An Adaptive Evolutionary Approach to Option Pricing via Genetic Programming

Abstract

We propose a methodology of Genetic Programming to approximate the relationship between the option price, its contract terms and the properties of the underlying stock price. An important advantage of the Genetic Programming approach is that we can incorporate currently known formulas, such as the Black-Scholes model, in the search for the best approximation to the true pricing formula. Using Monte Carlo simulations, we show that the Genetic Programming model approximates the true solution better than the Black-Scholes model when stock prices folow a jump-diffusion process. We also show that the Genetic Programming model outperforms various other models in many different settings. Other advantages of the Genetic Programming approach include its robustness to changing environment, its low demand for data, and its computational speed. Since genetic programs are flexible, self-learning and sefl-improving, they are an ideal tool for practitioners.