A Multivariate Jump-Driven Financial Asset Model

Abstract

In this paper, we propose a multivariate financial model for nancial assets which incorporates jumps, skewness, kurtosis and stochastic volatility, and discuss its applications in the context of equity and credit risk. In the former case we describe the stochastic behavior of a series of stocks or indexes, in the latter we apply the model in a multi-firm, value-based default model. Starting from a independent Brownian world, we will introduce jumps and other deviations from normality, as well as non-Gaussian dependence, by the simple but very strong technique of stochastic time-changing. We work out the details in the case of a Gamma time-change, thus obtaining a multivariate Variance Gamma (VG) setting. We are able to characterize the model from an analytical point of view, by writing down the joint distribution function of the assets at any point in time and by studying their association via the copula technique.

The model is also computationally friendly, since numerical results require a modest amount of time and the number of parameters grows linearly with the number of assets. The main feature of the model however is the fact that - opposite to other, non jointly Gaussian settings - its risk neutral dependence can be calibrated from univariate derivative prices. Examples from the equity and credit market show the goodness of fit attained.