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Estimating Correlated Jumps and Stochastic Volatilities

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  • Jiří Witzany

Abstract

We formulate a bivariate stochastic volatility jump-diffusion model with correlated jumps and volatilities. An MCMC Metropolis-Hastings sampling algorithm is proposed to estimate the model's parameters and latent state variables (jumps and stochastic volatilities) given observed returns. The methodology is successfully tested on several artificially generated bivariate time series and then on the two most important Czech domestic financial market time series of the FX (CZK/EUR) and stock (PX index) returns. Four bivariate models with and without jumps and/or stochastic volatility are compared using the deviance information criterion (DIC) confirming importance of incorporation of jumps and stochastic volatility into the model.

Suggested Citation

  • Jiří Witzany, 2013. "Estimating Correlated Jumps and Stochastic Volatilities," Prague Economic Papers, Prague University of Economics and Business, vol. 2013(2), pages 251-283.
    • Handle: RePEc:prg:jnlpep:v:2013:y:2013:i:2:id:451:p:251-283
    DOI: 10.18267/j.pep.451
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    1. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
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    Cited by:

    1. Karel Janda & Tran Van Quang & Pavel Zetek, 2015. "Faktory ovlivňující zapojení žen v mikrofinancích [The Factors Influencing the Participation of Women in Microfinance]," Politická ekonomie, Prague University of Economics and Business, vol. 2015(3), pages 363-381.
    2. Bohumil Stádník & Algita Miečinskienė, 2015. "Complex Model of Market Price Development and its Simulation," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 16(4), pages 786-807, August.
    3. Jan Hanousek & Evžen Kočenda & Jan Novotný, 2016. "Shluková analýza skoků na kapitálových trzích [Cluster Analysis of Jumps on Capital Markets]," Politická ekonomie, Prague University of Economics and Business, vol. 2016(2), pages 127-144.
    4. Milan Fičura & Jiří Witzany, 2018. "Use of Adapted Particle Filters in SVJD Models," European Financial and Accounting Journal, Prague University of Economics and Business, vol. 2018(3), pages 5-20.
    5. Milan Ficura & Jiri Witzany, 2016. "Estimating Stochastic Volatility and Jumps Using High-Frequency Data and Bayesian Methods," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 66(4), pages 278-301, August.

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    More about this item

    Keywords

    value at risk; jump-diffusion; stochastic volatility; MCMC; Monte Carlo;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G1 - Financial Economics - - General Financial Markets

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