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The Explicit Laplace Transform for the Wishart Process

Published online by Cambridge University Press:  30 January 2018

Alessandro Gnoatto*
LMU München
Martino Grasselli*
Università di Padova, Pole Universitaire Léonard de Vinci and Quanta Finanza S.R.L.
Postal address: Mathematisches Institut, LMU München, Theresienstrasse 39, D-80333 München, Germany. Email address:
∗∗ Postal address: Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy. Email address:
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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 ordinary differential equation, and the Runge-Kutta algorithm. The new formula turns out to be fast and accurate.

Research Article
© Applied Probability Trust 


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