The equivalent martingale measure: an introduction to pricing using expectations

We provide a self contained introduction to the risk neutral or martingale approach to the pricing of financial derivatives, while assuming no financial background. This approach to pricing provides a rich source of problems ideally suited to the application of Monte Carlo methods, thus forming a bridge between computational finance and some of the well developed tools available to engineers and scientists. We illustrate the power of the martingale approach by using it to develop the price of the European call option using only elementary methods and briefly discuss the pricing of the American put option as well as interest rate derivatives.