Monte Carlo Simulations

Abstract

Having recognized the fact that prices of financial instruments can be calculated as discounted future expectations (with respect to a risk-neutral probability measure), the idea of calculating such expectations by simulating the (stochastic) evolution of the underlyings several times and subsequently averaging the results somehow is not far removed. In fact, this relatively simple idea is widely used and is successful even in the valuation of very exotic options for which other methods are either too complicated or completely unsuitable, the only requirement being the availability of sufficient computation time. Before proceeding with financial applications of Monte Carlo techniques, we begin with a presentation of the technique itself.