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A Consistent Pricing Model for Index Options and Volatility Derivatives

Rama Cont

Imperial College London; CNRS; Norges Bank Research

Thomas Kokholm

School of Business and Social Sciences, Aarhus University

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.

Number of Pages in PDF File: 33

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

JEL Classification: G12, G13

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Date posted: September 19, 2009 ; Last revised: December 26, 2010

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

Contact Information

Rama Cont
Imperial College London ( email )
London, SW7 2AZ
United Kingdom
HOME PAGE: http://www3.imperial.ac.uk/people/r.cont
CNRS ( email )
Laboratoire de Probabilites & Modeles aleatoires
Universite Pierre & Marie Curie (Paris VI)
Paris, 75252
HOME PAGE: http://rama.cont.perso.math.cnrs.fr/
Norges Bank Research ( email )
P.O. Box 1179
Oslo, N-0107
Thomas Kokholm (Contact Author)
School of Business and Social Sciences, Aarhus University ( email )
Fuglesangs Allé 4
Aarhus, DK-8210
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