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Tempered stable and tempered infinitely divisible GARCH models

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Listed:
  • Shin Kim, Young
  • Rachev, Svetlozar T.
  • Leonardo Bianchi, Michele
  • Fabozzi, Frank J.

Abstract

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation. This model, which we refer to as the rapidly decreasing tempered stable (RDTS) GARCH model, takes into account empirical facts that have been observed for stock and index returns, such as volatility clustering, non-zero skewness, and excess kurtosis for the residual distribution. We review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, we can find the risk-neutral price process, thereby allowing application to option-pricing. We propose algorithms to generate scenarios based on GARCH models with CTS and RDTS innovations. To investigate the performance of these GARCH models, we report parameter estimates for the Dow Jones Industrial Average index and stocks included in this index. To demonstrate the advantages of the proposed model, we calculate option prices based on the index.

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  • Shin Kim, Young & Rachev, Svetlozar T. & Leonardo Bianchi, Michele & Fabozzi, Frank J., 2010. "Tempered stable and tempered infinitely divisible GARCH models," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2096-2109, September.
  • Handle: RePEc:eee:jbfina:v:34:y:2010:i:9:p:2096-2109
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    Cited by:

    1. Berninghaus, Siegfried K. & Todorova, Lora & Vogt, Bodo, 2011. "A simple questionnaire can change everything: Are strategy choices in coordination games stable?," Working Paper Series in Economics 37, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    2. Shin Kim, Young & Rachev, Svetlozar T. & Leonardo Bianchi, Michele & Fabozzi, Frank J., 2010. "Tempered stable and tempered infinitely divisible GARCH models," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2096-2109, September.
    3. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, pages 292-306.
    4. Stoyanov, Stoyan V. & Rachev, Svetlozar T. & Fabozzi, Frank J., 2013. "CVaR sensitivity with respect to tail thickness," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 977-988.
    5. Fabozzi Frank J. & Stoyanov Stoyan V. & Rachev Svetlozar T., 2013. "Computational aspects of portfolio risk estimation in volatile markets: a survey," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(1), pages 103-120, February.
    6. Young Kim & Frank Fabozzi & Zuodong Lin & Svetlozar Rachev, 2012. "Option pricing and hedging under a stochastic volatility Lévy process model," Review of Derivatives Research, Springer, vol. 15(1), pages 81-97, April.
    7. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Mitov, Ivan & Fabozzi, Frank J., 2011. "Time series analysis for financial market meltdowns," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1879-1891, August.
    8. Gong, Xiaoli & Zhuang, Xintian, 2017. "American option valuation under time changed tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 57-68.
    9. Meyborg, Mirja, 2011. "The impact of West-German universities on regional innovation activities: A social network analysis," Working Paper Series in Economics 35, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    10. Schosser, Stephan & Vogt, Bodo, 2011. "The public loss game: An experimental study of public bads," Working Paper Series in Economics 33, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    11. Choi, Jaehyung & Kim, Young Shin & Mitov, Ivan, 2015. "Reward-risk momentum strategies using classical tempered stable distribution," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 194-213.
    12. Jaehyung Choi, 2014. "Maximum drawdown, recovery and momentum," Papers 1403.8125, arXiv.org, revised Mar 2015.
    13. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    14. Kassberger, Stefan & Liebmann, Thomas, 2012. "When are path-dependent payoffs suboptimal?," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1304-1310.
    15. Michele Leonardo Bianchi & Frank J. Fabozzi & Svetlozar T. Rachev, 2014. "Calibrating the Italian smile with time-varying volatility and heavy-tailed models," Temi di discussione (Economic working papers) 944, Bank of Italy, Economic Research and International Relations Area.
    16. Schaffer, Axel, 2011. "Appropriate policy measures to attract private capital in consideration of regional efficiency in using infrastructure and human capital," Working Paper Series in Economics 31, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    17. Jaehyung Choi & Young Shin Kim & Ivan Mitov, 2014. "Reward-risk momentum strategies using classical tempered stable distribution," Papers 1403.6093, arXiv.org, revised Jun 2015.
    18. Michele Bianchi & Frank Fabozzi, 2014. "Discussion of ‘on simulation and properties of the stable law’ by Devroye and James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 353-357, August.
    19. Fabio Bellini & Lorenzo Mercuri, 2014. "Option pricing in a conditional Bilateral Gamma model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 373-390, June.
    20. Stoyanov, Stoyan V. & Rachev, Svetlozar T. & Racheva-Iotova, Boryana & Fabozzi, Frank J., 2011. "Fat-tailed models for risk estimation," Working Paper Series in Economics 30, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.

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