Option Pricing in a Regime Switching Stochastic Volatility Model

TL;DR

This paper develops a regime switching stochastic volatility model for option pricing, extending the Heston model by incorporating a non-Markov jump process to better capture market volatility regimes.

Contribution

It introduces a novel regime switching model with a non-Markov jump process for volatility, deriving a PDE for option prices under this framework.

Findings

Derived a Heston-type PDE for the new model

Provided locally risk minimizing option prices

Enhanced modeling of volatility regimes

Abstract

In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model has been successfully used where the volatility is expressed as a stochastic differential equation. In addition, we consider a regime switching model where the stock volatility dynamics depends on an underlying process which is possibly a non-Markov pure jump process. Under this model assumption, we find the locally risk minimizing pricing of European type vanilla options. The price function is shown to satisfy a Heston type PDE.