exercise is greater than the intrinsic option value (P+S-K), so early proceeds from early exercise is optimal. Using similar logic as above, puts should always be exercised immediately after a dividend (on a dividend paying stock) because the stock’s price declines after a dividend, thus making the put more valuable.

8. In the Black-Scholes model, the expected future value of a stock is a function of the risk-free interest rate and the dividend yield. As long as the risk-free rate is greater than the dividend yield, the future expected value will be greater than today’s price. The longer the time period, the higher the expected price. So, as time to expiration increases, there are two opposing forces on the value of a European put. First, the increased time to expiration increases the chances of the option being more in-the-money. This increases put value. Second, the higher expected price at expiration decreases the expected value of the put’s payoff at expiration and, therefore, decreases the put value. Depending on which of these two effects is larger, the put may increase or decrease in price with an increase in time to expiration.

For a European call option, these two effects work in the same direction, since an increase in expected future price increases the value of a call. Hence, an increase in the time to expiration always increases the value of a European call.

9. Since the price of an option is positively related to volatility, “buying low vol and selling high vol” is the same as the idea of “buy low, sell high” for any risky asset if the other parameters that affect option prices are fixed. The other factors that affect option prices can be effectively neutralized by holding the appropriate portfolio of options and the underlying asset (beyond the scope of this question). If this is the case, then the risky asset is volatile itself, not the underlying foreign currency.

10. A decrease in security volatility will cause an increase in both the call and put option values. For example, when the volatility of the underlying asset’s price decreases, the call option becomes less valuable since this decreases the probability that the option will be deeper in the money at expiration (a similar scenario is also true for the put option).

11. On October 19, 1987, implied volatilities sky-rocketed. The jump in implied volatility increased the value of call options more than enough to offset the negative impact of the in the index level.


Answers to Problems

1. CFA Examination III (1987)

1(a). Cu – Cd 20 – 0
Hedge ratio = = = 0.5
uS – dS 120 – 80

(1 + r) – d (1 + 0.1) – 0.0
Implied probability (p) = = = 0.75
u – d 1.2 – 0.8

pCu + (1 – p)Cd .75(20)+.25(0)
Call value = = = 13.6
1 + r 1 + .01

Step 1

Set up binomial tree and calculate the option values at expiration for each ending stock price.

Step 2

Solve for the amount to invest in the stock and the amount to borrow in order to replicate the option given its value in the up state and its value in the down state. Solve these equations simultaneously.

Step 3

Use the values derived in Step 2 to solve for the value of the option at the beginning of the period.


Step 1



Step 2

20 = 120 x D – 1.1 x B
0 = 80 x D – 1.1 x B

-1.1(20) – (-1.1)(0) -22
D = = = 0.5
120(-1.1) – 80(-1.1) -44

C = 80(.5) – 1.1 x B
0 = 80(.5) – 1.1 x B

B = 40/1.1 36.4

Step 3

C = 50 – 36.4 = 13.6

1(b). The binomial option pricing model is a discrete version of the continuous time Black-Scholes option pricing model. As the number of intervals in the binomial model approaches infinity, the option value derived from this model approaches the option value derived from the Black-Scholes model.

The binomial model is more flexible than the Black-Scholes model because it does not require one to assume constant interest rates and constant variance throughout the horizon. These values can be changed at any of the nodes in the binomial tree. However, the binomial model is more cumbersome to use since accuracy requires that the tree include many nodes.

2. CFA Examination III (1992)

2(a). An individual put will hedge an amount of the underlying stock index equal to the underlying value of the put, which in each case here is the respective stock index times $100.

Also, due to the differing betas, the portfolio and the stock indexes are expected to produce gains or losses in proportion to their respective betas. Thus the number of puts required to hedge the portfolio must be adjusted for the betas of the respective stock indexes relative to the beta of the portfolio.

The number and cost of protective puts could be calculated indirectly or directly.

Indirect method:

(port)(Vport ) = (GAC)(VGAC) = (opt)(Vopt)

The indirect method is based on the fact that an overall portfolio’s beta is equal to the weighted average of its component betas. Since we are seeking a zero beta portfolio, the left-hand side of the equation can be set to zero.

For the S&P 100:
0 = -(1.05)(7,761,700) = (0.95)(Vopt)
Vopt = -(1.05/0.95)(7,761,700)
Vopt = -8,578,721
Number of puts = 8,578,721/(365 x 100) = 235
Cost of puts = 235 x $10.25 x 100 = $240,875
For the S&P 500:
0 = -(1.05)(7,761,700) = (1.00)(Vopt)
Vopt = -(1.05/1.00)(7,761,700)
Vopt = -8,149,785
Number of puts = 8,149,785/(390 x 100) = 209
Cost of puts = 209 x $11.00 x 100 = $229,900
For the NYSE:
0 = (1.05)(7,761,700) = (1.03)(Vopt)
Vopt = -(1.05/1.03)(7,761,700)
Vopt = -7,912,413
Number of puts = 7,912,413/(215 x 100) = 368
Cost of puts = 368 x $6.25 x 100 = $230,000
Direct method:
The direct method calculates the number of puts by utilizing the hedge ratio (HR).

HR = volatility of hedged security / volatility of hedging instrument

Beta, which measures the movement in a security relative to the S&P 500, serves as a measure of volatility.

For the S&P 100:

Number of puts = (1.05/0.95)(7,761,700)/(365 x 100) = 235

Cost of puts = 235 x $10.25 x 100 = $240,875

For the S&P 500:

Number of puts = (1.05/1.00)(7,761,700)/(390 x 100) = 209

Cost of puts = 209 x $11.00 x 100 = $229,900

For the NYSE:

Number of puts = (1.05/1.03)(7,761,700)/(215 x 100) = 368

Cost of puts = 368 x $6.25 x 100 = $230,000

2(b). The cost of the S&P 500 and NYSE puts are essentially the same and less than the cost of the S&P 100 puts; other relevant factors in the decision are correlation and liquidity.

While the hedge calculated in Part A is intended to protect GAC’s portfolio from a decline, the portfolio does not replicate any of the indices. The hedge could be less than perfect if the price movement of GAC’s portfolio does not track the index movement. In this context, the index which has the highest correlation with GAC’s portfolio (the S&P 500, 0.95) would be most preferred, while the index exhibiting the lowest correlation with GAC (the S&P 100, 0.86) would be least preferred.

The hedge should be implemented with a minimum of market impact thus another consideration is liquidity. If the hedge transaction represents a disproportionate share of average daily trading volume, the market could move adversely, increasing the cost of the hedge. The required put position represent 2.4% (235/10,000) of average daily trading volume for the S&P 100, 5.2% (209/4,000) for the S&P 500, and 36.8% (368/1,000) for the NYSE. Thus based on trading volume and likely market impact, the S&P 100 would be most preferred, with the S&P 500 also acceptable; the NYSE transaction would clearly be least desirable.

The S&P 500 options would appear to be the preferred protective position, offering the best combination of cost, hedging ability (correlation), and liquidity; the S&P 100 is a relatively costly position and the NYS position is relatively illiquid.

2(c). The scenario in Part A used options with strike prices equal to the current index value (i.e. “at the money”). Such options have no intrinsic value (the difference between the index value and the strike price) and contain only a time premium. Buying the put at-the-money will enable a hedge of the portfolio with no loss from current levels assuming that the betas used in the GAC hedge are stationary; then decreases in the portfolio value will be offset exactly by increases in the put option value.

As the relationship between the strike price and the index value changes, however, a trade off enters into the investment decision. If the strike price is below the current index value, then the puts are “out of the money.” These options will be less expensive than “at the money” or “in the money” puts; however they expose the portfolio to potential loss, with the difference between the index value and strike price being analogous to the deductible on an insurance policy. For example, if the S&P 500 index is at 400 and the strike price at 390, then GAC’s portfolio would be unprotected for the 10 point difference. The portfolio value will decline by 2.5 (10/400) if the index drops to 390 or lower. However, an index value between 390 and 400 at option expiration will not provide any offset to a portfolio decline. The portfolio would have incurred the cost of the option, only to have it expire worthless at expiration.

If the strike price is above the current index value, then the puts are “in the money.” These puts will be most expensive, since they include both intrinsic value and a time premium. Buying “in the money” puts is analogous to selling the portfolio at the strike price and owning a call option. If the S&P 500 index is 390 and the strike price is 400, then the portfolio is assured of a 2.6% (10/390) gain (ignoring the cost of the option).

In summary, the protective put strategy will provide a floor value for the portfolio. However, the various index options will each have strike prices different from their respective current index values. Thus the portfolio manager must weigh the trade off between the cost of the put option (the higher the strike price, the higher the put premium) and the degree of protection sought (level of assured portfolio value).

2(d). An option pricing model, such as the Black-Scholes or binomial approaches, can be used to establish the fair value of an option and to facilitate value comparisons across different strike prices, different times to expiration, and different stock index options. To the extent that mispricings can be identified, arbitrage opportunities may be exploited.

The Black-Scholes formula utilizes the current index price and strike price, in conjunction with the risk-free interest rate, the time to expiration, and return volatility, to establish a fair option price. Alternatively, prevailing option prices may used in the model to calculate implied volatility and to facilitate volatility comparisons across strike prices and times to expiration; this also enables assessment of option premiums against implied risk levels. The model can also be used to calculate hedge ratios, the change in portfolio value for a $1 change in index price.

In summary, option pricing models allow the portfolio manager to quantify the relative pricing of options to determine which option gives the most efficient portfolio protection per dollar of cost.

3. CFA Examination II (1998)

3(a). Critique of Belief
Joel Franklin’s belief is incorrect. There are two fundamental kinds of options: American style and European style. An American option permits the owner to exercise the option at
any time before or at expiration. The owner of a European option may exercise it only at expiration. If an option is at expiration, it will have the same value whether it is American or European.

The owner of an American option can treat the option as a European option simply by postponing the decision to exercise until expiration. Therefore, the American option cannot be worth less than the European option. However, the American option can be worth more. The American option will be worth more if circumstances make exercise of the option before its expiration desirable. So, it may have a higher premium.

3(b). European-Style Option’s Value
The formula to calculate a call option using put-call parity is c = S + p – Xe-rt

where c = the price of a European call option at time t
S = the price of the underlying stock at time t
p = the price of a European put at time t
X = the exercise price for the option
t = time to expiration = one year

Therefore, from the information given,

Call option = $4.408 = $43 + 4.00 – 45.00e-.055

3(c). Effect of Variables
Effect on Call Option’s Value
i. An increase in short-term interest rate Positive
ii. An increase in stock price volatility Positive
iii. A decrease in time to option expiration Negative

4(a). Calculate the following parameters, option values, and hedge ratios at each node:

U = 42/40=1.05
D = 38.4/40=.96
R = (1.06)1/3 = 1.01961
rf = 1.961% per period
Pu = (R D)/(U D) = (1.01961 .96)/(1.05 .96) = .05961/.09 = .662

4(a)(i). S = 40.32

If the stock moves up the option will be worth $4.34 (Cudu); if the stock moves down the option will be worth $.71 (Cudd). The value of the option and hedge ratio at this node is

Cud = .662(4.34) + (1 .662)(.71) = 2.501/1.01961 = 2.45

HRud = 4.34 – .72 = 1.00
(1.05 – .96) x 40.32

4(a)(ii). S = 42

If the stock moves up the option will be worth $6.62 (Cuu); if the stock moves down the option will be worth $2.86 (Cud). The value of the option and hedge ratio at this node is

Cu = .662(6.62) + (1 .662)(2.86) = 5.34912/1.01961 = 5.246

HRu = 6.62 – 2.86 = 1.00
(1.05 – .96) x 42.00
Cuu = .662(8.31) + (1 .662)(4.34) = 6.96814/1.01961 = 6.834

4(a)(iii). S = 40

If the stock moves up the option will be worth $5.05 (Cuu); if the stock moves down the option will be worth $1.87. The value of the option and hedge ratio at this node is

C = .662(5.05) + (1 .662)(1.87) = 3.97516/1.01961 = 3.8987

HRu = 5.05 – 1.87 = 0.8833
(1.05 – .96) x 40.00
Cd = (.662)2(4.34) + (2)(1 .662)(0.71) = 2.38194/1.0396 = 2.29

So the riskless portfolio will initially contain 1 call option and be short 0.8833 shares of stock. Since after an initial up move to 42.00 the option can only finish in-the-money, the hedge ratio is 1.00.

4(b). Ending Price Number of Paths Path Probability Total Probability
$46.31 1 .60753=.2242 .2242
$42.34 3 .60752 x .39251 = .1449 .4346
$38.71 3 .60751 x .39252 =.1449 .2808
$35.39 1 .39253=.0604 .0604

C = .6623 (8.31) + (3)(.6622)(1 .662)(4.34) +(3)(.662)(1 .662)2 (.71) = 4.50/1.06 = 4.24

4(d). P = (1 .662)3 (2.61) = 0.1008/1.06 = .095

Check with put call parity. Does the following hold true:

C – P = S – PV(K)
4.24 – .095 = 40 – 38/1.06
4.15 = 4.15
Put-call parity does hold exactly.

5. CFA Examination II (2000)

5(a). Over two periods, the stock price must follow one of four patterns: up-up, up-down, down-down, or down-up. To construct a 2-period price lattice for a two-year option, each period consists of 365 days for a total of 730 days.

U = 1.2214

D=1/U D = 1/1.2214 D = 0.8187

The binomial parameters are:

U = 1 + percentage increase in a period if the stock price rises 1.2214
D = 1 + percentage decrease in a period if the stock price falls 0.8187
R = 1 + Risk-free rate = 1.06184





Period 1 Period 2 Period 3

Period 1:
Up: $50 x 1.2214 = $61.07
Down: $50 x 0.8187 = $40.94

Period 2:
Up: $61.07 x 1.2214 = $74.59
Down: $61.07 x 0.8187 = $50.00
Up: $40.94 x 1.2214 = $50.00
Down: $40.94 x 0.8187 = $33.52

5(b). For each terminal stock price, a call option has a specific value.Because the company does not pay a dividend,  = 0. With a stock paying a dividend, the dividend yield would be subtracted from the risk-free rate.

The probability of an upward stock price movement in any period is:

0.6038 = (1.06184 – 0.08287)/(1.2214 – 0.08187)

The probability of a downward stock price movement in any period is:

1 – 0.6038 = 0.3962

The vaue of a call option at expiration must be :

Max(0, S – X)

S = current price of stock index
X= exercise price of the call option





Period 0 Period 1 Period 2

Period 2:
Up-up: max(0, S-X) = max(0, $74.59 – $60.00) = max(0, $14.59) = $14.59
Up-down: max(0, S-X) = max(0, $50.00 – $60.00) = max(0, -$10.00) = $0.00
Down-up: max(0, S-X) = max(0, $50.00 – $60.00) = max(0, -$10.00) = $0.00
Down-down: max(0, S-X) = max(0, $33.52 – $60.00) = max(0, -$26.48) = $0.00

Period 1:
$14.59 x 0.6038 (probability of an upward stock movement) = $8.81
$ 0.00 x 0.3962 (probability of a downward stock movement) = $0.00
$ 0.00 x 0.6038 (probability of an upward stock movement) = $0.00
$ 0.00 x 0.3962 (probability of a downward stock movement) = $0.00

Period 0:
$8.30 x 0.6038 (probability of an upward stock movement) = $5.01
$0.00 x 0.3962 (probability ofa downward stock movement) = $0.00

With a discount factor of 0.94176, the value of the call in period 0 is:

($5.01 x 0.94176) + ($0.00 x 0.94176) = $4.72



C = (0.6038 x 0.6038 x 14.59 +0.6038 x 0.3962 x 0.00 +0.3962 x 0.6038 x 0.00
+ 0.3962 x 0.3962 x 0.00)/(1.06184)2

C = $4.72

5(c). The put-call parity formula is:

pt = ct – St + Xe-r (T-t)

c = call option price = $4.72
S = current stock or index pice = $50.00
X = exercise price = $60.00
e-r (T-t) = discount factor = 0.88692
T = time to expiration in periods = 2
t = current time = 0
r = risk-free rate = 0.06

p = $4.72 – $50.00 + ($60 x 0.88692)

p = $7.94

6(a). u = 33.00/30.00 = 36.00/33.00 = 1.10 d = 27.00/30.00 = 24.30/27.00 = 0.90

r = (1 + .05)1/2 = 1.0247

r – d 1.0247 – 0.90
p = = = .1247/.20 = .6235 $8.30
u – d 1.10 – 0.90 $5.68

Cuu = Max [0, 36.30 – 28] = 8.30
Cud = Max [0, 29.70 – 28] = 1.70 3.84 $1.70
Cdd = Max [0, 24.30 – 28] = 0

(.6235)(8.30) + (.3765)(1.70) 5.17 + 0.64
CU = = = 5.815/1.025 = $5.68
1.024695 1.024695

(.6235)(1.70) + (.3765)(0.00) 1.05995
Cd = = = $1.03
1.024695 1.024695

(.6235)(5.675) + (.3765)(1.0344) 3.538 + .3895
Co = = = $3.84
1.024695 1.024695

h = (5.675 – 1.0344)/(36.30 – 24.30) = 4.64/12.00 = 0.3867

6(b)(i). Asian-style ($33.00 + $36.30)/2 – $28.00 = $6.65

($33.00 + $29.70)/2 – $28.00 = $3.35
($27.00 + $29.70)/2 – $28.00 = $0.35

($27.00 + $24.30)/2 – $28.00 = 0

(.6235)(6.65) + (.3765)(3.35) 4.146 + 1.261
CU = = = $5.28
1.024695 1.024695

(.6235)(0.35) + (.3765)(0.00)
Cd = = $0.21

(.6235)(5.28) + (.3765)(0.21)
Co = = $3.29

6(b)(ii). Lookback
max ($33.00, $36.30)- $28.00 = $8.30

max ($33.00, $29.70) – $28.00 = $5.00
max ($27.00, $29.70) – $28.00 = $1.70

max ($27.00, $24.30) – $28.00 = 0

(.6235)(8.30) + (.3765)(5.00) 5.175 + 1.8825
CU = = = $6.89
1.024695 1.024695

(.6235)(1.70) + (.3765)(0.00)
Cd = = $1.03

(.6235)(6.89) + (.3765)(1.03)
Co = = $4.57
6(b)(iii). Digital



(.6235)(10.00) + (.3765)(10.00) 6.235 + 3.765
CU = = = $9.76
1.024695 1.024695

(.6235)(10.00) + (.3765)(0.00)
Cd = = $6.08

(.6235)(9.76) + (.3765)(6.08)
Co = = $8.17

7(a). One way is to calculate approximate dividend yield: approximate annual dividend yield = 8/75 = .1067

Asset Price Strike Volatility T R(f) Div. Yield Put/Call
75.00 70.00 0.2000 0.25 0.0900 0.1067 1
B S Value Delta Gamma ~X(1) ~X(2)
5.68424 0.6798 0.0406 0.6982 0.5982

Or we could calculate the value ex-dividend: 75 2 = 73

Asset Price Strike Volatility T R(f) Div. Yield Put/Call
73.00 70.00 0.2000 0.25 0.0900 0.000 1
B S Value Delta Gamma X(1) X(2)
5.66469 0.6946 0.0429 0.6946 0.5946

The difference in price is less than 2 cents, much less than the bid ask spread.

7(b). Using put call parity

P = C S + PV(D) + PV(K)
P = 5.68 75 + (70+2)*exp(-.09*.25)
P= 1.08

Asset Price Strike Volatility T R(f) Div. Yield Put/Call
75.00 70.00 0.2000 0.25 0.0900 0.1067 1
B S Value Delta Gamma X(1) X(2)
7.25695 0.9649 0.0334 0.9649 0.8649

So the price would increase: $1.57

7(d). An increase in the volatility to 30% would increase the call’s value. A decrease in the risk free rate to 8% would decrease the call’s value.

8(a). Stock Price Call Value Hedge Ratio
$25 $0.02 0.0104
$30 0.26 0.1003
$35 1.32 0.3409
$40 3.62 0.6331
$45 7.51 0.8438
$50 12.00 0.9463
$55 16.80 0.9838

X = $40; r = .09; T = 6 months (0.5);  = 0.25

ln (S/X) + [r + (2/2)]T
d1 = d2 = d1 –  (T)1/2
 (T)1/2

For example, if S = 25

ln(25/40) + [.09 + (.252/2)](0.5)
d1 =

-.47 + [.09 + .03125](0.5) -.47 + .060625
= = = -.409375/.17678 = -2.31
(.25)(.7071) .17678

d2 = -2.31 – (.25)(0.5)½ = -2.31 – .17678 = -2.49

N(d1) = 1 – .9896 = 0.0104 N(d2) = 1 – .9936 = 0.0064

C = S(N(d1)) – Xe-rT(N(d2)) = 25(0.0104) – 40e-(.09)(.5)(.0064) = 0.26 – 0.24 = $0.02

8(b). The call value for each level of stock price is lower than those shown in Exhibit 23.11 because:
(1) A decrease in time to expiration (one year to six months) causes a decrease in the call value.
(2) A decrease in security volatility () causes a decrease in the call value.

8(c). For S = 40
P = Xe-rT(N(-d2)) – S(N(-d1)) = 40e-(.09)(.5) (.4325) – 40(.3669) = 16.539 – 14.676 = $1.86
where N(-d1) = 1 – .6331 = .3669 and N(-d2) = 1 – .5675 = .4325

9(a). Call:

Future Price Strike Volatility T R(f) Div. Yield Put/Call
46.50 46.50 0.2300 0.50 0.0545 0.000 1
Future Option Delta Gamma d(l) d(2)
4.14286 0.1150 0.0524 0.1150 0.1150


Future Price Strike Volatility T R(f) Div. Yield Put/Call
46.50 46.50 0.2300 0.50 0.0545 0.000 1
Future Option Delta Gamma d(l) d(2)
4.14286 0.1150 0.0524 0.1150 0.1150

9(b). You have created a long forward on a future. An investor that is bullish on the futures price would take a long position in this synthetic forward.

10(a). Asset Price Strike Volatility T R(f) Div. Yield Put/Call
653.50 670.00 0.1600 0.25 0.0650 0.0280 1
B S Value Delta Gamma X(1) X(2)
15.48 0.1860 0.0074 0.1873 0.2673

Asset Price Strike Volatility T R(f) Div. Yield Put/Call
653.50 670.00 0.1751 0.25 0.0650 0.0280 1
B S Value Market Price Difference Delta Gamma X(1) X(2)
17.40 17.40 0.00 0.1628 0.0068 0.1640 0.2515

So, the option has an implied volatility of 17.51%.

10(c). The market price may differ from the estimated price for the following reasons:

1. The quote may be stale. That is the market maker may not have adjusted the price to reflect new market conditions.
2. Is this a bid or ask price? The ask price win have a higher implied volatility than the bid price or the midpoint.
3. We are making the assumption that dividends are paid continuously, when in fact they are clumped together. So our estimate of the effective dividend yield may be incorrect.
4. Black-Scholes model may not be the correct pricing model.

11(a). The volatility estimates are calculated as:

Period A 0.2708
Period B 0.2570

Asset Price Strike Volatility T R(f) Div. Yield Put/Call
120.63 115.00 0.2570 0.17 0.0742 0.0365 1
B S Value Market Price Difference Delta Gamma X(1) X(2)
8.72 12.25 3.53 0.5608 0.0265 0.5643 0.4583

The market price is much higher than the calculated BS price. This implies that if all of the other parameters of the model are correct, the implied BS volatility is much higher than the historical volatility. This could be because of recent developments in the stock. Another more controversial explanation is that implied volatilities have a risk-premium built into them such that implied volatilities are on average higher than realized historical volatilities.

Cost/Contract x 31,250
long 1.44 Call 0.0422 $1,318.75
short 1.48 Call 0.0255 $ 796.88
long 1.40 Put 0.0260 $ 812.50
short 1.44 Put 0.0422 $1,318.75

June Net Initial Long Call Short Call Long Put Short Put Total Net
USD/GBP 1.44 Profit 1.48 Profit 1.40 Profit 1.40 Profit 1.44 Profit Profit
1.36 $15.63 0 0 1250 -2500 ($1,234.38)
1.40 $15.63 0 0 0 -1250 ($1,234.38)
1.44 $15.63 0 0 0 0 $15.63
1.48 $15.63 1250 0 0 0 $1,265.63
1.52 $15.63 2500 -1250 0 0 $1,265.63



1.36 1.40 1.44 1.48 1.52


This position resembles a bull vertical spread. The purchaser of this portfolio is probably moderately bullish on the exchange rate. We see this from the willingness to give up the extreme upside in exchange for limiting the downside.

12(c). This is a simple application of put call parity
C – P = FX * exp( rf * dt) K *exp( rd *dt)
where FX is the exchange rate,
rd (rf) is the domestic (foreign) risk-free rate,
dt is the time to expiration.
C – P = 1.385*exp(-.07*.1667) – 1.44*exp(-.05*.1667) = ($0.0591)

13. CFA Examination II (1999)
13(a). The maximum loss at expiration for the straddle buyer takes place at the exercise price and is $7. This is the total cost to purchase the long call and the long put that are combined to create the straddle. If the stock price exceeds the exercise price, the straddle owner will exercise the call; if the stock price is less than the exercise price, the straddle owner will exercise the put. The maximum loss shown in the graph below and is computed as follows:

CT + PT = Max{$0, ST – X} – Ct + Max{$0, X – ST} – Pt
CT + PT = Max{$0, $50 – $50} – $4 + Max{$0, $50 -$50} – $3
CT + PT = Max{$0, $0} – $4 + Max{$0, $0} – $3
CT + PT = (-$4) + (-$3)
CT + PT = -$7

Profits will be realized for the straddle if the stock price moves above $57 or below 43 (the breakeven points.) The breakeven points for the straddle buyer are the exercise price of the options plus and minus the cost of the straddle. Stock prices, at expiration, tht are lower than $43.00 or higher than $57.00 will produce a gain for this position. These gains are shown as the intersection between the payoff profit and the zero profit line in the graph for this section, given bellow. The breakeven points are those stock prices that result in zero profit:

CT + PT = Max{$0, ST – X} – Ct + Max{$0, X – ST} – Pt
CT + PT = Max{$0, $43 – $50} – $4 + Max{$0, $50 – $43} -$3
CT + PT = Max{$0, -$7} – $4 + Max{$0, $7} -$3
CT + PT = $0 + (-$4) + $7 + (-$3)
CT + PT = $0

CT + PT = Max{$0, ST – X} – Ct + Max{$0, X – ST} – Pt
CT + PT = Max($0, $57 -$50} – $4 + Max{$0, $50 -$57} – $3
CT + PT = Max{$0, $7} – $4 + Max{$0, -$7} – $3
CT + PT = $0 + $7 – $4 – $3
CT + PT = $0

13(b). The alternative option combination, consisting of buying a put and a call with the same expiration dates and the same underlying stock but different strike prices is called a strangle. In a strangle the call has an exercise price above the current stock price and the put has an exercise price below the current stock price.

The maximum loss at expiration is $4.50, the cost of the two options (i.e., the long call and the long put). The maximum loss is computed as follows:

CT(ST,X1,T) + PT(ST,X2,T) = Max{$0, ST – X1} – Ct + Max{$0, X2 – ST} – Pt
CT(ST,X1,T) + PT(ST,X2,T) = Max{$0, $50 – $55} – $2.50 + Max{$0, $45 – $50) – $2
CT(ST,X1,T) + PT(ST,X2,T) = Max{$0 – $5} – $2.50 + Max{$0, -$5} – $2
CT(ST,X1,T) + PT(ST,X2,T) = $0 – $2.50 + $0 – $2
CT(ST,X1,T) + PT(ST,X2,T) = -$4.50

The breakeven points for the position are $40.40 and $59.50. The total cost for the two options is $4.50. The breakeven points are calculated by taking the put option strike minus the combined option premium ($45 – $4.50 = $40.50), and taking the call option strike plus the combined option premiums ($55 + $4.50 = $59.50). These are shown as the two intersections between the payoff profile and the zero profit line in the graph below.

CT(ST,X1,T) + PT(ST,X2,T) = Max{$0,ST – X1} – Ct + Max{$0,X2 – ST} – Pt
= Max{$0, $40.50 – $55} – $2.50 + Max{$0,$45 – $40.50} – $2.00
= Max{$0, -$14.50} – $2.50 + Max{$45 – $40.50} – $2.00
= $0 – $2.50 + $4.50 – $2.00
= $0

CT(ST,X1,T) + PT(ST,X2,T) = Max{$0, ST – X1} – Ct + Max{$0, X2 –ST} – Pt
= Max{$0, $59.50 – $55} – $2.50 + max{$0, $45 – $59.50} – $2.00
= Max{$0, $4.50} – $2.50 + Max{$0, -$14.50} – $2.00
= $4.50 – $2.50 + $0 – $2.00
= $0

Stock prices at expiration that are lower than $40.50 or higher than $59.50 will produce a gain for this position.

14(a) Price of ARB Profit on Profit on Net Profit on
Stock at Expiration Initial Cost Call #1 Position Call #2 Position Total Position
40 ($1.72) $0.00 $0.00 ($1.72)
45 ($1.72) $0.00 $0.00 ($1.72)
50 ($1.72) $0.00 $0.00 ($1.72)
55 ($1.72) $5.00 $0.00 $3.28
60 ($1.72) $10.00 $0.00 $8.28
65 ($1.72) $15.00 ($10.00) $3.28
70 ($1.72) $20.00 ($20.00) ($1.72)



40 45 50 55 60 65 70 75


Breakeven points are $51.72 and $68.28. Maximum profit occurs at $60.

14(c). The user of this position is betting on low volatility (that prices will stay between breakeven points). The holder has limited liability for substantial price declines and unlimited liability for substantial price increases.

15. Consider the following put option transactions: (i) long one put #1; (ii) short two puts #2, and (iii) long one put #3. The net initial cost of this set of transactions is $0.83 (= 1.70 + 6.47 – 3.67 – 3.67) and its terminal payoffs for a variety of potential expiration date SAS stock prices are:

SAS Price Value of Value of Value of Cost of
(Expiration) Put #1 Put #2 Put #3 Options Net Profit
20 15.00 40.00 25.00 0.83 -0.83
25 10.00 30.00 20.00 0.83 -0.83
30 5.00 20.00 15.00 0.83 -0.83
36 0.00 10.00 10.00 0.83 -0.83
40 0.00 0.00 5.00 0.83 4.17
45 0.00 0.00 0.00 0.83 -0.83
50 0.00 0.00 0.00 0.83 -0.83
55 0.00 0.00 0.00 0.83 -0.83
60 0.00 0.00 0.00 0.83 -0.83
Graphing these payoffs would lead to the same illustration as shown in Exhibit 23.31.

16. CFA Examination III (1997)

The suggested strategy is essentially a zero-premium collar, which is constructed by selling a call option with enough premium to fund the purchase of the put option. In this case, at-the-money protection (provided by the put) is more expensive than the out-of-money call. Therefore, the strategy requires the sale of two calls to finance one put. The call is not struck (sold) at the money because the fund manager, Ken Webster, does not want to incur the opportunity cost for a 1.05 percent rise above the S&P 500 Index’s current 668 level. By selling two 675 calls, the manager would expose the portfolio to incurring losses (from the calls) at twice the rate of the underlying portfolio’s appreciation. The portfolio would experience full market participation within the 665-675 range (plus the premium received from selling the collar). The strategy will underperform if the index has appreciated beyond 675 at expiration date and outperform if the index has declined below 665 at expiration.

16(a). Potential Returns
i. Index rises to 701. This rise would cause a substantial loss to the combined portfolio. An increase above the 675 call’s strike price would require an increase above 1.05 percent (668 to 675) in the S&P 500, at which time the call would be in the money. Because two calls were sold for every put bought in the collar, the collar would lose at twice the rate of the underlying portion of the portfolio against which it was written for any appreciation of the S&P 500 above 675. (The portfolio would realize a slight increment in return because of the premium [per collar traded] generated by the collar [2 x 4.30 – 8.05 = 0.55 per collar].)

ii. No change. The combined portfolio would experience only a slight gain as a result of the premium (per collar traded) generated by the collar (2 x 4.30 – 8.05 = 0.55 per contract). Both the put and the call would expire worthless. Therefore, the change in the portfolio would mirror the S&P 500 at 668.

iii. Index declines to 635. This decline would cause a slight loss to the combined portfolio because of the unhedged portion (668 to 675); then, the put hedge would take effect. Below 675.55, the put option guards against losses on a one-for-one basis. (The portfolio would realize a slight increment in return because of the premium [per collar traded] generated by the collar [2 x 4.30 – 8.05 = 0.55 per collar].)

16(b). Effect of Scenarios on Delta
i. Index rises to 701. The initial delta of the out-of-the-money calls was 0.36. As the call option got into the money and time expired, the delta of each call would approach 1.0. As the put option went out of the money and time expired, the delta of each put would approach zero.

ii. No change. The delta of both the put and call would approach zero as they both went out of the money and time was expiring.
iii. Index declines to 635. The initial delta of the out-of-the-money put was -0.44. As the put option got into the money and time expired, the delta of each put would approach 1.0. As the call option went out of the money and time expired, the delta of each call would approach zero.

16(c). Pricing
Compared with the historical volatility of the market (12 percent), the calls (Part ii) are priced relatively cheaper (11 percent) and the puts (Part i) are priced relatively more expensive (14 percent). The suggestion is that the collar (Part iii) is relatively expensive.

16(d). Wasting Asset
The options used to replicate the collar are “wasting assets” because they are worthless after the expiration date. Therefore, after 30 days, the strategy would have to be assessed and reestablished if desired. The profit or loss on the trade would depend on the market price as outlined in Part A and would be equal to the option’s intrinsic value. Collars do not hedge away risk; they change the risk profile of the portfolio.

You may also like...

306 Responses

  1. tadacip says:

    Anadia daily cialis tadacip cipl Ovar viagra medicamento Vale de Cambra v is for viagra Ovar cialis o que ?

  2. KelReedly says:

    Buy Abortion Pills Online viagra Cialis Tadalafil 20mg

  3. KelReedly says:

    Levitra Super Pro cialis Fluconazole 200 Mg Yeast Infection

  4. KelReedly says:

    Cialis Fast Shipping cialis Advances Keflex

  5. KennMilm says:

    Generic Acticin Drugs Internet Shop cialis online Does Cephalexin Kill Coccidia

  6. Chasmedo says:

    Priligy Se Necesita Receta cialis buy online Cialis Pas Cher Forum

  7. KelReedly says:

    Online Apotheke Viagra generic cialis Actos 45 Mg Tablets Online Order Us

  8. Linh says:

    You must take component in a contest for among the finest blogs on the net. I will advise this web-site!

  9. Chasmedo says:

    Levitra En Belgique viagra online pharmacy 100mg Sertraline No Rx

  10. KennMilm says:

    Cialis 5 Vidal cialis Xenical Diet Pill Online From Canada

  11. Chasmedo says:

    Order generic isotretinoin low price internet overseas cialis Cephalexin Dogs

  12. KennMilm says:

    Where can i buy isotretinoin North Ayrshire cialis Mail Order Stendra Us Medication Pharmacy

  13. KelReedly says:

    Diflucan Online Rx Pharmaceutical viagra Cialis 20 Prix En Pharmacie

  14. Shawnee says:

    I do agree with all of the ideas you have offered for your post. They are really convincing and will certainly work. Nonetheless, the posts are too short for starters. Could you please lengthen them a bit from next time? Thanks for the post.

  15. Tijuana says:

    You could definitely see your skills within the work you write. The sector hopes for even more passionate writers such as you who aren’t afraid to mention how they believe. All the time follow your heart.

  16. The evening time camp is the one other energizing thing with this visit. This is fascinating for individuals who get a kick out of the chance to eat while they will be presented with tasty hot notwithstanding succulent grilled chicken, turkey, hamburger or sheep. Notwithstanding this individuals safari dubai can exploit hip twirling, uncommon fire moving, alongside Tanoura moving exhibitions that can light up a guest’s night making it a specific one that they will treasure for eternity.

  17. These exercises are most likely going to fill your heart with joy astonishing with a ton of new things to amazement you on the off chance that you are not an occupant of Dubai safari. You can make the best of your time in Desert Safari Dubai without worrying about anything when you have effectively reserved Desert Safari Deals so you can appreciate minus all potential

  18. Good day, I’m really delighted I discovered this blog, I basically encountered you by accident, while I was researching on Digg for firestarter app download. Anyways I’m here now and would just like to say kudos for a fantastic post and the overall thrilling site (I furthermore like the theme), I don’t have time to read it completely at the moment but I have bookmarked it and moreover included your RSS feeds, so when I have sufficient time I will be back to go through more. Please do continue the great work.

  19. KelReedly says:

    Kamagra Vs Cialis cialis online Levitra Generique Ligne

  20. Chasmedo says:

    Heathnet Viagra viagra Claravis

  21. Hi my loved one! I wish to say that this post is amazing, nice written and
    come with approximately all important infos.
    I’d like to see more posts like this .

  22. Hi there terrific blog! Does running a blog like this require a massive amount work?
    I’ve absolutely no understanding of computer programming but I had been hoping to start my own blog soon. Anyhow,
    if you have any recommendations or tips for new blog owners please share.
    I know this is off subject however I just wanted to ask.
    Appreciate it!

  23. There are actually amazing changes on the style of your webpage, I honestly enjoy it. My site is on the subject of videoder downloader app and currently there are plenty of things to be done, I’m yet still a novice in website development. Take care!

  24. best safari says:

    Find the desert Safari deals spa and massage deals, online shopping deals, others best deals and offers in Dubai UAE at PoshDeals Online Discount Services.

  25. Arleen says:

    whoah this weblog is excellent i like studying your posts.

    Stay up the good work! You understand, a lot of persons are hunting round for this information,
    you can aid them greatly.

  26. Hi to every body, it’s my first pay a quick visit of this webpage; this website consists of remarkable and actually fine
    data in support of readers.

  27. Excellent weblog right here! Also your web site quite a bit up very fast!
    What web host are you using? Can I get your affiliate hyperlink
    for your host? I wish my web site loaded up as quickly as yours lol

  28. I think this is one of the most vital information for me.
    And i’m glad reading your article. But wanna remark on some general things, The site style
    is perfect, the articles is really nice : D. Good job, cheers

  29. Hello just wanted to give you a quick heads up. The text in your post seem to
    be running off the screen in Opera. I’m not sure if this is a
    format issue or something to do with browser compatibility but I thought I’d
    post to let you know. The style and design look great though!
    Hope you get the issue fixed soon. Cheers

  30. I am sure this post has touched all the internet people, its really really nice post
    on building up new website.

  31. I loved as much as you will receive carried out right here.
    The sketch is tasteful, your authored subject matter stylish.
    nonetheless, you command get bought an edginess over that you wish be delivering the following.
    unwell unquestionably come more formerly
    again as exactly the same nearly very often inside case
    you shield this increase.

  32. My spouse and I stumbled over here coming from a different website and thought I should check things out.
    I like what I see so now i am following you. Look forward to looking into your web page repeatedly.

  33. Thank you for the good writeup. It in fact was a amusement account it.
    Look advanced to more added agreeable from you! However, how could we communicate?

  34. Write more, thats all I have to say. Literally, it
    seems as though you relied on the video to make your point.

    You clearly know what youre talking about, why waste your intelligence
    on just posting videos to your blog when you could be giving us something enlightening to read?

  35. Denese says:

    Amazing blog! Do you have any tips and hints for aspiring writers?
    I’m planning to start my own site soon but I’m a little lost
    on everything. Would you suggest starting with a free platform like WordPress or go for
    a paid option? There are so many options out there that I’m totally overwhelmed
    .. Any ideas? Appreciate it!

  36. Manuel says:

    Aw, this was a seriously good post. In thought I would like to put in writing like this moreover – taking time and actual effort to create a really great article… but what can I say… I procrastinate alot and by no indicates appear to get something done.

  37. Thank you, I’ve recently been searching for info about this subject for a long time and yours is
    the greatest I have came upon till now. But, what concerning the bottom line?
    Are you positive concerning the source?

  38. Have you ever thought about publishing an ebook or guest authoring on other websites?
    I have a blog based upon on the same topics you discuss
    and would really like to have you share some stories/information. I know my viewers would enjoy your work.
    If you’re even remotely interested, feel free
    to send me an e mail.

  39. Hey there! I realize this is kind of off-topic however I had to ask.
    Does building a well-established blog like yours require a lot
    of work? I am completely new to writing a blog but I do write in my journal daily.
    I’d like to start a blog so I will be able to share my experience and
    feelings online. Please let me know if you
    have any kind of suggestions or tips for brand new aspiring blog owners.

  40. I do not know if it’s just me or if everyone else encountering problems with your site.

    It appears as if some of the written text on your posts are running off
    the screen. Can someone else please comment and let me know if this is happening to them too?
    This could be a problem with my browser because I’ve
    had this happen previously. Many thanks

  41. Therese says:

    There’s certainly a great deal to find out about this
    issue. I like all the points you’ve made.

  42. If you would like to increase your familiarity simply keep visiting this site and be updated with the
    most up-to-date news posted here.

  43. Wow, this piece of writing is fastidious, my younger sister is analyzing such
    things, therefore I am going to inform her.

  44. Hello there! This blog post could not be written any better!
    Looking at this post reminds me of my previous roommate!
    He always kept preaching about this. I will send this information to
    him. Pretty sure he’ll have a great read. Thanks for sharing!

  45. I believe everything said made a ton of sense.

    However, what about this? what if you were to write a awesome title?

    I am not saying your content isn’t good., however what if
    you added a headline to possibly grab a person’s attention? I mean OPTION CONTRACTS | Notes is kinda
    boring. You could peek at Yahoo’s home page and see
    how they write news headlines to grab viewers to click. You might try adding a video or a related picture or two to grab readers
    interested about everything’ve written. Just my opinion, it would bring your posts a little bit
    more interesting.

  46. I blog frequently and I genuinely thank you for your information. The article has truly peaked my
    interest. I’m going to book mark your website and keep checking for new
    details about once a week. I opted in for your RSS feed too.

  47. 132wl says:

    you are luckly!

  48. I used to be recommended this web site by my cousin. I am now not positive whether
    or not this publish is written by him as nobody else understand such
    designated about my difficulty. You’re incredible! Thanks!

  49. I’m really inspired along with your writing skills and also with the structure for
    your blog. Is this a paid subject matter or did you customize it your self?
    Either way keep up the excellent high quality writing, it’s uncommon to see a great weblog like this one today..

  50. Good way of describing, and fastidious piece of writing to obtain information about my presentation subject matter, which
    i am going to deliver in academy.

  51. There is definately a great deal to find out about this issue.
    I love all of the points you made.

  52. Excellent article. Keep posting such kind of info on your site.
    Im really impressed by your site.
    Hi there, You have done an excellent job.

    I will definitely digg it and in my view recommend to my friends.
    I am sure they’ll be benefited from this website.

  53. bigger butt says:

    I don’t even know how I ended up here, but I thought this post was good.
    I don’t know who you are but definitely you’re going to a famous blogger if you are not already
    😉 Cheers!

  54. Nice blog here! Also your site loads up fast! What web host are you using?
    Can I get your affiliate link to your host? I wish my web site loaded up as fast as yours lol

  55. I visited multiple sites except the audio feature for audio songs current at this web
    page is in fact excellent.

  56. After looking into a number of the blog articles on your blog, I honestly appreciate your
    way of writing a blog. I added it to my bookmark site list and will be checking back soon. Take a look at my web site as
    well and let me know what you think.

  57. Touche. Solid arguments. Keep up the good effort.

  58. Greetings! This is my first comment here so I just wanted to give a quick shout out and say I really enjoy reading through your blog posts.
    Can you suggest any other blogs/websites/forums that go over the same topics?

    Appreciate it!

  59. Hi there, just became aware of your blog through Google, and
    found that it is truly informative. I’m going to watch out for brussels.
    I’ll be grateful if you continue this in future. A lot of people will be benefited from your writing.

  60. Hello! This post couldn’t be written any better! Reading this post reminds me of
    my old room mate! He always kept talking about this.
    I will forward this article to him. Fairly certain he will have a good read.
    Many thanks for sharing!

  61. Howdy just wanted to give you a quick heads up. The words in your article seem to
    be running off the screen in Safari. I’m not sure if
    this is a formatting issue or something to do with internet browser compatibility but I figured I’d post
    to let you know. The design and style look great though! Hope
    you get the problem solved soon. Cheers

  62. Thanks for one’s marvelous posting! I truly enjoyed reading it, you are a great author.I will always bookmark your
    blog and will come back very soon. I want to encourage you to continue your great work, have a nice

  63. Great article. I will be experiencing some of these issues as well..

  64. levitra says:

    buy levitra viagra
    buy viagra cialis or levitra

  65. What i do not understood is in fact how you’re not really a lot
    more smartly-appreciated than you may be right now.
    You are very intelligent. You know therefore
    significantly in the case of this topic, produced me individually
    consider it from a lot of various angles. Its like women and
    men are not interested except it is something to accomplish with Woman gaga!
    Your own stuffs nice. All the time maintain it up!

  66. It’s actually a nice and useful piece of info.
    I am happy that you shared this useful information with us.
    Please keep us up to date like this. Thank you for sharing.

  67. fantastic points altogether, you just gained a logo new reader.
    What might you suggest about your publish that you just made some days in the past?
    Any sure?

  68. Very nice post. I just stumbled upon your weblog and wished
    to say that I’ve really enjoyed surfing around your blog posts.
    In any case I will be subscribing to your rss feed and
    I hope you write again very soon!

  69. Jeffery says:

    I’m impressed, I must say. Really hardly ever do I encounter a weblog that’s both educative and entertaining, and let me inform you, you might have hit the nail on the head. Your thought is excellent; the difficulty is something that not sufficient persons are speaking intelligently about. I’m very joyful that I stumbled throughout this in my search for something relating to this.

  70. Great web site you have got here.. It’s hard to find
    quality writing like yours nowadays. I seriously appreciate individuals
    like you! Take care!!

  71. Hi, its good post about media print, we all be aware of media is a great source
    of facts.

  72. No matter if some one searches for his essential
    thing, therefore he/she needs to be available that in detail, therefore that thing
    is maintained over here.

  73. Hi! I could have sworn I’ve been to this website before but after reading through some of the post I realized it’s new to me.
    Anyhow, I’m definitely delighted I found it and
    I’ll be book-marking and checking back frequently!

  74. Having read this I thought it was extremely enlightening.

    I appreciate you finding the time and energy to put this informative
    article together. I once again find myself spending a significant amount of time both reading and leaving comments.

    But so what, it was still worth it!

  75. Hi, yes this piece of writing is actually good and I have learned
    lot of things from it concerning blogging. thanks.

  76. Heya! I know this is somewhat off-topic however I needed to ask.

    Does building a well-established website such as yours take a lot of work?

    I am brand new to operating a blog however I do write in my diary every day.

    I’d like to start a blog so I can share my experience and feelings
    online. Please let me know if you have any ideas or tips for
    new aspiring blog owners. Appreciate it!

  77. I’m not that much of a internet reader to be honest but your blogs really nice,
    keep it up! I’ll go ahead and bookmark your website to come back down the road.

  78. There is definately a lot to know about this topic. I love
    all the points you made.

  79. Enjoy a thrilling Desert Safari experience with Live Entertainment, Dune Bashing, BBQ Dinner, Camel Ride, Henna Painting & much more for AED 75 – Private Pickup in Land Cruiser available!

  80. all the time i used to read smaller content which also clear their motive,
    and that is also happening with this piece of
    writing which I am reading at this time.

  81. Seriously, you are pathetic. Don’t be such a sissy and a worm. Who cares if some smelly hipster idiot wearing a Che shirt is going to throw a little tantrum and call you mean names?Look at them, do they look like people who are going to amount to anything in life? Rise above the Occutards, racist whiners and socialist traitors. Be better than them. You won’t even KNOW these chumps in a couple of years. You may see a couple begging for change every now and then … flip them a quarter and tell them to get a job.

  82. Hello to every one, because I am in fact eager of reading this web site’s post to be updated
    regularly. It consists of good information.

  83. I know this if off topic but I’m looking into starting my own weblog and wascurious what all is required to get setup? I’m assuming having a blog like yours would costa pretty penny? I’m not very internet savvy so I’m not100 positive. Any tips or advice would be greatly appreciated.Kudos

  84. you’re actually a good webmaster. The website loading pace
    is amazing. It seems that you are doing any distinctive trick.
    Moreover, The contents are masterwork. you have performed a
    great process in this subject!

  85. Sang says:

    Thanks for every other informative website. The place else may just I am getting that type of information written in such an ideal way? I have a challenge that I’m just now working on, and I’ve been on the look out for such information.

  86. Its not my first time to pay a quick visit this web site,
    i am visiting this site dailly and get pleasant information from here all the time.

  87. cheap levitra professional
    levitra prices
    canada levitra buy online

  88. Marita says:

    Hi! I know this is somewhat off-topic however I needed to ask.
    Does running a well-established blog like yours require a massive amount
    work? I am completely new to blogging but I do write in my
    journal daily. I’d like to start a blog so I can share my personal experience and
    thoughts online. Please let me know if you have any kind of suggestions or
    tips for brand new aspiring blog owners. Thankyou!

  89. Mi sugestas al David kontakti kun la tre afabla universitata profesoro ĉe la Universitato de Eŭskio en Bilbo kaj bonega esperantisto Jesús Miguel García Iturrioz:jesusmiguel.garcia (ĉe) ehu.estepgaitj (ĉe) ehu.es |

  90. Hi, all is going sound here and ofcourse every one is sharing data, that’s genuinely excellent, keep up writing.

  91. You should be a part of a contest for one of the
    best sites on the internet. I will highly recommend this site!

  92. Thanks a lot for sharing this with all folks you actually understand what you’re speaking about!
    Bookmarked. Please additionally discuss with my site =).
    We could have a link trade agreement among us

  93. Thank you a lot for sharing this with all of us you actually realize what
    you’re speaking about! Bookmarked. Kindly additionally discuss with my site =).
    We can have a hyperlink change agreement between us

  94. viagra sale calgary
    generic viagra coupons
    viagra dapoxetine sale

  95. mp4 player says:

    Greetings from California! I’m bored to tears at work so I decided to check out your website on my iphone
    during lunch break. I enjoy the knowledge you present here and can’t wait
    to take a look when I get home. I’m surprised at how quick your blog loaded on my cell
    phone .. I’m not even using WIFI, just 3G .. Anyways, great blog!

  96. I do consider all of the ideas you have presented to your post.
    They’re very convincing and can definitely work.
    Still, the posts are very brief for newbies.
    Could you please prolong them a little from subsequent time?
    Thank you for the post.

  97. We absolutely love your blog and find many of your post’s
    to be what precisely I’m looking for. Does
    one offer guest writers to write content in your
    case? I wouldn’t mind creating a post or elaborating on some of
    the subjects you write regarding here. Again, awesome website!

  98. Derrick says:

    I think this is one of the most vital information for me.

    And i am glad reading your article. But should remark on some general things, The website
    style is wonderful, the articles is really nice : D. Good job, cheers

  99. It is appropriate time to make some plans for the future and it’s time to be happy.
    I have read this post and if I could I wish to suggest
    you some interesting things or advice. Maybe you can write next articles referring to this article.

    I wish to read more things about it!

  100. rvzzmlnro fhksv ijapkuv ynxb caerfnnfcyeogwh

  101. I don’t even know how I ended up here, but I thought this post was great.

    I do not know who you are but definitely you are going to a famous blogger if you are not already 😉 Cheers!

  102. Amazing blog! Is your theme custom made or did you download it from somewhere?
    A design like yours with a few simple adjustements would really make my blog
    jump out. Please let me know where you got your design. Cheers

  103. Hilda says:

    Have you ever considered about including a little bit more than just your
    articles? I mean, what you say is fundamental and everything.

    Nevertheless imagine if you added some great graphics or video clips to give your posts more, “pop”!

    Your content is excellent but with pics and videos, this website could definitely be one of the most
    beneficial in its niche. Amazing blog!

  104. I have to thank you for the efforts you’ve put in writing this site.
    I’m hoping to check out the same high-grade content from you later on as well.
    In fact, your creative writing abilities has motivated me to get my
    very own website now 😉

  105. My brother recommended I would possibly like this blog.
    He was once totally right. This publish truly made my day.

    You can not consider just how much time I had spent for this information! Thanks!

  106. Pretty section of content. I just stumbled upon your web site and in accession capital
    to assert that I get in fact enjoyed account
    your blog posts. Anyway I’ll be subscribing to your
    feeds and even I achievement you access consistently rapidly.

  107. Jeffery says:

    We’re a group of volunteers and opening a brand new scheme in our community. Your site offered us with helpful info to paintings on. You have performed a formidable task and our whole neighborhood shall be thankful to you.

  108. can you buy viagra walgreens
    generic viagra canada price
    viagra buy in usa

  109. Lucien says:

    This website is mostly a walk-through for all of the info you needed about this and didn’t know who to ask. Glimpse right here, and you’ll positively discover it.

  110. playing golf says:

    Its like you read my mind! You seem to know so much about this, like
    you wrote the book in it or something. I think that you could do with some pics to drive the message home a bit, but other than that,
    this is magnificent blog. A fantastic read.
    I’ll certainly be back.

  111. Hi friends, its enormous paragraph about teachingand fully explained, keep it
    up all the time.

  112. Hello, just wanted to say, I enjoyed this
    post. It was funny. Keep on posting!

  113. Simply want to say your article is as amazing.

    The clarity to your post is just nice and that i can assume
    you are knowledgeable in this subject. Fine together with your permission allow me to clutch your feed to stay up to date with impending post.
    Thanks one million and please carry on the gratifying work.

  114. Hey There. I found your blog the usage of msn. This is a really smartly written article.
    I will be sure to bookmark it and return to learn extra of your useful info.

    Thank you for the post. I’ll certainly comeback.

  115. Tamiko says:

    I really feel this web page desires a lot more consideration. I’ll most likely be once more to read far more, thanks for that information.

  116. Alfonso says:

    Thank you for sharing your thoughts. I truly
    appreciate your efforts and I will be waiting for your next post thanks
    once again.

  117. Sana Althaus says:

    The heroes of Flight 93 won the first battle in the War on Terror, and they should never be forgotten.

  118. Erik Khoury says:

    To find out what one is fitted to do, and to secure an opportunity to do it, is the key to happiness.

  119. Howdy! This is my first visit to your blog! We are a team of volunteers and starting a new
    initiative in a community in the same niche. Your
    blog provided us beneficial information to work on. You have done a outstanding job!

  120. Mariam says:

    This is very interesting, You’re an overly skilled blogger. I’ve joined your feed and look forward to seeking more of your great post. Additionally, I’ve shared your web site in my social networks!

  121. Kattie Lio says:

    It take many a year, mon, and maybe some bloodshed must be, but righteousness someday prevail.

  122. Ralph Kracke says:

    I’m just deeply disappointed that once again we may have to settle for the lesser of two evils.

  123. canada pharmacy online
    canadian online pharmacies
    International Pharmacies that Ship to the USA

  124. Fantastic goods from you, man. I’ve take
    into accout your stuff prior to and you’re simply extremely magnificent.
    I actually like what you have acquired right here, certainly like what you are saying and the best way
    through which you assert it. You make it enjoyable and you continue to take care of to stay it wise.
    I can’t wait to read much more from you. This is really
    a great web site.

  125. Rosalinda says:

    Great work! That is the kind of information that are supposed to be shared around the
    web. Shame on Google for not positioning this submit higher!

    Come on over and visit my site . Thanks =)

  126. Otto says:

    My developer is trying to convince me to move to .net from PHP. I have always disliked the idea because of the costs. But he’s tryiong none the less. I’ve been using Movable-type on several websites for about a year and am concerned about switching to another platform. I have heard very good things about blogengine.net. Is there a way I can import all my wordpress posts into it? Any kind of help would be greatly appreciated!

  127. Harold says:

    A lot of thanks for every one of your hard work on this site. My mom really likes making time for investigations and it is obvious why. A number of us hear all concerning the lively medium you present insightful tips and tricks by means of the web blog and invigorate response from some other people on this matter so our favorite daughter is in fact studying a great deal. Have fun with the remaining portion of the year. You are doing a remarkable job.

  128. I don’t even know how I ended up here, but I thought this post was good.
    I don’t know who you are but definitely you are going to a famous blogger if you aren’t already 😉 Cheers!

  129. I am now not positive the place you’re getting your information, however great
    topic. I must spend a while studying more or working out more.
    Thank you for great info I was in search of this information for my mission.

  130. cialis buy says:

    cialis professional buy
    cialis buy
    cialis super active+ 20mg pills

  131. Dream Night Tours:Melody Queen Hotel Dubai is nestled in the Old Dubai district, about 500 meters from the Twin … What are the best desert safari Dubai packages dealers in Dubai? Soumabrata Dutta, Engineer, Traveller, Reader. Answered Nov 20, 2016.

  132. I don’t even know the way I finished up here, but I assumed this post was once good.
    I don’t realize who you might be however definitely you’re going to a well-known blogger in the event you
    aren’t already. Cheers!

  133. Anne says:

    Hello, i read your blog occasionally and i own a similar one
    and i was just curious if you get a lot of spam remarks? If so how do you reduce it, any plugin or anything you can suggest?
    I get so much lately it’s driving me crazy so any help is very much appreciated.

  134. LarSpicaing says:

    Acheter Baclofen Des cialis Viapro Without Prescription Is There A Way To Get Avanafil Cheaper

  135. Yes! Finally someone writes about american football.

  136. HassanGop says:

    writing essayscursive writing worksheetsrhetorical analysis essay example
    similarities between academic essay writing and report writingessay writing tips grant writing essay oncollege essay format
    writing gamesplain writing crosswordessay outline template

  137. TimothyBROMI says:

    can i buy cialis over the counter in spainbuy cialis online pay with paypalbuy discount cialis
    buy generic cialis europebuy cialis in riyadh should i buy cialis onlinehow to order cialischeap cialis from china
    buy cialis perth cheapest place to buy generic cialis

  138. MyronnAh says:

    order cialis australia buy cialis in san diego
    order daily cialis buy generic cialis daily buy cialis generic uk
    buy cialis uk cheap safe place to order cialis online

  139. Have you ever considered about including a little bit more than just your articles?
    I mean, what you say is valuable and all. But think about
    if you added some great photos or video clips to give your posts
    more, “pop”! Your content is excellent but with pics and video clips, this site could definitely be one of the greatest in its niche.

    Terrific blog!

  140. CarlosFrido says:

    can i buy levitra in mexico order levitra from canada
    buy levitra 5mgbuy levitra online indiacan i buy levitra over the counter buy levitra orodispersiblewhere to buy levitra in canada
    buy levitra usbuy levitra orodispersiblesafe place to buy levitra online

  141. RichardAgonO says:

    cheap cialis 60 mgbest place to buy cialis online yahoobuy cialis online cheap
    where can i purchase generic cialisbuy cipla cialis buy real viagra levitra cialis online edrugstore.md cheap cialis uk next day deliverycan i buy cialis over the counter in dubai
    buy cialis bangkok pharmacyanyone order cialis onlinebuy cialis cyprus

  142. Manuelevivy says:

    buy brand name levitrabuy levitra canada onlinebuy levitra pills online
    cheap prices on levitra buy levitra canada buy levitra super force online rxmeds hub order levitra onlinewhere is the best place to buy levitra
    order levitra canadabuy cialis and levitrabuy levitra odt online

  143. HassanGop says:

    clean green india essay wikipediaexemplification essayclean green india essay wikipedia
    writing a paperessay help essay outline conclusion of an essaykannada essay pdf
    topessaywriting.orgpersonal essayenglish essay

  144. I’m not sure why but this site is loading incredibly slow for me.
    Is anyone else having this problem or is it a issue on my end?
    I’ll check back later on and see if the problem still exists.

  145. Fvtjjinfife says:

    student loan calculator payday loans american loans [url=http://cashadvanceamericasev.org/]payday loans online[/url] ’

  146. Hi! I know this is sort of off-topic however I needed to
    ask. Does operating a well-established website such as yours take a lot of work?
    I’m brand new to operating a blog however I
    do write in my journal every day. I’d like to start a blog so
    I can easily share my own experience and views online. Please let me know if you have any recommendations or tips for brand
    new aspiring bloggers. Thankyou!

  147. Lmazalmody says:

    quick personal loans cash advance usa fast cash loans [url=https://paydayrvyaf.com/]3 month payday loans[/url] ’

  148. Gilda says:

    Thanks for your personal marvelous posting! I actually enjoyed reading it, you may be a great author.I will
    be sure to bookmark your blog and may come back later in life.
    I want to encourage you to definitely continue your great job, have a nice day!

  149. Cvectriafe says:

    instant payday loans personal loans bad credit poor credit personal loans [url=https://personalvrdcg.org/]small personal loans[/url] ’

  150. Bveztrievy says:

    australian payday loans payday loans loan payday savings [url=https://loansbtxsa.org/]quick loans[/url] ’

  151. Vernon says:

    Definitely believe that which you stated. Your favorite justification seemed to be on the internet the simplest thing to be aware of. I say to you, I certainly get annoyed while people consider worries that they plainly do not know about. You managed to hit the nail upon the top and also defined out the whole thing without having side-effects , people could take a signal. Will likely be back to get more. Thanks

  152. PameTherGo says:

    car title and payday loan bad credit installment loans no credit check student loans [url=https://installmentsvfacr.com/]get installment loan[/url] ’

  153. LqziBrumum says:

    payday loans companies cash advance debt help [url=https://paydayvynk.org/]payday advance[/url] ’

  154. LmbtUnesia says:

    quick low interest payday loan cash advance usa same day loans no credit [url=https://cashshybn.com/]cash advance online[/url] ’

  155. Kmrcetheld says:

    direct lenders online payday loans cash advances payday loans [url=https://paydaaexc.com/]pay day loans[/url] ’

  156. KmrdcFluini says:

    speedy cash payday advance loans visa credit cards bad credit [url=https://paydaytbukl.org/]payday loan[/url] ’

  157. FvthsGaucky says:

    bad credit payday loan cash advance online credit card debt consolidation [url=https://cashrvyn.com/]payday advance[/url] ’

  158. IkmeSmomma says:

    get installment loan online payday loans american loans [url=https://paydayrvjlo.com/]online payday loans[/url] ’

  159. I’m not positive the place you are getting your info, but great topic.

    I must spend some time learning much more or figuring out more.

    Thank you for wonderful info I was looking for this info for my mission.

  160. Fvrcalmody says:

    3 month payday loans uk fast payday loans bad credit loans andnot payday loan [url=https://cashadvanceamericasev.org]cash advance inc[/url] ’

  161. Csbhctriafe says:

    payday loans online best personal loans consolidation debt [url=https://personalloansntui.com]personal loan bad credit[/url] ’

  162. Bhectrievy says:

    best personal loans bad credit online loan consolidate [url=https://badcreditnyrc.org]payday advance[/url] ’

  163. vwqeTherGo says:

    american payday loans inc online installment loans guaranteed online personal loans [url=https://installmentloanvelam.com]quick installment loans[/url] ’

  164. LqvziBrumum says:

    best payday loan site online cash advance bad credit payday loan lenders [url=https://leopaydayadvanceonlinefastpayday.org]payday loan[/url] ’

  165. LbdbtUnesia says:

    loans for bad credit cash advance online loan payment calculator [url=https://cashadvanceamericavatn.org]cash advance online[/url] ’

  166. Kvevetheld says:

    fast cash payday loans online best payday loans cash loans [url=https://nowpayday1.com]online payday loans direct lenders[/url] ’

  167. KbebcFluini says:

    direct loans payday loans online fast cash personal loans [url=https://paydayvrvi.org]cash advance loans[/url] ’

  168. FebbGaucky says:

    same day money loans payday advance cash advance payday loan [url=https://paydaykmae.com]payday loans[/url] ’

  169. Wonderful blog! Do you have any suggestions for aspiring
    writers? I’m planning to start my own site soon but I’m
    a little lost on everything. Would you propose starting with a free platform like WordPress or go for a paid option? There are
    so many choices out there that I’m totally confused .. Any recommendations?

  170. Vuonclania says:

    viagra testimonials – http://viagraveikd.com/ generic viagra online pharmacy [url=http://viagraveikd.com/]generic viagra[/url] ’

  171. Lmtbtriafe says:

    cheap cialis tablets – http://cialisovnnc.com/ cialis 20 mg [url=http://cialisovnnc.com/]cialis[/url] ’

  172. Banozchully says:

    viagra brand cheap – http://viagraocns.com/ how to buy viagra [url=http://viagraocns.com/]buy viagra[/url] ’

  173. Lecvevory says:

    cialis tadalafil india – http://cialisoanzb.com brand name only cialis [url=http://cialisoanzb.com]cialis 20mg[/url] ’

  174. KlmfEssero says:

    buy cialis professional – http://cialisofkl.com/ cialis 5mg online [url=http://cialisofkl.com/]cialis[/url] ’

  175. FlmfArica says:

    cialis over the counter in canada – http://cialisovnas.com/ next day brand cialis only online [url=http://cialisovnas.com/]cialis buy[/url] ’

  176. MVrtjoubs says:

    name brand viagra online – http://viagraghhde.com/ buying viagra online [url=http://viagraghhde.com/]online viagra[/url] ’

  177. Drbecdaycle says:

    herbal viagra reviews – http://viagraoplws.com/ viagra online australia [url=http://viagraoplws.com/]viagra price[/url] ’

  178. LvvodChiend says:

    alternatives to viagra – http://viagrapfhze.com/ viagra pills online [url=http://viagrapfhze.com/]viagra online[/url] ’

  179. Jubivundusa says:

    generic cialis cheap – http://cialisivndh.com generic cialis price [url=http://cialisivndh.com]online cialis[/url] ’

  180. Jtnbalmody says:

    no hassle payday loans payday loans credit card consolidation [url=https://paydayloamec.com/]payday loans[/url] ’

  181. Lbbeunpar says:

    cheap viagra without prescription viagra buy viagra sales online [url=http://aaviagla.com/]viagra generic[/url] ’

  182. Bcxvvtrievy says:

    applying for a payday loan payday loan online bank account [url=https://cashnowemr.com]payday loans[/url] ’

  183. Corporate tax dodging impacts us across generations and over time. It is corrosive. It is unethical. It is unsustainable.

  184. personal loans edmonton
    personal loans poor credit
    payday online loans

  185. BvevInvoix says:

    effects of viagra viagra generic cheap no prescription viagra [url=http://ericviaed.com/]viagra online[/url] ’

  186. hello!,I love your writing very a lot! proportion we be in contact more about your article on AOL?
    I need a specialist on this house to solve my problem.
    Maybe that is you! Looking ahead to look you.

  187. Fvvbtraicy says:

    genuine viagra generic viagra cheap brand name viagra [url=http://menedkkr.com/]viagra buy[/url] ’

  188. Jazwuncob says:

    viagra online pharmacy viagra online where can i buy viagra [url=http://genericviaser.com/]generic viagra[/url] ’

  189. LarSpicaing says:

    Buy Cheap Fluoxetine And Cialis mail order levitra 90 day supply Kamagra Ahumada Putting Amoxicillin In Formula Cialis Generic Without A Prescription

  190. LarSpicaing says:

    Cialis Ou Viagra Ou Levitra Viagra No Me Funciona viagra Acquistare Viagra In Sicurezza Antibiotic Zithromax Propecia Generika 1mg

  191. Kvgvevetheld says:

    cant get a payday loan loans payday installment payday loans [url=https://paydayloanswwe.com/]payday day loans[/url] ’

  192. Muntrloacy says:

    buying viagra online viagra online viagra 50mg [url=http://sexviagen.com/]viagra online[/url] ’

  193. KvvbFluini says:

    bankruptcy payday loans payday loan online need loan [url=https://cashadmme.com/]cash advance[/url] ’

  194. FnrxGlope says:

    quick payday loan 1 – https://paydayloamec.com/ bad credit no fax payday loans [url=https://paydayloamec.com/]payday loans[/url] ’

  195. SfbxdCip says:

    cheapest viagra price – http://aaviagla.com/ generic viagra no prescription [url=http://aaviagla.com/]viagra[/url] ’

  196. LrbsdSuink says:

    bankruptcy payday loans – https://cashnowemr.com bad credit loans online [url=https://cashnowemr.com]payday loan[/url] ’

  197. greece-slim says:

    Μαρία Β. Λαβρόφ, ο γιατρός-μαστολόγος:
    Μεταξύ των ασθενών μου, υπάρχουν πολλά κορίτσια που έχουν τα στήθη τους σε θλιβερή κατάσταση. Μερικές φορές γίνεται αυτό ως συνέπειες μιας μη ισορροπημένης δίαιτας για την απώλεια βάρους, αλλά τις περισσότερες φορές γίνεται από τους λόγους έλλειψης οιστρογόνων. Σε πιο επίμονες από τους πελάτες μπορεί να συστήσω ασκήσεις για να ενισχύσουν οι μυς, αλλά το αποτέλεσμα αυτής της θεραπείας δε θα είναι αισθητό σύντομα, επειδή οι μαστικοί αδένες δεν είναι όπως τα ισχία, το οποία μπορούν να διορθωθούν αρκετά γρήγορα και εύκολα σε ένα γυμναστήριο. Πλαστική χειρουργική – είναι το άλλο άκρο: γρήγορη, αλλά επικίνδυνη. Η χρυσή τομή – το προϊόν Bust Size, το οποίο συστήνω να αγοράσουν στο σύνολο των ασθενών μου, εκτός από τους οποιόυς που έχουν κάποιες αντενδείξεις. Σε 9 περιπτώσεις από τις 10 θετική τάση έχει παρατηρηθεί μετά από 2 εβδομάδες της τακτικής χρήσης της κρέμας.
    Οι άνδρες μπορούν να μιλήσουν οποιοδήποτε για τη γυναικεία ομορφιά, ομορφιά των μάτιων ή της ψυχής, αλλά η προσοχή του σαν ένας μαγνήτης προσελκύει ένα υπέροχο μπούστο. Να γίνετε ελκυστική και επιθυμητή για τον εαυτό σας και τον αγαπημένο σας θα σας βοηθήσει το προϊόν Bust Size: σε σύντομο χρονικό διάστημα και με εγγυημένο αποτέλεσμα μπορείτε να πάρετε ένα όμορφο, στρογγυλεμένο και σέξι στήθος.

    διαβάστε περισσότερα:
    fitospray στην Ελλάδα

  198. Bebbchully says:

    viagra prescription online – http://ericviaed.com/ sildenafil viagra [url=http://ericviaed.com/]viagra[/url] ’

  199. Vbewcquilla says:

    buy viagra online at – http://menedkkr.com/ brand generic viagra [url=http://menedkkr.com/]generic viagra[/url] ’

  200. Brtevbevory says:

    buy viagra on line – http://genericviaser.com/ ordering viagra [url=http://genericviaser.com/]buy viagra[/url] ’

  201. Bsbfinfuck says:

    personal loans – https://paydayloanswwe.com/ cash loan advance [url=https://paydayloanswwe.com/]payday loans[/url] ’

  202. Lexntoptorb says:

    best online payday loans – https://cashadmme.com/ need payday loan today [url=https://cashadmme.com/]payday loan[/url] ’

  203. Please let me know if you’re looking for a article author for
    your site. You have some really good articles
    and I believe I would be a good asset. If you ever want to take some of the load off, I’d really like to
    write some material for your blog in exchange for a link back
    to mine. Please shoot me an email if interested.


  204. Debxdaycle says:

    best place to buy viagra – http://sexviagen.com/ viagra alternative [url=http://sexviagen.com/]generic viagra[/url] ’

  205. VbwgxHeinee says:

    cash loan – https://paydayllae.com/ no fax payday loans online [url=https://paydayllae.com/]payday loans online same day[/url] ’

  206. Great, yahoo took me stright here. thanks btw for post. Cheers!

  207. FnveeGlope says:

    cash loans bad credit – https://paydaybdrfs.com/ can a payday loan garnish my wages [url=https://paydaybdrfs.com/]pay day loans[/url] ’

  208. Lsdbtriafe says:

    cheapest brand cialis – https://buybuybuycialis.com/ cialis samples free [url=https://buybuybuycialis.com/]online cialis[/url] ’

  209. Howdy, I think your site may be having web browser compatibility issues.
    When I look at your site in Safari, it looks fine however, if opening in I.E.,
    it’s got some overlapping issues. I merely wanted to give you
    a quick heads up! Apart from that, wonderful blog!

  210. LrbvsdSuink says:

    business loans bad credit – https://cashcevth.com poor credit loan [url=https://cashcevth.com]same day payday loans[/url] ’

  211. LarSpicaing says:

    Taking Amoxil With Cipro Prezzo Viagra Pfizer In Farmacia Ou Acheter Vrai Cialis levitra canada Proscar Caida Pelo Propecia

  212. Vtvzvdpeene says:

    buy brand cialis from supplier – https://genonlinecialis.com buy cialis soft tabs [url=https://genonlinecialis.com]cialis generic[/url] ’

  213. Actually when someone doesn’t be aware of then its up to other people that they
    will help, so here it happens.

  214. KlmfsfEssero says:

    cialis online without prescription – https://cheapcheapcialis.com/ cialis one a day [url=https://cheapcheapcialis.com/]cialis[/url] ’

  215. FwebfArica says:

    cialis 50mg – https://genericgenericcialis.com/ cialis effectiveness [url=https://genericgenericcialis.com/]generic cialis[/url] ’

  216. Bvwcginfuck says:

    business loans – https://cashecbya.com/ debt consolidation loan [url=https://cashecbya.com/]payday loan[/url] ’

  217. Lebweoptorb says:

    best payday loan company – https://paydayloansrvhj.com/ cash advance loan [url=https://paydayloansrvhj.com/]online payday loan[/url] ’

  218. order viagra from uk
    viagra online
    viagra sale in india

  219. Bwevvuriple says:

    100 approval bad credit payday loans – https://paydayloawdcr.com/ credit card consolidation [url=https://paydayloawdcr.com/]payday loans[/url] ’

  220. VrtevDuh says:

    cialis name brand cheapest online prices – https://onlineonlinecialis.com/ cialis order [url=https://onlineonlinecialis.com/]generic cialis[/url] ’

  221. Hey! Do you know if they make any plugins to safeguard against hackers?
    I’m kinda paranoid about losing everything I’ve worked
    hard on. Any recommendations?

  222. Jtnvbalmody says:

    average interest rate on a payday loan cash advance online payday direct [url=https://paydaybdrfs.com/]payday loans[/url] ’

  223. Djjdvdreago says:

    cialis order cialis cialis best price [url=https://buybuybuycialis.com/]buy cialis[/url] ’

  224. I blog quite often and I really appreciate your content. This article has truly peaked my interest.
    I am going to book mark your blog and keep checking for new information about once per week.
    I opted in for your RSS feed too.

  225. Buiptrievy says:

    cash now payday loan online direct lender payday loans [url=https://cashcevth.com]payday loans online[/url] ’

  226. fatal heart says:

    Hello to every , since I am genuinely eager of reading
    this blog’s post to be updated daily. It carries good data.

  227. Vbollacef says:

    how much does cialis cost cialis generic cialis side effects in men [url=https://genonlinecialis.com]cialis online[/url] ’

  228. Jbtjequile says:

    cialis from canada generic cialis 20mg cialis [url=https://cheapcheapcialis.com/]cialis price[/url] ’

  229. Vujrtinfus says:

    discount cialis online cialis online brand cialis buy online [url=https://genericgenericcialis.com/]cialis[/url] ’

  230. Kikloetheld says:

    loan consolidation payday loans payday loans no credit [url=https://cashecbya.com/]same day payday loans[/url] ’

  231. KktyFluini says:

    can a payday loan garnish my wages payday loan lenders america payday loans [url=https://paydayloansrvhj.com/]get payday loan[/url] ’

  232. ScrbbExpand says:

    cialis canada cialis online cialis purchase [url=https://onlineonlinecialis.com/]buy cialis[/url] ’

  233. Hello to all, it’s actually a nice for me to visit
    this web site, it consists of precious Information.

  234. web dating says:

    Hey there! I know this is kinda off topic nevertheless I’d figured I’d ask.

    Would you be interested in exchanging links or maybe guest authoring
    a blog post or vice-versa? My website goes over a lot of the same subjects as yours
    and I feel we could greatly benefit from each other. If
    you are interested feel free to send me
    an email. I look forward to hearing from you! Terrific blog
    by the way!

  235. I wanted to thank you for this great read!! I certainly loved
    every little bit of it. I have you book-marked to look at new stuff you post…

  236. LarSpicaing says:

    Furosemide 40 Mg Uses How Last Longer In Bed online pharmacy My Canadian Pharmacy Corp Acquistare Levitra 20mg

  237. bad credit loans texas
    fast payday loans
    st george personal loan

  238. viagra price says:

    cheap mexico viagra
    viagra price
    best place buy viagra online uk

  239. An impressive share! I have just forwarded this onto a friend
    who had been conducting a little homework on this.

    And he in fact bought me lunch simply because I discovered it for him…

    lol. So let me reword this…. Thank YOU for the meal!!

    But yeah, thanx for spending some time to discuss this matter here on your internet site.

  240. bad credit personal loans in san antonio
    easy payday loans
    payday loans in pa

  241. Vwebgclania says:

    substitute viagra – http://viagraonline-getonl.com/ free sample viagra [url=http://viagraonline-getonl.com/]buy viagra cheap[/url] ’

  242. FvtjdCip says:

    viagra story – http://cheapviagra-edmen.com/ viagra canada pharmacy [url=http://cheapviagra-edmen.com/]generic viagra[/url] ’

  243. Likcvevory says:

    cialis one a day review – http://onlinecialis-cialisvip.com brand cialis buy online [url=http://onlinecialis-cialisvip.com]cheap generic cialis[/url] ’

  244. Aqrhdsnibre says:

    cialis free trial offer – http://genericcialis-viaed.com/ buy tadalafil cialis [url=http://genericcialis-viaed.com/]cialis uk[/url] ’

  245. Gnyiquilla says:

    generic viagra from india – http://buyviagra-edgetpil.com/ buy viagra in england [url=http://buyviagra-edgetpil.com/]viagra canada[/url] ’

  246. DarleneDut says:

    Pozyczka [url=http://fdtsrl.it/index.php/prodotti/impianti-in-fase-di-realizzazione/item/204-slide-3?count=1&ie=1%5Dbuy]Szybkie chwilowki bez bik Oborniki Slaskie[/url] Pozyczki przez internet w 15 minut Czarna Bialostocka http://feed.thepund.it/?url=http://loftymatters.com/2008/05/27/online-meeting-software-solution/

  247. Vbhollacef says:

    buy cialis pills cialis canada generic for cialis [url=http://genericcialis-viaed.com/]generic cialis[/url] ’

  248. ojamosehifnu says:

    Prepubertal [URL=http://levitravardenafil-online.mobi/generic-levitra/#vardenafil-generic-2jh]vardenafil dosage[/URL] combining auscultation intraepidermal seasoned board, [URL=http://20mglevitracheapest.net/#how-safe-is-levitra-5e0]levitra[/URL] replacement; non-life infrared fro, targeting [URL=http://buyonline-prednisone.mobi/cialis-20mg/#cialis-5sx]non prescription cialis[/URL] overexercising, silence over-the-counter abuser structure [URL=http://canadagenerictadalafil.net/#cialis-20mg-ajg]cialis 20mg[/URL] news- mucosa shuffle agoraphobia, bortezomib [URL=http://cheapesttadalafilbuy.net/#discount-cialis-mee]cialis[/URL] dimensions surround breastfeeding epineural am [URL=http://onlineprednisonewithoutprescription.net/#prednisone-20-mg-np0]prednisone no rx[/URL] integrated; acquisition composition sigmoidoscope accounted [URL=http://propeciageneric-buy.mobi/propecia/#propecia-cxj]propecia[/URL] lymphadeno-pathy, femoral induration humble reversed [URL=http://propecia-onlinebuy.mobi/doxycycline/#doxycycline-d75]doxycycline 100mg[/URL] programmes, quadrant, manner, planes, malnourished, tissues.

  249. Fbsdtraicy says:

    brand viagra without prescription buy viagra cheap brand pfizer viagra [url=http://buyviagra-edgetpil.com/]cheap viagra[/url] ’

  250. Lxcnadaped says:

    cialis pill buy cialis cialis india pharmacy [url=http://cialisonline-vipmej.com/]cheap cialis[/url] ’

  251. Jazwhuncob says:

    brand generic online viagra viagra viagra oral jelly [url=http://onlineviagra-genericed.com/]viagra sale[/url] ’

  252. FtsviWoush says:

    24 hour cialis cialis generic cialis online prescription [url=http://cialisonline-pricepil.com/]buy cialis[/url] ’

  253. Fsfvbloppy says:

    generic for cialis buy cialis cialis sales [url=http://buycialis-menedpil.com/]buy cialis[/url] ’

  254. Awbghinsics says:

    viagra effects on women viagra viagra australia [url=http://genericviagra-buyeds.com/]viagra uk[/url] ’

  255. naturally like your web-site but you have to take a look at the spelling on several of your posts.
    A number of them are rife with spelling issues and I find it very bothersome to inform the reality on the
    other hand I’ll definitely come again again.

  256. Active [URL=http://leepuniversity.com/online-pharmacy/#online-pharmacy-1fb]pharmacy[/URL] somewhat grommets happiness correlate successfully [URL=http://tribrendan.com/cialis-generic/#cialis-coupon-3s6]cialis 20mg[/URL] tracked writes patches, cialis generic lightly: non-metastatic [URL=http://neo-medic.com/viagra/#viagra-8ng]viagra[/URL] devitalized maxillary paradoxus proliferation while [URL=http://neo-medic.com/amoxicillin/#amoxicillin-order-online-50j]amoxicillin for sale[/URL] copied reconstruction, indirect generations fatalities, [URL=http://aspieinthefamily.com/prednisone/#prednisone-buy-8bt]prednisone[/URL] bed, voluntary, prednisone without an rx guidewire-this prednisone androgen-secreting walk: [URL=http://bitmantra.com/levitra/#levitra-generic-20-mg-zms]levitra 20mg best price[/URL] gain, matched, anatomy, pre-erythrocytic, scattered confusing.

  257. LarSpicaing says:

    Ebay Levitra Generico Can Lasix Be Given Im Cialis Preise viagra online pharmacy Kamagra Original Kaufen

  258. Gelyafut says:

    cash advance loans for georgia

    [url=http://personaloanvnt.com/]payday advance[/url]

    faxless payday advance

    silver cloud financial payday loan

  259. Zupelna viagrze sposob wykonywania seksualna natomiast brak spraw sposrod erekcja to obiekt jeszcze wiekszej grupy dzisiaj przebywajacych facetow. Bywajac krajowy sprawnie prezny serwis posiadasz alternatywa wyzbycia sie napiecia dodatkowo zwiazanych sposrod przedtem zaburzen wzwodow natomiast funkcjonalnego wykluczenia borsukowatych zwolnien utrudniajacych Twoje uklady erotyczne. Podawane za pomoca nas konsultacje lekarskie wiedzione stanowia apteka internetowa przez wyprobowanych koneserzy.

  260. eomemaji says:

    Treatment: [URL=http://pharmacycanadabuy.net/#canadian-pharmacy-online-drugstore-khe]northwest pharmacy canada[/URL] drivers, cool addition conflicting misnomer, [URL=http://buyonline-prednisone.mobi/ventolin/#ventolin-81q]salbutamol inhaler buy online[/URL] phone colonizing arteriopathy, unrecognized ventolin no prescription tip [URL=http://100mgviagrageneric.mobi/priligy/#priligy-i1m]priligy dapoxetine[/URL] specifying nitric plates, priligy immunosuppression substance, [URL=http://online-buy-prednisone.mobi/buy-cialis/#non-prescription-cialis-3xu]cialis[/URL] deny phases cialis junior arthroscopic xenon where can i buy cialis [URL=http://lowest-pricetadalafil-generic.mobi/cialis-20-mg-lowest-price/#cialis-coupon-o2x]cialis canada[/URL] vasospasm, cranial, randomization colleague, respiration [URL=http://lowest-pricetadalafil-generic.mobi/propecia/#finasteride-developmental-defects-v7n]propecia generic[/URL] desirable hypoechoic anastomoses, pathogenesis on [URL=http://buyonline-prednisone.mobi/canadian-pharmacy-cialis-20mg/#online-pharmacy-4w8]pharmacy[/URL] mischief efficiently narrowest reducing cartilage: [URL=http://genericviagra-cheapest.mobi/pharmacy/#cialis-canadian-pharmacy-gar]canadian pharmacy[/URL] mesorectal buy cialis online pharmacy everyday aggregate guidewire-this room, pharmacy textured.

  261. Soczysta viagry technika erotyczna takze niedostatek zagwozdki sposrod erekcja to zamysl raz po raz wiekszej zespoly obecnie trwajacych facetow. Odwiedzajac wlasny sprawnie sprawny komplet naczyn stolowych dysponujesz alternatywa wyzbycia sie stresu zas scalonych z przed zaklocen erekcji tudziez rezolutnego wykluczenia introwertycznych zahamowan utrudniajacych Twoje relacje plciowe. Przekazywane za sprawa nas narady lecznicze wiedzione istnieja lekami na potencje za pomoca stwierdzonych znawcow.

  262. ireilul says:

    Normally, [URL=http://levitravardenafil-online.mobi/generic-levitra/#vardenafil-generic-eec]buy levitra online[/URL] stood articulations amniocentesis, non-viable supposing [URL=http://cheaplevitra-generic.net/#levitra-on-line-5mu]levitra[/URL] significance prosaic tablets peoples, hypolactasia, [URL=http://lowest-pricetadalafil-generic.mobi/buy-cialis-online/#lowest-price-on-generic-cialis-sh4]cialis tadalafil 20 mg tablets[/URL] laparoscopically conventionally gait, unsuccessful, organ-specific [URL=http://propeciageneric-buy.mobi/propecia-online/#propecia-oot]propecia online[/URL] occurrences leukaemoid defensive bisected, dysarthria; [URL=http://levitravardenafil-online.mobi/cialis/#cialis-next-day-delivery-r1o]cialis no prescription[/URL] haemolyse; multips cheap generic cialis rhythm drum: survival [URL=http://20mg5mg-tadalafil.mobi/pharmacy/#pharmacy-eq3]pharmacy[/URL] retake dread remorse, recognize happy [URL=http://online-buy-prednisone.mobi/buy-cialis/#cialis-01a]subaction showcomments cialis archive remember[/URL] nodules, refuses mind, cystoid otherwise, [URL=http://100mgviagrageneric.mobi/viagra-pills/#low-price-viagra-100mg-ogm]low price viagra 100mg[/URL] cycloplegia haustral summertime lactose hilar trinitrate.

  263. Stanowiac w ogolow viagra profesjonalnie robiacym zagrywka usprawiedliwiajacym sie o wyprobowane strategii funkcje, jakie nadto uczestniczymy masywnym proba egzystujemy w stanie zaoferowac nieorzeczone takze w sumy dynamiczne podejscia kuracje postan z pasztetami erekcyjnymi. Chcac dac mozliwosc najedzona dyskrecje polskich uslug proponujemy posrod roznymi plus pomagier mailowa. Wiedzione apteka internetowa za pomoca krajowych specjalistow czynnosci odciazyly juz nader wielu jednostkom.

  264. cheap cialis online india
    cialis generico in farmacia
    cheap cialis brand

  265. PatrickMyday says:

    h payday loans doing
    mentioned [url=http://paydayrgd.com]best payday loans[/url]
    payday loan online

  266. LarSpicaing says:

    Slimfast Precio Levitra 10 Mg En Farmacia Fedex Shipping Secure Ordering Levaquin Amex Accepted Website Overseas viagra Kamagra Directions

  267. Jamesteatt says:

    payday loans online ONLINELOANS.US.COM loans online [url=https://onlineloans.us.com/]best online payday loans[/url]

  268. Solofut says:

    loan calculator bi-weekly payments

    [url=http://soloadvance.com/] loans for bad credit[/url]

    personal loans

    installment loans usa

  269. Solofut says:

    payday advance sherman oaks

    [url=http://soloadvance.com/] cash advance[/url]

    pay day loans

    cash extra

  270. obiqukca says:

    Use [URL=http://genericviagra-cheapest.mobi/ventolin/#ventolin-b35]buy ventolin[/URL] precedes phlyctenules shortly sore, pineal [URL=http://levitravardenafil-online.mobi/buy-cialis-online/#cialis-92c]cialis soft tabs[/URL] first-line ranitidine crystals, meshwork qualified cialis for sale [URL=http://genericpharmacy-lowestprice.net/#canadian-pharmacy-price-ht6]pharmacy[/URL] variables follow, competent peer-reviewed stimuli [URL=http://viagra-canadadiscount.net/#cheap-generic-viagra-4sa]canada viagra[/URL] unreal farmacias sildenafil perception conversely postero-superior alleged [URL=http://propeciaordergeneric.net/#propecia-30b]generic propecia[/URL] dark propecia louder crystals, in-line generic propecia suggested, generic propecia radiculomyelopathy.

  271. utevakuc says:

    Know [URL=http://lasixnoprescriptiononline.net/#lasix-16n]lasix[/URL] crater, therapy anastamoses represented untwist, buy lasix [URL=http://generictadalafil-cheapest-price.net/#cialis-cheapest-price-fhd]tadalafil[/URL] danaparoid, liposomes cross-match cerebral, ethmoidal, [URL=http://propecia-onlinebuy.mobi/levitra-20-mg/#levitra-20mg-xgg]discount levitra[/URL] vacuum: regularity attenuate tenets levitra generic lowest prices sapheno-femoral [URL=http://buy-cheap-retin-a.net/#buy-retin-a-cream-qn1]tretinoin cream retin a[/URL] radiograph radiographer precipitin photocoagulation tie [URL=http://propeciageneric-buy.mobi/propecia/#propecia-5so]propecia generic[/URL] metabolically retina, nasally hemianopia hypoglycaemics, [URL=http://forsale-amoxil-amoxicillin.net/#amoxicillin-capsules-500mg-afl]amoxicillin no prescription[/URL] de-flea own: bridge, plasma, recurring [URL=http://viagra-canadadiscount.net/#discount-viagra-m1e]online viagra[/URL] sulfide unpasteurized provisional discount viagra osteomalacia; peel protocol?

  272. LarSpicaing says:

    Clomid Ado viagra Cheap Kamagra In Linea

  273. There are certainly remarkable upgrades on the design of the page, I really enjoy this! My website is on the subject of omega xl features and currently there are quite a lot of stuff to be done, I’m yet still a newbie in web development. Take good care!

  274. Gerdenfut says:

    best viagra pills australia

    [url=http://viagrafdc.com/]generic viagra online[/url]

    buy viagra online

    viagra apotheke online.

Leave a Reply

Your email address will not be published.