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An unscented Kalman smoother for volatility extraction: Evidence from stock prices and options

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  • Li, Junye

Abstract

A smoothing algorithm based on the unscented transformation is proposed for the nonlinear Gaussian system. The algorithm first implements a forward unscented Kalman filter and then evokes a separate backward smoothing pass by only making Gaussian approximations in the state but not in the observation space. The method is applied to volatility extraction in a diffusion option pricing model. Both simulation study and empirical applications with the Heston stochastic volatility model indicate that in order to accurately capture the volatility dynamics, both stock prices and options are necessary.

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  • Li, Junye, 2013. "An unscented Kalman smoother for volatility extraction: Evidence from stock prices and options," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 15-26.
    • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:15-26
    DOI: 10.1016/j.csda.2011.06.001
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    References listed on IDEAS

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    Cited by:

    1. Chen, Si & Zhou, Zhen & Li, Shenghong, 2016. "An efficient estimate and forecast of the implied volatility surface: A nonlinear Kalman filter approach," Economic Modelling, Elsevier, vol. 58(C), pages 655-664.
    2. Skaug, Hans J. & Yu, Jun, 2014. "A flexible and automated likelihood based framework for inference in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 642-654.
    3. Son Le, 2018. "Algorithmic Trading with Fitted Q Iteration and Heston Model," Papers 1805.07478, arXiv.org.
    4. Rocco S., Claudio M. & Emmanuel Ramirez-Marquez, José, 2015. "Assessment of the transition-rates importance of Markovian systems at steady state using the unscented transformation," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 212-220.
    5. 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.
    6. Eddelbuettel, Dirk & Sanderson, Conrad, 2014. "RcppArmadillo: Accelerating R with high-performance C++ linear algebra," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1054-1063.
    7. Boudreault, Mathieu & Gauthier, Geneviève & Thomassin, Tommy, 2015. "Estimation of correlations in portfolio credit risk models based on noisy security prices," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 334-349.
    8. Rocco Sanseverino, Claudio M. & Ramirez-Marquez, José Emmanuel, 2014. "Uncertainty propagation and sensitivity analysis in system reliability assessment via unscented transformation," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 176-185.

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