Your brother-in-law has been reading too many get rich quick articles and wants to try his hand at investing in derivatives. He has turned to you, the business school all-star, for advice on valuing and exercising stock options. Currently he is tracking a particular stock and has noticed that the price fluctuates quite a lot even though it doesnt change that much in the long run. He feels that if he buys call options on the stock, he can profit from this volatility with minimal risk and investment on his part. Since you have studied finance, you know that a call option is a contract that gives you the right to purchase a share of a specified stock at some future date, at a pre-determined price (the strike price). If you exercise the option (meaning: buy the shares), it is assumed that you immediately re-sell the shares at the prevailing market price and pocket any gains. If the market price is below the strike price when the option expires, obviously you would not exercise the option, and anything you paid for the option contract will be lost.

Your brother has asked you to help him determine how much he should be willing to pay for such an option, on a per share basis. You explain that the value of the option to him depends entirely on his assumptions about the stock price movements over time. He replies that the stock is currently trading at $100/share, and while he doesnt expect any long-term change, over the course of an average month he expects the price to either go up or down by $15, with equal probability. He can buy a 90-day (three-month) call option with a strike price of $110.

Model this as a European call option, purchased on Nov. 1. A European call can only be exercised on a specific date three months from now: the end of January. Also, model the stock price movements to take place once per month. What is the value of this option to your brother-in-law, per share? (Show your work.)