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Bayesian Inference for Discretely Sampled Markov Processes with Closed-Form Likelihood Expansions

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  • Osnat Stramer
  • Matthew Bognar
  • Paul Schneider

Abstract

This article proposes a new Bayesian Markov chain Monte Carlo (MCMC) methodology for estimation of a wide class of multidimensional jump-diffusion models. Our approach is based on the closed-form (CF) likelihood approximations of Aït-Sahalia�(2002,�2008). The CF likelihood approximation does not integrate to 1; it is very close to 1 when in the center of the distribution but can differ markedly from 1 when far in the tails. We propose an MCMC algorithm that addresses the problems that arise when the CF approximation is applied in a Bayesian context. The efficacy of our approach is demonstrated in a simulation study of the Cox--Ingersoll--Ross and Heston models and is applied to two well-known datasets. Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

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Bibliographic Info

Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 8 (2010)
Issue (Month): 4 (Fall)
Pages: 450-480

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Handle: RePEc:oup:jfinec:v:8:y:2010:i:4:p:450-480

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Cited by:
  1. Varughese, Melvin M., 2013. "Parameter estimation for multivariate diffusion systems," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 417-428.
  2. Isambi Mbalawata & Simo Särkkä & Heikki Haario, 2013. "Parameter estimation in stochastic differential equations with Markov chain Monte Carlo and non-linear Kalman filtering," Computational Statistics, Springer, vol. 28(3), pages 1195-1223, June.
  3. Lee, Yoon Dong & Song, Seongjoo & Lee, Eun-Kyung, 2014. "The delta expansion for the transition density of diffusion models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 694-705.
  4. Filipović, Damir & Mayerhofer, Eberhard & Schneider, Paul, 2013. "Density approximations for multivariate affine jump-diffusion processes," Journal of Econometrics, Elsevier, vol. 176(2), pages 93-111.
  5. Mario Cerrato & Chia Chun Lo & Konstantinos Skindilias, 2011. "Adaptive continuous time Markov chain approximation model to general jump-diffusions," Working Papers 2011_16, Business School - Economics, University of Glasgow.
  6. Sarno, Lucio & Schneider, Paul & Wagner, Christian, 2010. "Properties of Foreign Exchange Risk Premia," MPRA Paper 21302, University Library of Munich, Germany.

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