A Consistent Pricing Model for Index Options and Volatility Derivatives

27 Pages Posted: 6 Mar 2013

See all articles by Rama Cont

Rama Cont

University of Oxford; CNRS

Thomas Kokholm

School of Business and Social Sciences, Aarhus University

Multiple version iconThere are 2 versions of this paper

Date Written: April 2013

Abstract

We propose a flexible framework for modeling the joint dynamics of an index and a set of forward variance swap rates written on this index. Our model reproduces various empirically observed properties of variance swap dynamics and enables volatility derivatives and options on the underlying index to be priced consistently, while allowing for jumps in volatility and returns. An affine specification using Lévy processes as building blocks leads to analytically tractable pricing formulas for volatility derivatives, such as VIX options, 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.

Keywords: volatility derivatives, jump processes, variance swap, VIX, Levy process, affine processes

Suggested Citation

Cont, Rama and Kokholm, Thomas, A Consistent Pricing Model for Index Options and Volatility Derivatives (April 2013). Mathematical Finance, Vol. 23, Issue 2, pp. 248-274, 2013. Available at SSRN: https://ssrn.com/abstract=2229084 or http://dx.doi.org/10.1111/j.1467-9965.2011.00492.x

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

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

CNRS ( email )

LPSM
Sorbonne University
Paris
France

HOME PAGE: http://rama.cont.perso.math.cnrs.fr/

Thomas Kokholm

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

Fuglesangs Allé 4
Aarhus, DK-8210
Denmark

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