The fractional volatility model and rough volatility

TL;DR

This paper introduces a fractional volatility model driven by fractional noise to better understand volatility roughness, providing examples and deriving an option pricing equation using advanced calculus techniques.

Contribution

It presents a novel fractional volatility model incorporating fractional noise and derives an option pricing equation using Malliavin calculus.

Findings

Demonstrates the applicability of fractional noise in modeling volatility roughness

Derives an explicit option pricing equation for the fractional volatility model

Provides examples illustrating the model's behavior and implications

Abstract

The question of the volatility roughness is interpreted in the framework of a data-reconstructed fractional volatility model, where volatility is driven by fractional noise. Some examples are worked out and also, using Malliavin calculus for fractional processes, an option pricing equation and its solution are obtained.