Binomial Stock Option Modeling
Suppose you have the opportunity to buy the following contract, a stock call option, on March 1.
The contract allows you to buy 100 shares of XYZ stock at the end of either March, April, or May at a guaranteed price of $50 per share.You can exercise this option at most once. For example, if you purchase the stock at the end of March, you can't purchase more in April or May at the guaranteed price. The current price of the stock is $50. Each month, assume that the stock price either goes up by a dollar (with probability 0.55) or goes down by a dollar (with probability 0.45). If you buy the contract, you are obviously hoping that the stock price will go up. The reasoning is that if you buy the contract and the price goes up to $51, you buy the stock (that is, exercise your option) for $50, and then immediately sell it for $51 and make a profit of $1 per share. On the other hand, if the stock price goes down, you don't have to exercise the option; you can just let it expire.
a. If you buy the contract, what is your optimal strategy, that is: when and under what conditions would you exercise the option? Show your work in some organized way.
b. How much should you be willing to pay (max) for such a contract?