Continuous Time Wishart Process for Stochastic Risk

Christian Gourieroux

Econometric Reviews, 2006, vol. 25, issue 2-3, 177-217

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

Keywords: JEL Number; G12; G13 (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (35)

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DOI: 10.1080/07474930600713234

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