Pricing American Options under Irrational Behavior with Numerical Approach

Abstract

In this paper, we consider the pricing problem of American options under an irrational exercise strategy with a rationality parameter. Irrational behavior of option holders as reactions to market movements can lead to an exercising option strategy at a time that might not be optimal. Under the irrational exercising time strategy, the pricing problem of the American-style option leads to an overvalued price. A standard way to study the irrational behavior of option holders and its impact on the American option pricing problem is to consider intensity-based models with stochastic intensity parameters. Under these models, the option pricing problem leads to a nonlinear parabolic partial differential equation (PDE) with an additional term to the PDE of the American option under rational strategy (classical American option with optimal exercise strategy) due to the intensity functions of models. It's shown that the American option price with intensity parameter converges to the corresponding American option price (classical American option price) when the parameter tends to infinity, but the classical boundary conditions cannot apply under the finite intensity parameter. We propose a finite element method to solve the resulting PDE with a numerical approach. We also illustrate some examples to point out the accuracy of the proposed numerical method.