In the following, S0 is the stock price in dollars as of today, K is the strike price in dollars, r is the continuously-compounded risk-free interest (as a decimal), q is the continuous dividend yield (as a decimal), sigma is the volatility (as a decimal) and T is the time to maturity in years. Compute option prices in dollars for the following types of options and the following parameter values with a three step binomial tree.

A). S0 = 100, K = 100, r = 0.07, q = 0.05, sigma = 0.3, T = 1. European call. What is the price in dollars today?

B). S0 = 100, K = 100, r = 0.07, q = 0.05, sigma = 0.3, T = 1. American call. What is the price in dollars today?

C). What is the Early exercise premium when K = 60?

D). In the case that S0 = 100, r = 0.07, q = 0.05, sigma = 0.3, T = 1, and for an American call option with strike K = 60, what is the price in dollars today? At what time would a holder of the option optimally exercise?

E). What is the Early exercise premium when the dividend yield q = 0.10 and K = 75?

F). If q = 0.10 and K = 75, what is the Delta (position in stock to make portfolio of the stock and a short position in one option riskless) of the American and European calls.

Answer rating: 100% (QA)

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