CVA in fractional and rough volatility models

TL;DR

This paper develops a general formula for pricing vulnerable European options and their CVA in stochastic volatility models, including rough volatility, with numerical and theoretical analysis of approximation accuracy and roughness effects.

Contribution

It introduces a unified representation formula for CVA in both rough and classical stochastic volatility models, with new approximation methods and analysis of roughness impact.

Findings

The representation formula accurately approximates CVA in various models.

Numerical results show good agreement with Monte Carlo simulations.

Roughness significantly influences option pricing and CVA.

Abstract

In this work we present a general representation formula for the price of a vulnerable European option, and the related CVA in stochastic (either rough or not) volatility models for the underlying's price, when admitting correlation with the default event. We specialize it for some volatility models and we provide price approximations, based on the representation formula. We study numerically their accuracy, comparing the results with Monte Carlo simulations, and we run a theoretical study of the error. We also introduce a seminal study of roughness influence on the claim's price.