Density Approximations for Multivariate Affine Jump-Diffusion Processes

TL;DR

This paper develops fast, accurate, and stable closed-form density expansions for multivariate affine jump-diffusion processes, enhancing applications in credit risk, inference, and option pricing.

Contribution

It introduces a general approximation framework for transition densities of affine jump-diffusions, with conditions ensuring their existence and differentiability.

Findings

Expansions are computationally fast to evaluate.

Approximations are highly accurate and numerically stable.

Empirical applications demonstrate practical usefulness.

Abstract

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existence and differentiability 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.