Power-type derivatives for rough volatility with jumps

TL;DR

This paper introduces a new framework for pricing and hedging volatility derivatives that incorporates rough volatility and jumps, providing semi-closed form characteristic functions and flexible power-type derivatives.

Contribution

It presents a novel model combining fractional Ornstein-Uhlenbeck processes with Lévy processes for better volatility derivative pricing and hedging, with efficient calibration demonstrated on real data.

Findings

Model captures short-term dependence in volatility

Characteristic function obtained in semi-closed form

Framework effectively calibrates to VIX options data

Abstract

In this paper we propose a novel pricing-hedging framework for volatility derivatives which simultaneously takes into account rough volatility and volatility jumps. Our model directly targets the instantaneous variance of a risky asset and consists of a generalized fractional Ornstein-Uhlenbeck process driven by a L\'{e}vy subordinator and an independent sinusoidal-composite L\'{e}vy process. The former component captures short-term dependence in the instantaneous volatility, while the latter is introduced expressly for rectifying the activity level of the average forward variance. Such a framework ensures that the characteristic function of average forward variance is obtainable in semi-closed form, without having to invoke any geometric-mean approximations. To analyze swaps and European-style options on average forward volatility, we introduce a general class of power-type derivatives on the average forward variance, which also provide flexible nonlinear leverage exposure. Pricing-hedging formulae are based on a modified numerical Fourier transform technique. A comparative empirical study is conducted on two independent recent data sets on VIX options, before and during the COVID-19 pandemic, to demonstrate that the proposed framework is highly amenable to efficient model calibration under various choices of kernels.