Malliavin differentiability of fractional Heston-type model and applications to option pricing

TL;DR

This paper proves the Malliavin differentiability of a fractional Heston-type model with applications to option pricing, extending previous work to models driven by fractional Brownian motion and providing simulation results.

Contribution

It introduces a fractional Heston-type model, proves its Malliavin differentiability, and derives payoff expressions, extending prior models to fractional Brownian motion.

Findings

Model is Malliavin differentiable.

Derived explicit payoff expressions.

Performed simulations of stock and option prices.

Abstract

This paper defines fractional Heston-type (fHt) model as an arbitrage-free financial market model with the infinitesimal return volatility described by the square of a single stochastic equation with respect to fractional Brownian motion with Hurst parameter H in (0, 1). We extend the idea of Alos and [Alos, E., & Ewald, C. O. (2008). Malliavin differentiability of the Heston volatility and applications to option pricing. Advances in Applied Probability, 40(1), 144-162.] to prove that fHt model is Malliavin differentiable and deduce an expression of expected payoff function having discontinuity of any kind. Some simulations of stock price process and option prices are performed.