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

Author

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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.

Suggested Citation

  • Osnat Stramer & Matthew Bognar & Paul Schneider, 2010. "Bayesian Inference for Discretely Sampled Markov Processes with Closed-Form Likelihood Expansions," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(4), pages 450-480, Fall.
  • Handle: RePEc:oup:jfinec:v:8:y:2010:i:4:p:450-480
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbp027
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    Citations

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    Cited by:

    1. Fernández-Villaverde, Jesús & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Estimating dynamic equilibrium models with stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 216-229.
    2. 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.
    3. 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.
    4. Kleppe, Tore Selland & Yu, Jun & Skaug, Hans J., 2014. "Maximum likelihood estimation of partially observed diffusion models," Journal of Econometrics, Elsevier, vol. 180(1), pages 73-80.
    5. Li, Chenxu & Chen, Dachuan, 2016. "Estimating jump–diffusions using closed-form likelihood expansions," Journal of Econometrics, Elsevier, vol. 195(1), pages 51-70.
    6. 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.
    7. Varughese, Melvin M., 2013. "Parameter estimation for multivariate diffusion systems," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 417-428.
    8. 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.
    9. Cerrato, Mario & Lo, Chia Chun & Skindilias, Konstantinos, 2011. "Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions," SIRE Discussion Papers 2011-53, Scottish Institute for Research in Economics (SIRE).
    10. Sarno, Lucio & Schneider, Paul & Wagner, Christian, 2010. "Properties of Foreign Exchange Risk Premia," MPRA Paper 21302, University Library of Munich, Germany.
    11. Choi, Seungmoon, 2015. "Explicit form of approximate transition probability density functions of diffusion processes," Journal of Econometrics, Elsevier, vol. 187(1), pages 57-73.

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