Density Approximations for Multivariate Affine Jump-Diffusion Processes
42 Pages Posted: 26 May 2011 Last revised: 17 Mar 2013
Date Written: May 24, 2011
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 option pricing, credit risk, and likelihood inference highlight the usefulness of our expansions. The approximations are extremely fast to evaluate, and they perform very accurately and numerically stable.
Keywords: Affine Processes, Asymptotic Expansion, Density Approximation, Orthogonal Polynomials
JEL Classification: G12, C13, C32
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