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Estimating Latent Variables and Jump Diffusion Models Using High-Frequency Data

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  • George J. Jiang
  • Roel C. A. Oomen

Abstract

This article proposes a new approach to exploit the information in high-frequency data for the statistical inference of continuous-time affine jump diffusion (AJD) models with latent variables. For this purpose, we construct unbiased estimators of the latent variables and their power functions on the basis of the observed state variables over extended horizons. With the estimates of the latent variables, we propose a generalized method of moments (GMM) procedure for the estimation of AJD models with the distinguishing feature that moments of both observed and latent state variables can be used without resorting to path simulation or discretization of the continuous-time process. Using high frequency return observations of the S&P 500 index, we implement our estimation approach to various continuous-time asset return models with stochastic volatility and random jumps. Copyright 2007, Oxford University Press.

Suggested Citation

  • George J. Jiang & Roel C. A. Oomen, 2007. "Estimating Latent Variables and Jump Diffusion Models Using High-Frequency Data," Journal of Financial Econometrics, Oxford University Press, vol. 5(1), pages 1-30.
    • Handle: RePEc:oup:jfinec:v:5:y:2007:i:1:p:1-30
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbl007
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    Cited by:

    1. Fleming, Jeff & Paye, Bradley S., 2011. "High-frequency returns, jumps and the mixture of normals hypothesis," Journal of Econometrics, Elsevier, vol. 160(1), pages 119-128, January.
    2. Christensen, Kim & Oomen, Roel C.A. & Podolskij, Mark, 2014. "Fact or friction: Jumps at ultra high frequency," Journal of Financial Economics, Elsevier, vol. 114(3), pages 576-599.
    3. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, New Economic School (NES).
    4. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    5. Baum, Christopher F. & Zerilli, Paola & Chen, Liyuan, 2021. "Stochastic volatility, jumps and leverage in energy and stock markets: Evidence from high frequency data," Energy Economics, Elsevier, vol. 93(C).
    6. Hanousek Jan & Kočenda Evžen & Novotný Jan, 2012. "The identification of price jumps," Monte Carlo Methods and Applications, De Gruyter, vol. 18(1), pages 53-77, January.
    7. Dempster, M.A.H. & Medova, Elena & Tang, Ke, 2018. "Latent jump diffusion factor estimation for commodity futures," Journal of Commodity Markets, Elsevier, vol. 9(C), pages 35-54.
    8. esposito, francesco paolo & cummins, mark, 2015. "Filtering and likelihood estimation of latent factor jump-diffusions with an application to stochastic volatility models," MPRA Paper 64987, University Library of Munich, Germany.

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