Question: Consider a binomial model. S0 = 4. In each period, the stock price doubles with a probability of 1/2 and halves with a probability of

Consider a binomial model. S0 = 4. In each period, the stock price doubles with a probability of 1/2 and halves with a probability of 1/2. The interest rate is r = 2 . Suppose N = 2. An American contract yields: if exercised at time t = 0, a payment of $0; if exercised at time t = 1, a payment of $6 dollars if the stock price has decreased and of $0 otherwise; if exercised at time t = 2, a payment of $36 if the stock price has jumped twice, of $18 if the stock price is equal to $4 and of $0 otherwise.

What is the fair price of the contract at time t = 0?

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