Approximate Pricing of Derivatives Under Fractional Stochastic Volatility Model

TL;DR

This paper develops an approximate method for pricing derivatives within a fractional stochastic volatility framework, incorporating fractional Ornstein-Uhlenbeck processes, and demonstrates its effectiveness through numerical simulations highlighting long-range dependence effects.

Contribution

It introduces a novel approximation formula for derivative pricing under fractional stochastic volatility models involving fractional Ornstein-Uhlenbeck processes.

Findings

The approximation is feasible and practical for derivative pricing.

Long-range dependence significantly impacts derivative prices.

Numerical results validate the approximation's accuracy.

Abstract

We investigate the problem of pricing derivatives under a fractional stochastic volatility model. We obtain an approximate expression of the derivative price where the stochastic volatility can be composed of deterministic functions of time and fractional Ornstein-Uhlenbeck process. Numerical simulations are given to illustrate the feasibility and operability of the approximation, and also demonstrate the effect of long-range on derivative prices.