Long memory stochastic volatility in option pricing

TL;DR

This paper introduces a stochastic model incorporating long-memory effects in volatility to improve option pricing accuracy, deriving asymptotic equations with fractional Brownian motion to establish pricing bands.

Contribution

It presents a novel approach integrating long-range dependence in volatility into the Black-Scholes framework, leading to new asymptotic equations for option pricing.

Findings

Derived asymptotic equations involving fractional Brownian motion.

Established pricing bands accounting for long-memory effects.

Enhanced understanding of volatility's impact on option prices.

Abstract

The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range dependence. We consider the option price as a sum of classical Black-Scholes price and random deviation describing the risk from the random volatility. By using the fact the option price and random volatility change on different time scales, we find the asymptotic equation for the derivation involving fractional Brownian motion. The solution to this equation allows us to find the pricing bands for options.