Wishart Processes

By Oliver Pfaffel. 2012

243 citations recorded by the source corpus.

Based on a student research project this article gives a short review on Wishart processes. A Wishart procces is a matrix valued continuous time stochastic process with a marginal Wishart distribution. The Wishart distribution is a matrix variate generalization of the chi-squared distribution. Since Wishart processes are defined as a solution to a stochastic differential equation, the existence and uniqueness of strong solutions will be discussed comprehensively. It is also shown that some solutions of the stochastic differential equation can be expressed as squares of matrix variate Ornstein-Uhlenbeck processes. Wishart processes have the property of being symmetric positive definite and are therefore heavily used for modeling interest rates or the covariance matrix in stochastic volatility models.

Subfields: Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/451f2aae8c5a80a76aacfe29bd38cb3e828834d0

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In Economics and Econometrics

Citations in the corpus

Estimating the Wishart Affine Stochastic Correlation Model using the empirical characteristic function (2014, unknown): “…and Sufana (2004), this affine model can be regarded as a multivariate version of the Heston (1993) model: in fact, the volatility matrix is assumed to evolve according to the Wishart dynamics (mathematically developed by Bru, 1991), the matrix analogue of the mean reverting square root process.”
Multidimensional Yamada-Watanabe theorem and its applications to particle systems (2011, methodology): “It was introduced by Bru [3] by first writing the SDE for Xt = N T t Nt and next replacing the parameter n by α.”
Affine Processes on Positive Semidefinite Matrices (2009, unknown): “For illustration, let us consider a multi-variate stochastic volatility model consisting of a d-dimensional logarithmic price process with risk-neutral dynamics dYt = (r1− 12Xdiagt )dt +√Xt dBt , Y0 = y,(1.1) Received October 2009; revised April 2010.”
Gaussian Process Regression Networks (2011, methodology): “We compare to full BEKK MGARCH (Engle and Kroner, 1995), the generalised Wishart process (Wilson and Ghahramani, 2010b), the original Wishart process (Bru, 1991; Gouriéroux et al., 2009), and using the empirical covariance of the training set.”
Derivative Pricing With Wishart Multivariate Stochastic Volatility (2010, methodology): “It corresponds to the continuoustime WAR introduced by Bru (1991) and studied in Gourieroux, Jasiak, and Sufana (2009) and Gourieroux (2006) as a tool for modeling the dynamics of volatility matrices.”