Applications of Monte Carlo quasi-Monte Carlo methods in finance: Option pricing

The pricing of options is a very important problem encountered in financial markets today. The famous Black-Scholes model provides explicit closed form solutions for the values of certain (European style) call and put options. But for many other options, either there are no closed form solutions, or if such closed form solutions exist, the formulas exhibiting them are complicated and difficult to evaluate accurately by conventional methods. In this case, Monte Carlo methods may prove to be valuable. In this paper, we illustrate two separate applications of Monte Carlo and/or quasi-Monte Carlo methods to the pricing of options: first, the method is used to estimate multiple integrals related to the evaluation of European style options; second, an adaptive Monte Carlo method is applied to a finite difference approximation of a partial differential equation formulation of a class of finance problems. Some of the advantages in using the Monte Carlo method for such problems are discussed.