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

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.