Wishart Autoregressive Model for Stochastic Risk

Christian Gourieroux

No 2005-43, Working Papers from Center for Research in Economics and Statistics

Abstract: Risks are usually represented and measured by volatility-covolatility matrices.Wishart processes are models for a dynamic analysis of multivariaterisk, that describe the evolution of stochastic volatility-covolatility matrices,constrained to be symmetric positive definite. The autoregressive Wishartprocess (WAR) is the multivariate extension of the Cox, Ingersoll, Ross (CIR)process introduced for scalar stochastic volatility. As the CIR process it allowsfor closed form solutions for a number of financial problems, such as termstructure of T-bonds and corporate bonds, derivative pricing in multivariatestochastic volatility model and structural model for credit risk. Moreoverthe Wishart dynamics are very flexible and are serious competitors for lessstructural multivariate ARCH models.

Pages: 53
Date: 2005
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