The explicit Laplace transform for the Wishart process

2011/07/14 by Alessandro Gnoatto, Gnoatto, Alessandro, Martino Grasselli +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #60H35 #65C30 #91B70 #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Risk Management (q-fin.RM) #math.PR #msc:60H35 #msc:65C30 #msc:91B70 #q-fin.CP #q-fin.PR #q-fin.RM

paper · pdf · doi:10.48550/arxiv.1107.2748

Accepted on: Journal of Applied Probability 51(3), 2014

arxiv created 2013/08/20 · arxiv updated 2013/08/21

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. 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 and accurate.

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