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Sequential Bayesian Analysis of Time-Changed Infinite Activity Derivatives Pricing Models

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  • Junye Li

Abstract

This article investigates time-changed infinite activity derivatives pricing models from the sequential Bayesian perspective. It proposes a sequential Monte Carlo method with the proposal density generated by the unscented Kalman filter. This approach overcomes to a large extent the particle impoverishment problem inherent to the conventional particle filter. Simulation study and real applications indicate that (1) using the underlying alone cannot capture the dynamics of states, and by including options, the precision of state filtering is dramatically improved; (2) the proposed method performs better and is more robust than the conventional one; and (3) joint identification of the diffusion, stochastic volatility, and jumps can be achieved using both the underlying data and the options data.

Suggested Citation

  • Junye Li, 2011. "Sequential Bayesian Analysis of Time-Changed Infinite Activity Derivatives Pricing Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 468-480, October.
    • Handle: RePEc:taf:jnlbes:v:29:y:2011:i:4:p:468-480
    DOI: 10.1198/jbes.2010.08310
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    Cited by:

    1. Michele Leonardo Bianchi & Svetlozar T. Rachev & Frank J. Fabozzi, 2018. "Calibrating the Italian Smile with Time-Varying Volatility and Heavy-Tailed Models," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 339-378, March.
    2. Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2014. "Nonlinear Kalman Filtering in Affine Term Structure Models," Management Science, INFORMS, vol. 60(9), pages 2248-2268, September.
    3. Hanxue Yang & Juho Kanniainen, 2017. "Jump and Volatility Dynamics for the S&P 500: Evidence for Infinite-Activity Jumps with Non-Affine Volatility Dynamics from Stock and Option Markets," Review of Finance, European Finance Association, vol. 21(2), pages 811-844.
    4. Jiling Cao & Xinfeng Ruan & Shu Su & Wenjun Zhang, 2021. "Specification analysis of VXX option pricing models under Lévy processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(9), pages 1456-1477, September.
    5. Fulop, Andras & Heng, Jeremy & Li, Junye & Liu, Hening, 2022. "Bayesian estimation of long-run risk models using sequential Monte Carlo," Journal of Econometrics, Elsevier, vol. 228(1), pages 62-84.
    6. Michele Bianchi & Frank Fabozzi, 2015. "Investigating the Performance of Non-Gaussian Stochastic Intensity Models in the Calibration of Credit Default Swap Spreads," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 243-273, August.

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