The explicit Laplace transform for the Wishart process

TL;DR

This paper derives an explicit formula for the joint Laplace transform of the Wishart process and its integral, providing a fast and accurate method that extends previous approaches and compares favorably with alternative numerical techniques.

Contribution

The paper introduces a new explicit formula for the joint Laplace transform of the Wishart process, extending Bru's approach and offering improved computational efficiency.

Findings

The new formula is fast and accurate.

It extends previous methods for the Wishart process.

Comparison shows advantages over alternative numerical methods.

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.