We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The approximations rely on a general theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish properties of transition densities of affine models and show how they naturally fit into the approximation framework. Empirical applications in credit risk, likelihood inference, and option pricing highlight the usefulness of our expansions. The approximations are extremely fast to evaluate, and they perform very accurately and numerically stable.

Keywords: Affine model; Density approximation; Polynomial models

Biography: Paul Schneider received his doctoral degree in 2006 from the Vienna University of Economics and Business. After a 2-year post doc period in Vienna he joined Warwick Business School in late 2008. Paul is interested broadly in asset pricing, continuous-time econometrics, and computational statistics. He has papers forthcoming in journals such as the Journal of Financial and Quantitative Analysis, and the Annals of Statistics.