A Consistent Pricing Model for Index Options and Volatility Derivatives

33 Pages Posted: 19 Sep 2009 Last revised: 26 Dec 2010

See all articles by Rama Cont

Rama Cont

University of Oxford

Thomas Kokholm

School of Business and Social Sciences, Aarhus University

Multiple version iconThere are 2 versions of this paper

Date Written: November 2010


We propose and study a flexible modeling framework for the joint dynamics of an index and a set of forward variance swap rates written on this index, allowing options on forward variance swaps and options on the underlying index to be priced consistently. Our model reproduces various empirically observed properties of variance swap dynamics and allows for jumps in volatility and returns.

An affine specification using Lévy processes as building blocks leads to analytically tractable pricing formulas for options on variance swaps as well as efficient numerical methods for pricing of European options on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves.

We show that our model can simultaneously fit prices of European options on S&P 500 across strikes and maturities as well as options on the VIX volatility index. The calibration of the model is done in two steps, first by matching VIX option prices and then by matching prices of options on the underlying.

Keywords: variance swap, volatility derivative, VIX, VIX options, stochastic volatility, jump process, jumps, index options.

JEL Classification: G12, G13

Suggested Citation

Cont, Rama and Kokholm, Thomas, A Consistent Pricing Model for Index Options and Volatility Derivatives (November 2010). Available at SSRN: https://ssrn.com/abstract=1474691 or http://dx.doi.org/10.2139/ssrn.1474691

Rama Cont

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://https://www.maths.ox.ac.uk/people/rama.cont

Thomas Kokholm (Contact Author)

School of Business and Social Sciences, Aarhus University ( email )

Fuglesangs Allé 4
Aarhus, DK-8210

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