Optimal and Enhanced Pricing of American and European Options Incorporating a Rationality Parameter: A Computational Approach Using the Finite Element Method

This paper investigates the pricing problem of American options under a regime-switching jump-diffusion model that allows for non-optimal exercise policies (early or late exercise), also known as irrational strategies. Empirical evidence from financial markets indicates that, owing to the irrational behavior of investors, option holders sometimes exercise American options at non-optimal times. Consequently, the value of an option exercised under such non-optimal strategies differs from that of the corresponding American option exercised under the optimal strategy. In this study, we adopt an intensity-function-based model with a rationality parameter to capture the features of irrational behavior and to improve the accuracy of American option pricing. Moreover, to overcome the shortcomings of the classical Black-Scholes-Merton model in financial markets, we propose, among the available alternatives, a jump-diffusion model combined with a regime-switching framework. Under this model, we formulate the American option pricing problem in the presence of irrational decision-making by option holders as a partial integro-differential equation (PIDE). To solve the resulting system of PIDES, we use a finite difference method to discretize the time dimension and a finite element method to approximate the spatial solution. Numerical results are presented to confirm the efficiency and accuracy of the proposed model and of the applied numerical method.

Keywords:

irrational exercise strategy , rationality parameter , American option , regime-switching jump-diffusion model , finite element method