The aim of this article is to give a general introduction to the theory of interacting particle methods, and an overview of its applications to computational finance. We survey the main techniques and results on interacting particle systems and explain how they can be applied to the numerical...

Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion "Samuelson" market model (also known as the Black-Scholes model because it is used in that most...

The Gaussian Affine Term Structure Model (ATSM) introduced by Duffie and Kan is often used in finance to price derivatives written on interest rates or to compute the reserve to hedge a portfolio of credits (CreditVaR), and in macroeconomic applications to study the links between real activity...

This paper examines how credit derivatives have changed the construction of an efficient portfolio. Credit derivatives provide a way of gaining exposure to credit risk alone, to the exclusion of interest rate risk. They also permit a relatively easy use of leverage. We examine two types of...

Dependence is an important issue in credit risk portfolio modeling and pricing. We discuss a straightforward common factor model of credit risk dependence, which is motivated by intensity models such as Duffie and Singleton (1998), among others. In the empirical analysis, we study dependence...

This doctoral thesis develops regime-switching models of the term structure of interest rates. A general framework is proposed to model the joint dynamics of yield curves associated with different debtors (Chapter 2). This framework is exploited to analyse the fluctuations of ten euro-area...