Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model

TL;DR

This paper introduces a novel discrete-time Markov switching stochastic volatility model with co-jumps for option pricing, providing an efficient computational method for European and American options, and offering insights into variance derivatives.

Contribution

The paper develops a computationally efficient approach to price options under a complex stochastic volatility model with co-jumps, extending to American options and variance derivatives.

Findings

Efficient algorithm for European option pricing under the model

Accurate pricing of American options via European option portfolio conversion

Numerical results demonstrate high efficiency and accuracy of the methods

Abstract

We consider option pricing using a discrete-time Markov switching stochastic volatility with co-jump model, which can model volatility clustering and varying mean-reversion speeds of volatility. For pricing European options, we develop a computationally efficient method for obtaining the probability distribution of average integrated variance (AIV), which is key to option pricing under stochastic-volatility-type models. Building upon the efficiency of the European option pricing approach, we are able to price an American-style option, by converting its pricing into the pricing of a portfolio of European options. Our work also provides constructive guidance for analyzing derivatives based on variance, e.g., the variance swap. Numerical results indicate our methods can be implemented very efficiently and accurately.