Orthogonal Expansions for VIX Options Under Affine Jump Diffusions

Quantitative Finance 18.6 (2018): 951-967. Accepted August 17, 2017. DOI: 10.1080/14697688.2017.1371322.

26 Pages Posted: 24 Feb 2017 Last revised: 27 Jul 2018

See all articles by Andrea Barletta

Andrea Barletta

Department of Economics and Business Economics - Aarhus BSS

Elisa Nicolato

Aarhus University - Department of Business and Economics

Date Written: December 22, 2016

Abstract

In this work we derive new closed-form pricing formulas for VIX options in the jump-diffusion SVJJ model proposed by Duffie et al. (2000). Our approach is based on the classic methodology of approximating a density function with an orthogonal expansion of polynomials weighted by a kernel. Orthogonal expansions based on the Gaussian distribution, such as Edgeworth or Gram-Charlier expansions, have been successfully employed by a number of authors in the context of equity options. However, these expansions are not quite suitable for volatility or variance densities as they inherently assign positive mass to the negative real line. Here we approximate option prices via expansions that instead are based on kernels defined on the positive real line. Specifically, we consider a flexible family of distributions, which generalizes the gamma kernel associated with the classic Laguerre expansions. The method can be employed whenever the moments of the underlying variance distribution are known. It provides fast and accurate price computations, and therefore it represents a valid and possibly more robust alternative to pricing techniques based on Fourier transform inversions.

Keywords: VIX options, Affine jump diffusion, Orthogonal polynomials, Laguerre expansions

JEL Classification: C60, G12, G13

Suggested Citation

Barletta, Andrea and Nicolato, Elisa, Orthogonal Expansions for VIX Options Under Affine Jump Diffusions (December 22, 2016). Quantitative Finance 18.6 (2018): 951-967. Accepted August 17, 2017. DOI: 10.1080/14697688.2017.1371322.. Available at SSRN: https://ssrn.com/abstract=2923081 or http://dx.doi.org/10.2139/ssrn.2923081

Andrea Barletta

Department of Economics and Business Economics - Aarhus BSS ( email )

Fuglesangs Allé
Aarhus V, 8210
Denmark
+45 8716 5372 (Phone)

HOME PAGE: http://pure.au.dk/portal/en/abarletta@econ.au.dk

Elisa Nicolato (Contact Author)

Aarhus University - Department of Business and Economics ( email )

Nordre Ringgade 1
Aarhus C, DK-8000
Denmark

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