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Density Approximations for Multivariate Affine Jump-Diffusion Processes

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  • Damir Filipovi'c
  • Eberhard Mayerhofer
  • Paul Schneider

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.

Suggested Citation

  • Damir Filipovi'c & Eberhard Mayerhofer & Paul Schneider, 2011. "Density Approximations for Multivariate Affine Jump-Diffusion Processes," Papers 1104.5326, arXiv.org, revised Oct 2011.
    • Handle: RePEc:arx:papers:1104.5326
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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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