The Explicit Laplace Transform for the Wishart Process

18 Pages Posted: 15 Jul 2011 Last revised: 20 Aug 2013

See all articles by Alessandro Gnoatto

Alessandro Gnoatto

University of Verona - Department of Economics

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center

Date Written: August 20, 2013

Abstract

We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru (1991). We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix Riccati ODE’s and the Runge-Kutta algorithm. The new formula turns out to be fast, accurate and very useful for applications when dealing with stochastic volatility and stochastic correlation modelling.

Keywords: Affine Processes, Wishart Process, ODE, Laplace Transform

JEL Classification: G13, C51

Suggested Citation

Gnoatto, Alessandro and Grasselli, Martino, The Explicit Laplace Transform for the Wishart Process (August 20, 2013). Journal of Applied Probability, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1885847 or http://dx.doi.org/10.2139/ssrn.1885847

Alessandro Gnoatto

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

Martino Grasselli (Contact Author)

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center ( email )

Paris La Défense
France

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