Problem 2.

Suppose an investor has the opportunity to buy the following contract, a stock call option, on March 1. The contract allows her to buy 100 shares of ABC stock at the end of March, April, of May, at a guaranteed price of $50 per share. He can "exercise" this option at most once. For example, if she purchases the stock at the end of March, she cannot purchase more in April or May at the guaranteed price. The current price of the stock is $50. Each month, we assume that the stock price either goes up by a dollar (with probability 0.6) or goes down by a dollar (with probability 0.4). If the investor buys the contract, he is hoping that the stock price will go up. The reasoning is that if she buys the stock (that is, she exercises her option) for $50, the she can turn around, and sell the stock for $51 and make a profit of $1 per share. On the other hand, if the stock price goes down, she doesn't have to exercise her option; she can just throw the contract away.

a.What is the investor's optimal strategy; i.e., when should she exercise the option, assuming that she purchases the contract?

b.How much should she be willing to pay for such a contract?