Option Pricing Model Based on a Markov-modulated Diffusion with Jumps

TL;DR

This paper introduces a novel option pricing model based on a Markov-modulated diffusion with jumps, capturing stock price dynamics during financial cycles and providing explicit pricing formulas.

Contribution

It develops a new class of models using inhomogeneous telegraph processes and jump diffusions with switching volatilities, including explicit option pricing formulas.

Findings

Model captures stock dynamics during financial cycles

Explicit formulas for European option prices derived

Martingale measures characterized for the incomplete market

Abstract

The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are switching. We argue that such a model captures well the stock price dynamics under periodic financial cycles. The distribution of this process is described in detail. For this model we obtain the structure of the set of martingale measures. This incomplete model can be completed by adding another asset based on the same sources of randomness. Explicit closed-form formulae for prices of the standard European options are obtained for the completed market model.