A Fractional Heston-Type Model as a Singular Stochastic Equation Driven by Fractional Brownian Motion

Abstract

This paper introduces the fractional Heston-type (fHt) model as a stochastic system comprising the stock price process modeled by a geometric Brownian motion. In this model, the infinitesimal return volatility is characterized by the square of a singular stochastic equation driven by a fractional Brownian motion with a Hurst parameter H∈(0,1). We establish the Malliavin differentiability of the fHt model and derive an expression for the expected payoff function, revealing potential discontinuities. Simulation experiments are conducted to illustrate the dynamics of the stock price process and option prices.

Keywords

• fractional Heston model
• fractional Brownian motion
• fractional Cox–Ingersoll–Ross process
• Malliavin differentiability