Pricing a financial derivative - the call option

Suppose you want to make some money on the stock market. The usual place to start is to buy a stock and hope its price goes up. However, if it goes down you risk losing a lot of money! Alternatively, you could buy an call option on the stock. This is a financial product that grants you the right to purchase a stock at a fixed future date, for a fixed pre-agreed price. If the stock ends up above the agreed price you are in to make a profit. If the stock crashes, you simply don’t use the option, and only lose the amount you paid for it.

In this talk I discuss what is a good price to pay for an option given the unpredictability of stock prices, and derive an explicit formula when modelling the stock price as a mean-reverting stochastic process.