Reading 62: Option Markets and Contracts-LOS b 习题精选 center, assets, interest, interpret, 2011

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Session 17: Derivative Investments: Options, Swaps, and Interest Rate and Credit Derivatives
Reading 62: Option Markets and Contracts

LOS b: Calculate and interpret prices of interest rate options and options on assets using one- and two-period binomial models.

 

 

A stock is priced at 38 and the periodic risk-free rate of interest is 6%. 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%?

A) $0.64.

B) $2.58.

C) $0.57.

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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.

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A stock is priced at 40 and the periodic risk-free rate of interest is 8%. 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 is closest to:

A) $9.13.

B) $9.25.

C) $3.57.

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First, calculate the probability of an up move or a down move:
U = 1.20 so D = 0.833

P_u = (1 + 0.08 ? 0.833) / (1.20 ? 0.833) = 0.673
P_d = 1 ? 0.673 = 0.327

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(0.673) + 3(0.327)] / 1.08 = 13.745

C^- = [3(0.673) + 0 (0.327)] / 1.08 = 1.869

Call value today = [13.745(0.673) + 1.869(0.327)] / 1.08 = 9.13