Integrated Wishart bridges and their applications

Abstract

This thesis focuses on the study of Wishart processes, which can be considered as the matrix-valued square-root processes. In mathematical finance, the square-root processes find applications in interest rates modelling (the Cox-Ingersoll-Ross model), and in the Heston volatility model where the square-root processes model the stochastic volatility of a risky asset.

The main results of this thesis are concerned with the change of measure and time integrals of Wishart processes, which we shall call the integrated Wishart processes, as well as the generalised Hartman-Watson law of Wishart processes. In particular, we are interested in the joint conditional Laplace transform of the time integral of a Wishart process and its generalised Hartman-Watson law. Applications of the integrated Wishart processes in Monte Carlo simulation and path simulation of multi-factor stochastic volatility processes are also discussed.