A decomposition formula for fractional Heston jump diffusion models

TL;DR

This paper develops an efficient approximation formula for pricing European options in a fractional Heston jump diffusion model, capturing market effects like leverage and providing insights into parameter sensitivities.

Contribution

It introduces a novel first order approximation for option prices in a fractional Heston jump diffusion model, enhancing computational efficiency and understanding of parameter impacts.

Findings

Provides a martingale representation for the volatility process

Develops a first order approximation formula for option prices

Improves computational efficiency over traditional methods

Abstract

We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility processes have jumps in order to capture the market effect known as leverage effect. We show how to compute a martingale representation for the volatility process. Finally, using It\^o calculus for processes with discontinuous trajectories, we develop a first order approximation formula for option prices. There are two main advantages in the usage of such approximating formulas to traditional pricing methods. First, to improve computational effciency, and second, to have a deeper understanding of the option price changes in terms of changes in the model parameters.