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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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    References listed on IDEAS

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    1. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    2. 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.
    3. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 361-384.
    7. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    8. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    9. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    10. Jacquier, Eric & Johannes, Michael & Polson, Nicholas, 2007. "MCMC maximum likelihood for latent state models," Journal of Econometrics, Elsevier, vol. 137(2), pages 615-640, April.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.

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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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