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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.

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File URL: http://arxiv.org/pdf/1104.5326
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Paper provided by arXiv.org in its series Papers with number 1104.5326.

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Date of creation: Apr 2011
Date of revision: Oct 2011
Handle: RePEc:arx:papers:1104.5326

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Web page: http://arxiv.org/

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  1. Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, vol. 134(2), pages 507-551, October.
  2. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
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Cited by:
  1. Matyas Barczy & Leif Doering & Zenghu Li & Gyula Pap, 2013. "Stationarity and ergodicity for an affine two factor model," Papers 1302.2534, arXiv.org, revised Sep 2013.
  2. Viktor Todorov & Iaryna Grynkiv & George Tauchen, 2010. "Realized Laplace Transforms for Estimation of Jump Diffusive Volatility Models," Working Papers 10-75, Duke University, Department of Economics.

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