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Bayesian analysis of stochastic volatility models with Lévy jumps: application to risk analysis

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Abstract

In this paper I analyze a broad class of continuous-time jump diffusion models of asset returns. In the models, stochastic volatility can arise either from a diffusion part, or a jump part, or both. The jump component includes either compound Poisson or Lvy alpha-stable jumps. To be able to estimate the models with latent Lvy alpha-stable jumps, I construct a new Markov chain Monte Carlo algorithm. I estimate all model specifications with S&P500 daily returns. I find that models with Levy alpha-stable jumps perform well in capturing return characteristics if diffusion is a source of stochastic volatility. Models with stochastic volatility from jumps and models with Poisson jumps cannot represent excess kurtosis and tails of return distribution. In density forecast and VaR analysis, the model with Levy alpha-stable jumps and joint stochastic volatility performs the best among all other specifications, since both diffusion and infinite activity jump part provide information about latent volatility.

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  • Pawel J. Szerszen, 2009. "Bayesian analysis of stochastic volatility models with Lévy jumps: application to risk analysis," Finance and Economics Discussion Series 2009-40, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2009-40
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    Cited by:

    1. Qi Wang & Jos'e E. Figueroa-L'opez & Todd Kuffner, 2019. "Bayesian Inference on Volatility in the Presence of Infinite Jump Activity and Microstructure Noise," Papers 1909.04853, arXiv.org.
    2. Kostrzewski, Maciej & Kostrzewska, Jadwiga, 2019. "Probabilistic electricity price forecasting with Bayesian stochastic volatility models," Energy Economics, Elsevier, vol. 80(C), pages 610-620.
    3. Kaeck, Andreas & Rodrigues, Paulo & Seeger, Norman J., 2018. "Model Complexity and Out-of-Sample Performance: Evidence from S&P 500 Index Returns," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 1-29.

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