# Option pricing in fractional Heston-type model

## TL;DR

This paper develops discretization schemes for option pricing in a fractional Heston model with H>1/2, analyzes their convergence, and employs Malliavin calculus to handle discontinuous payoffs.

## Contribution

It introduces new discretization methods for the fractional Heston model and derives convergence rates, also applying Malliavin calculus for discontinuous payoffs.

## Key findings

- Discretization schemes converge as mesh size decreases.
- Convergence rate of the expectation approximation is established.
- Malliavin calculus provides an alternative expectation formula for discontinuous payoffs.

## Abstract

In this paper, we consider option pricing in a framework of the fractional Heston-type model with $H>1/2$. As it is impossible to obtain an explicit formula for the expectation $\mathbb E f(S_T)$ in this case, where $S_T$ is the asset price at maturity time and $f$ is a payoff function, we provide a discretization schemes $\hat Y^n$ and $\hat S^n$ for volatility and price processes correspondingly and study convergence $\mathbb E f(\hat S^n_T) \to \mathbb E f(S_T)$ as the mesh of the partition tends to zero. The rate of convergence is calculated. As we allow $f$ to have discontinuities of the first kind which can cause errors in straightforward Monte-Carlo estimation of the expectation, we use Malliavin calculus techniques to provide an alternative formula for $\mathbb E f(S_T)$ with smooth functional under the expectation.