Question: Problem 3: Consider the following binomial option pricing problem involving an American call. This call has two (one year each) periods to go before expiring.

Problem 3: Consider the following binomial option pricing problem involving an American call. This call has two (one year each) periods to go before expiring. Its stock price is $32, and its exercise price is $27. The risk free rate is .05, stock's standard deviation of returns is 25%. The stock pays a dividend at the end of the first period at the rate of 8%. Find the value of the American call. (must show all work)

a)

What are the stock prices at each point?

Su (pre dividend)

Su (ex-dividend)

Suu

Sud

Sd (pre dividend)

Su (ex-dividend)

Sdd

b)

What is the value of p (the probability of the stock price increasing)?

c)

What are the final period call prices?

Cuu

Cud

Cdd

d)

What are the 1st period call prices?

Cu

Cd

e)

What is the value of the American call at time 0?

C

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