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CVaR sensitivity with respect to tail thickness

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  • Stoyanov, Stoyan V.
  • Rachev, Svetlozar T.
  • Fabozzi, Frank J.

Abstract

We consider the sensitivity of conditional value-at-risk (CVaR) with respect to the tail index assuming regularly varying tails and exponential and faster-than-exponential tail decay for the return distribution. We compare it to the CVaR sensitivity with respect to the scale parameter for stable Paretian, the Student's t, and generalized Gaussian laws and discuss implications for the modeling of daily returns and marginal rebalancing decisions. Finally, we explore empirically the impact on the asymptotic variability of the CVaR estimator with daily returns which is a standard choice for the return frequency for risk estimation.

Suggested Citation

  • Stoyanov, Stoyan V. & Rachev, Svetlozar T. & Fabozzi, Frank J., 2011. "CVaR sensitivity with respect to tail thickness," Working Paper Series in Economics 29, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  • Handle: RePEc:zbw:kitwps:29
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    References listed on IDEAS

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    1. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 53-89.
    2. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2002. "Stationarity of stable power-GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 97-107, January.
    3. 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.
    4. Markus Haas & Stefan Mittnik & Marc Paolella, 2006. "Modelling and predicting market risk with Laplace-Gaussian mixture distributions," Applied Financial Economics, Taylor & Francis Journals, vol. 16(15), pages 1145-1162.
    5. L. Jeff Hong & Guangwu Liu, 2009. "Simulating Sensitivities of Conditional Value at Risk," Management Science, INFORMS, vol. 55(2), pages 281-293, February.
    6. Michael Grabchak & Gennady Samorodnitsky, 2010. "Do financial returns have finite or infinite variance? A paradox and an explanation," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 883-893.
    7. Mittnik, Stefan & Paolella, Marc S., 2003. "Prediction of Financial Downside-Risk with Heavy-Tailed Conditional Distributions," CFS Working Paper Series 2003/04, Center for Financial Studies (CFS).
    8. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Fabozzi, Frank J., 2008. "Financial market models with Lévy processes and time-varying volatility," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1363-1378, July.
    9. Chen, Carl R. & Su, Yuli & Huang, Ying, 2008. "Hourly index return autocorrelation and conditional volatility in an EAR-GJR-GARCH model with generalized error distribution," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 789-798, September.
    10. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Li, Leon, 2017. "Testing and comparing the performance of dynamic variance and correlation models in value-at-risk estimation," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 116-135.
    2. repec:eee:apmaco:v:282:y:2016:i:c:p:187-203 is not listed on IDEAS
    3. 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.
    4. Mikhail Semenov & Daulet Smagulov, 2017. "Portfolio Risk Assessment using Copula Models," Papers 1707.03516, arXiv.org.
    5. Gong, Xiaoli & Zhuang, Xintian, 2017. "Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 148-159.
    6. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    7. 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.

    More about this item

    Keywords

    fat-tailed distributions; regularly varying tails; conditional value-at-risk; marginal rebalancing; asymptotic variability;

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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