Pricing Early-Exercise Options Using
Genetic Optimization

Abstract

One of the classic problems in option pricing theory is valuing the American put. It is easy to show the existence of an early exercise boundary for the price of the underlying asset such that each point in time, if the price is below the boundary exercise is optimal, while above the boundary it is not. But deriving a closed form valuation equation for this so-called free-boundary problem is not possible. Other types of options with early-exercise features, like Bermudan contracts, calls on dividend-paying stocks, and options on futures and forwards all present similar difficulties, and introducing a wider range of returns processes, such as jump-diffusions, does not make things easier. Many ideas for approximating solutions for early-exercise options have been proposed over the years. In this article, Powell explores a different approach using genetic optimization. This powerful search technique has not been used much in finance, but the results presented here suggest that it is capable of producing approximate valuations that are as good as other methods using rather simple computer technology. The purpose of the article is to illustrate the potential of genetic optimization for this class of problems, leaving possibilities for fine-tuning it to increase efficiency, for example by imposing known properties of the early-exercise boundary a priori, are left for future exploration.