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The Uncertain Shape of Grey Swans: Extreme Value Theory with Uncertain Threshold

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  • Hamidreza Arian
  • Hossein Poorvasei
  • Azin Sharifi
  • Shiva Zamani

Abstract

Extreme Value Theory (EVT) is one of the most commonly used approaches in finance for measuring the downside risk of investment portfolios, especially during financial crises. In this paper, we propose a novel approach based on EVT called Uncertain EVT to improve its forecast accuracy and capture the statistical characteristics of risk beyond the EVT threshold. In our framework, the extreme risk threshold, which is commonly assumed a constant, is a dynamic random variable. More precisely, we model and calibrate the EVT threshold by a state-dependent hidden variable, called Break-Even Risk Threshold (BRT), as a function of both risk and ambiguity. We will show that when EVT approach is combined with the unobservable BRT process, the Uncertain EVT's predicted VaR can foresee the risk of large financial losses, outperforms the original EVT approach out-of-sample, and is competitive to well-known VaR models when back-tested for validity and predictability.

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  • Hamidreza Arian & Hossein Poorvasei & Azin Sharifi & Shiva Zamani, 2020. "The Uncertain Shape of Grey Swans: Extreme Value Theory with Uncertain Threshold," Papers 2011.06693, arXiv.org.
    • Handle: RePEc:arx:papers:2011.06693
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    1. Christoffersen, Peter & Hahn, Jinyong & Inoue, Atsushi, 2001. "Testing and comparing Value-at-Risk measures," Journal of Empirical Finance, Elsevier, vol. 8(3), pages 325-342, July.
    2. Herrera, Rodrigo & Schipp, Bernhard, 2013. "Value at risk forecasts by extreme value models in a conditional duration framework," Journal of Empirical Finance, Elsevier, vol. 23(C), pages 33-47.
    3. Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
    4. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    5. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 315-346, December.
    6. Ulrich, Maxim, 2013. "Inflation ambiguity and the term structure of U.S. Government bonds," Journal of Monetary Economics, Elsevier, vol. 60(2), pages 295-309.
    7. Brooks, C. & Clare, A.D. & Dalle Molle, J.W. & Persand, G., 2005. "A comparison of extreme value theory approaches for determining value at risk," Journal of Empirical Finance, Elsevier, vol. 12(2), pages 339-352, March.
    8. Jalal, Amine & Rockinger, Michael, 2008. "Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 868-877, December.
    9. Takashi Ui, 2010. "The Ambiguity Premium vs. the Risk Premium under Limited Market Participation," Review of Finance, European Finance Association, vol. 15(2), pages 245-275.
    10. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    11. Dolores Furió & Francisco J. Climent, 2013. "Extreme value theory versus traditional GARCH approaches applied to financial data: a comparative evaluation," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 45-63, January.
    12. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    13. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    14. Bi, Jia & Zhu, Yifeng, 2020. "Value at risk, cross-sectional returns and the role of investor sentiment," Journal of Empirical Finance, Elsevier, vol. 56(C), pages 1-18.
    15. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 84-108.
    16. Brenner, Menachem & Izhakian, Yehuda, 2018. "Asset pricing and ambiguity: Empirical evidence⁎," Journal of Financial Economics, Elsevier, vol. 130(3), pages 503-531.
    17. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    18. 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 Management.
    19. Rossignolo, Adrian F. & Fethi, Meryem Duygun & Shaban, Mohamed, 2012. "Value-at-Risk models and Basel capital charges," Journal of Financial Stability, Elsevier, vol. 8(4), pages 303-319.
    20. Bee, Marco & Dupuis, Debbie J. & Trapin, Luca, 2016. "Realizing the extremes: Estimation of tail-risk measures from a high-frequency perspective," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 86-99.
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