A Multivariate Jump-Driven Financial Asset Model

by Elisa Luciano of the University of Turin and ICER, and
Wim Schoutens of Katholieke Universiteit Leuven

October 16, 2006

Abstract: We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behavior of a series of stocks or indexes and to study a multi-firm, value-based default model.

Starting from an independent Brownian world, we introduce jumps and other deviations from normality, including non-Gaussian dependence. We use a stochastic time-change technique and provide the details for a Gamma change.

The main feature of the model is the fact that - opposite to other, non jointly Gaussian settings - its risk neutral dependence can be calibrated from univariate derivative prices, providing a surprisingly good fit.

JEL Classification: G12, G10.

Keywords: Lévy processes, multivariate asset modelling, copulas, risk neutral dependence.

Published in: Quantitative Finance, Vol. 6, No. 5. (October 2006), pp. 385-402.

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