A Homotopy Analysis Method for the Option Pricing PDE in Post-Crash Markets

Abstract

Abstract We investigate a solution for the option pricing partial differential equation (PDE) in a market suffering from a financial crisis. The post-crash model assumes that the volatility is stochastic. It is an extension of the famous Black and Scholes model. Therefore, the option pricing PDE for the crisis model is a generalization of the Black and Scholes PDE. However, to the best knowledge, it does not have a closed form solution for the general case. In this paper, we provide a solution for the pricing PDE of a European option during financial crisis using the homotopy analysis method.