A multivariate jump-driven financial asset model

Abstract

We discuss a Levy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behaviour 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.Levy processes, Multivariate asset modelling, Copulas, Risk neutral dependence,

Multivariate Downside Risk: Normal Versus Variance Gamma

“…Monroe, 1978). Following this approach, Luciano & Schoutens (2006) propose a common Gamma subordinator and an uncorrelated multidimensional Brownian motion. Cont & Tankov (2004) and Leoni & Schoutens (2008) extend this model to correlated Brownian motions, which allows for uncorrelated asset returns.…”

Inference procedures for the variance gamma model and applications

“…Earlier instances of this model are the normal-lognormal model of Clark [1], the compound events model of Press [2], and the normal-inverse gamma distribution of Praetz [3], where the corresponding intrinsic time involves a lognormal, a Poisson, or an inverse gamma distribution, respectively; for nice reviews of the subordinated processes, the reader is referred to [4,5, §5.1]. In this category also lies the so-called (normal)-variance gamma (VG) model, which first appeared in [6] and was later studied in detail by Madan and Seneta [7]; for multivariate extensions and applications, the reader is referred to [8,9]. The VG model is constructed by allowing the variance of the corresponding (conditional) normal variate to be distributed as gamma.…”

Pricing multiasset equity options: How relevant is the dependence function?

“…The first approach involves adopting some flexible multivariate density specification to jointly model the underlying assets, such as multivariate stochastic volatility models, multivariate extreme value distributions or multivariate correlated jump processes (Harvey et al, 1994;Luciano and Schoutens, 2006;Khaliq et al, 2007). This choice is appealing from a theoretical standpoint, since it allows a complete specification of the multivariate process that drives the underlying assets.…”