Equity Correlations Implied by Index Options: Estimation and Model Uncertainty Analysis

35 Pages Posted: 19 Apr 2010  

Rama Cont

Imperial College London; CNRS; Norges Bank Research

Romain Deguest

Fundvisory

Multiple version iconThere are 2 versions of this paper

Date Written: April 19, 2010

Abstract

We propose a method for constructing an arbitrage-free multi-asset pricing model which is consistent with a set of observed single- and multi-asset derivative prices. The pricing model is constructed as a random mixture of N reference models, where the distribution of mixture weights is obtained by solving a well-posed convex optimization problem. Application of this method to equity and index options shows that, while multivariate diffusion models with constant correlation fail to match the prices of index and component options simultaneously, a jump-diffusion model with a common jump component affecting all stocks enables to do so. Furthermore, we show that even within a parametric model class, there is a wide range of correlation patterns compatible with observed prices of index options. Our method allows, as a by product, to quantify this model uncertainty with no further computational effort and propose static hedging strategies for reducing the exposure of multi-asset derivatives to model uncertainty.

Keywords: Correlation matrix, basket options, model calibration, inverse problems, Monte Carlo simulations, model uncertainty, Bayesian model averaging, convex duality

JEL Classification: C11, C30, G12, G13

Suggested Citation

Cont, Rama and Deguest, Romain, Equity Correlations Implied by Index Options: Estimation and Model Uncertainty Analysis (April 19, 2010). Available at SSRN: https://ssrn.com/abstract=1592531 or http://dx.doi.org/10.2139/ssrn.1592531

Rama Cont (Contact Author)

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
France

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

Norges Bank Research ( email )

P.O. Box 1179
Oslo, N-0107
Norway

Romain Deguest

Fundvisory ( email )

48 rue du Chateau Landon
Paris, 75010
France

HOME PAGE: http://www.fundvisory.com/

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