Power-type derivatives for rough volatility with jumps

ABSTRACT

This paper proposes a novel analytical pricing–hedging framework for volatility derivatives which simultaneously takes into account rough volatility and volatility jumps. Directly targeting the instantaneous variance of a risky asset, our model consists of a generalized fractional Ornstein–Uhlenbeck process driven by a Lévy subordinator and an independent sinusoidal-composite Lévy process, and allows the characteristic function of average forward variance to be obtainable in semiclosed form, without having to invoke any geometric-mean approximations. Pricing–hedging formulae are proposed for a general class of power-type derivatives, in the spirit of numerical Fourier transform. A comparative empirical study is conducted on two independent recent data sets on Volatility Index 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. The price dynamics of the underlying asset can be readily considered and the possibility of studying rough volatility of volatility is given as well. © 2022 Wiley Periodicals LLC.