A general framework for a joint calibration of VIX and VXX options

TL;DR

This paper introduces a multi-factor stochastic-local volatility model that jointly calibrates VIX futures and VXX options, improving upon previous models by capturing the joint dynamics of these derivatives.

Contribution

The paper presents a novel multi-factor stochastic-local volatility framework for joint calibration of VIX and VXX options, addressing limitations of existing models.

Findings

Model successfully calibrates to real market data

Parameters significantly influence implied volatility surfaces

Joint calibration improves pricing accuracy for VIX and VXX options

Abstract

We analyze the VIX futures market with a focus on the exchange-traded notes written on such contracts, in particular we investigate the VXX notes tracking the short-end part of the futures term structure. Inspired by recent developments in commodity smile modelling, we present a multi-factor stochastic-local volatility model that is able to jointly calibrate plain vanilla options both on VIX futures and VXX notes, thus going beyond the failure of purely stochastic or simply local volatility models. We discuss numerical results on real market data by highlighting the impact of model parameters on implied volatilities.