Power-type derivatives for rough volatility with jumps

Liang Wang and Weixuan Xia

Papers from arXiv.org

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.

Date: 2020-08, Revised 2021-11
New Economics Papers: this item is included in nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2008.10184

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