Question: As discussed in the text compensation options are prematurely exercised

As discussed in the text, compensation options are prematurely exercised or canceled for a variety of reasons. Suppose that compensation options both vest and expire in 3 years and that the probability is 10% that the executive will die in year 1 and 10% in year 2. Thus, the probability that the executive lives to expiration is 80%. Suppose that the stock price is $100, the interest rate is 8%, the volatility is 30%, and the dividend yield is 0.
a. Value the option by computing the expected time to exercise and plugging this into the Black-Scholes formula as time to maturity.
b. Compute the expected value of the option given the different possible times until exercise.
c. Why are the answers for the two calculations different?

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