Volatility options in rough volatility models

TL;DR

This paper explores pricing and hedging volatility options within rough volatility models, introduces efficient computational methods, and proposes modulated Volterra processes to better fit market VIX smile data.

Contribution

It develops Monte Carlo and asymptotic methods for rough volatility models and introduces modulated Volterra processes to accurately model VIX smiles.

Findings

Efficient Monte Carlo methods for rough volatility options

Asymptotic approximations for hedge ratios

Modulated Volterra processes capture VIX smile

Abstract

We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where log-volatility follows a Gaussian Volterra process. While providing a good fit for European options, these models are unable to reproduce the VIX option smile observed in the market, and are thus not suitable for VIX products. To accommodate these, we introduce the class of modulated Volterra processes, and show that they successfully capture the VIX smile.