1.A stock is priced at 40 and the periodic risk-free rate of interest is 8 percent. What is the value of a two-period European call option with a strike price of 37 on a share of stock using a binomial model with an up factor of 1.20 and a (risk-neutral) up probability of 67 percent? A) $20.60. B) $3.57. C) $9.07. D) $9.25. The correct answer was C) Two up moves produce a stock price of 40 × 1.44 = 57.60 and a call value at the end of two periods of 20.60. An up and a down move leave the stock price unchanged at 40 and produce a call value of 3. Two down moves result in the option being out of the money. The value of the call option is discounted back one year and then discounted back again to today. The calculations are as follows: C+ = [20.6(0.67) + 3(0.33)] / 1.08 = 13.6962 C- = [3(0.67) + 0 (0.33)] / 1.08 = 1.8611 Call value today = [13.696(0.67) + 1.8611(0.33)] / 1.08 = 9.07 2.A two-period interest rate tree has the following expected one-period rates: t = 0 |
| t = 1 |
| t = 2 | | |
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| 7.12% | | | 6.83% |
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| 6.00% | |
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| 6.84% | | | 6.17% |
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| | |
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| 6.22% |
The price of a two-period European interest-rate call option on the one-period rate with a strike rate of 6.25 percent and a principal amount of $100,000 is closest to: A) $725.86. B) $449.33. C) $423.89. D) $704.22. The correct answer was C) 1. Calculate the payoffs on the call in percent for I++ and I+- (= I-+):
I++ value = (0.0712 - 0.0625) / 1.0712 = 0.00812173.
I+- value = (0.0684 - 0.0625) / 1.0684 = 0.00552228.
Remember that the payoff on the call value is the present value of the interest rate difference based on the rate realized at t = 2 because the payment is received at t = 3. 2. Calculate the t =1 values (the probabilities in an interest rate tree are 50%):
At t = 1 the values are I+ = [0.5 (0.00812173) + 0.5 (0.00552228)] / 1.0683 = 0.00638585.
At t = 1 the values are I- = [0.5 (0) + 0.5 (.00552228)] / 1.0617 = 0.00260068. 3. Calculate the t = 0 value:
At t = 0 the option value is [0.5(0.00638585) + 0.5(.00260068)] / 1.06 = 0.00423893 .00423893 x 100,000 = $423.89. 3.A stock is priced at 38 and the periodic risk-free rate of interest is 6 percent. What is the value of a two-period European put option with a strike price of 35 on a share of stock using a binomial model with an up factor of 1.15 and a risk-neutral probability of 68 percent? A) $2.58. B) $0.64. C) $0.57. D) $2.90. The correct answer was C) Given an up probability of 1.15, the down probability is simply the reciprocal of this number 1/1.15=0.87. Two down moves produce a stock price of 38 × 0.872 = 28.73 and a put value at the end of two periods of 6.27. An up and a down move, as well as two up moves leave the put option out of the money. The value of the put option is [0.322 × 6.27] / 1.062 = $0.57. | 
发表于 2008-4-22 11:41
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