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Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices

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  • Michael S. Johannes
  • Nicholas G. Polson
  • Jonathan R. Stroud
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    Abstract

    This paper provides an optimal filtering methodology in discretely observed continuous-time jump-diffusion models. Although the filtering problem has received little attention, it is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines time-discretization schemes with Monte Carlo methods. It is quite general, applying in nonlinear and multivariate jump-diffusion models and models with nonanalytic observation equations. We provide a detailed analysis of the filter's performance, and analyze four applications: disentangling jumps from stochastic volatility, forecasting volatility, comparing models via likelihood ratios, and filtering using option prices and returns. The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. 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 Studies in its journal The Review of Financial Studies.

    Volume (Year): 22 (2009)
    Issue (Month): 7 (July)
    Pages: 2559-2599

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    Handle: RePEc:oup:rfinst:v:22:y:2009:i:7:p:2559-2599

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    Cited by:
    1. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, vol. 112(1), pages 69-90.
    2. Stan Hurn & Andrew McClelland & Kenneth Lindsay, 2010. "A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions," NCER Working Paper Series 65, National Centre for Econometric Research.
    3. Luc Luc & Arnaud Dufays & Jeroen V.K. Rombouts, 2011. "Marginal Likelihood for Markov-switching and Change-point Garch Models," CREATES Research Papers 2011-41, School of Economics and Management, University of Aarhus.
    4. Calvet, Laurent-Emmanuel & Czellar , Veronika, 2011. "state-observation sampling and the econometrics of learning models," Les Cahiers de Recherche 947, HEC Paris.
    5. Chen, Bin & Hong, Yongmiao, 2011. "Generalized spectral testing for multivariate continuous-time models," Journal of Econometrics, Elsevier, vol. 164(2), pages 268-293, October.
    6. Bates, David S., 2012. "U.S. stock market crash risk, 1926–2010," Journal of Financial Economics, Elsevier, vol. 105(2), pages 229-259.
    7. Fulop, Andras & Li, Junye, 2013. "Efficient learning via simulation: A marginalized resample-move approach," Journal of Econometrics, Elsevier, vol. 176(2), pages 146-161.
    8. Worapree Maneesoonthorn & Gael M. Martin & Catherine S. Forbes & Simone Grose, 2010. "Probabilistic Forecasts of Volatility and its Risk Premia," Monash Econometrics and Business Statistics Working Papers 22/10, Monash University, Department of Econometrics and Business Statistics.
    9. Kaeck, Andreas & Alexander, Carol, 2012. "Volatility dynamics for the S&P 500: Further evidence from non-affine, multi-factor jump diffusions," Journal of Banking & Finance, Elsevier, vol. 36(11), pages 3110-3121.
    10. Moreno, Manuel & Serrano, Pedro & Stute, Winfried, 2011. "Statistical properties and economic implications of jump-diffusion processes with shot-noise effects," European Journal of Operational Research, Elsevier, vol. 214(3), pages 656-664, November.
    11. Salima El Kolei, 2013. "Parametric estimation of hidden stochastic model by contrast minimization and deconvolution," Metrika, Springer, vol. 76(8), pages 1031-1081, November.

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