A Non-Structural Investigation of VIX Risk Neutral Density

45 Pages Posted: 1 Apr 2017 Last revised: 16 Nov 2018

See all articles by Andrea Barletta

Andrea Barletta

Nordea Bank

Paolo Santucci de Magistris

Aarhus University - CREATES

Francesco Violante

Maastricht University - Department of Economics

Date Written: January 21, 2018

Abstract

We propose a non-structural method to retrieve the risk-neutral density (RND) implied by options on the CBOE Volatility Index (VIX). The methodology is based on orthogonal polynomial expansions around a kernel density and yields the RND of the underlying asset without the need for a parametric specification. The classic family of Laguerre expansions is extended to include the GIG and the generalized Weibull kernels. We show that orthogonal polynomial expansions yield accurate approximations of the RND of VIX and, in some cases, they outperform commonly used non-parametric methods. Based on a panel of observed VIX options, we retrieve the variance swap term structure, the time series of VVIX, the VIX risk-neutral moments and the Volatility-at-Risk, which reveal a number of stylized facts on the RND of VIX.

Keywords: VIX options, orthogonal expansions, risk-neutral moments, volatility jumps, volatility tail-risk

JEL Classification: C01, C02, C58, G12, G13

Suggested Citation

Barletta, Andrea and Santucci de Magistris, Paolo and Violante, Francesco, A Non-Structural Investigation of VIX Risk Neutral Density (January 21, 2018). Journal of Banking and Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2943964 or http://dx.doi.org/10.2139/ssrn.2943964

Andrea Barletta (Contact Author)

Nordea Bank ( email )

Christianbro
Strandgade 3
Copenhagen, 1401
Denmark

HOME PAGE: http://https://sites.google.com/view/andreabarletta/home

Paolo Santucci de Magistris

Aarhus University - CREATES ( email )

Department of Economics and Business Economics
Fuglesangs Allè 4
Aarhus V, 8210
Denmark

Francesco Violante

Maastricht University - Department of Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

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