Introduction

The premise of a stock option is that someone sells the right to buy their shares of a particular stock at a certain price by a certain date. For example, if Microsoft (MSFT) is at $50 on October 1st, the price of the option to purchase a share of MSFT at $50 anytime before October 15th might cost me $2. If MSFT is still at $50 on October 15, I will lose my $2. However, if MSFT is at $60 on October 15th, I can still purchase the shares at $50, and therefore make a 10-2 = $8 profit, a good profit since I only put $2 at risk. Further, if MSFT goes down to $40, or lower, I still only lose the $2 I spent for the option. If I had simply bought shares of MSFT, I would have been down $10. But the question remains, is the option I bought worth $2, or is it worth more than $2, or less? Many models have been proposed to answer this question.