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Benchmarking of Unconditional VaR and ES Calculation Methods: A Comparative Simulation Analysis with Truncated Stable Distribution

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  • Takashi Isogai

    (Bank of Japan)

Abstract

This paper analyzes Value at Risk (VaR) and Expected Shortfall (ES) calculation methods in terms of bias and dispersion against benchmarks computed from a fat-tailed parametric distribution. The daily log returns of the Nikkei-225 stock index are modeled by a truncated stable distribution. The VaR and ES values of the fitted distribution are regarded as benchmarks. The fitted distribution is also used as a sampling distribution; sample returns with different sizes are generated for the simulations of the VaR and ES calculations. Two parametric methods: normal distribution and generalized Pareto distribution and two non-parametric methods: historical simulation and kernel smoothing are selected as the targets of this analysis. A comparison of the simulated VaR, ES, and the ES/VaR ratio with the benchmarks at multiple confidence levels reveals that the normal distribution approximation has a significant downward bias, especially in the ES calculation. The estimates by the other three methods are much closer to the benchmarks on average, although some of them become unstable with smaller sample sizes and/or at higher confidence levels. Specifically, ES tends to be more biased and unstable than VaR at higher confidence levels.

Suggested Citation

  • Takashi Isogai, 2014. "Benchmarking of Unconditional VaR and ES Calculation Methods: A Comparative Simulation Analysis with Truncated Stable Distribution," Bank of Japan Working Paper Series 14-E-1, Bank of Japan.
    • Handle: RePEc:boj:bojwps:wp14e01
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    References listed on IDEAS

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    1. Borak, Szymon & Misiorek, Adam & Weron, Rafal, 2010. "Models for Heavy-tailed Asset Returns," MPRA Paper 25494, University Library of Munich, Germany.
    2. Juan-Juan Cai & John H. J. Einmahl & Laurens Haan & Chen Zhou, 2015. "Estimation of the marginal expected shortfall: the mean when a related variable is extreme," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 417-442, March.
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    4. Adam Misiorek & Rafal Weron, 2010. "Heavy-tailed distributions in VaR calculations," HSC Research Reports HSC/10/05, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    5. 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.
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    7. Alexander, Carol & Sheedy, Elizabeth, 2008. "Developing a stress testing framework based on market risk models," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2220-2236, October.
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    9. Giovanni Barone‐Adesi & Kostas Giannopoulos & Les Vosper, 2002. "Backtesting Derivative Portfolios with Filtered Historical Simulation (FHS)," European Financial Management, European Financial Management Association, vol. 8(1), pages 31-58, March.
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    Cited by:

    1. Toshinao Yoshiba, 2015. "Risk Aggregation with Copula for Banking Industry," IMES Discussion Paper Series 15-E-01, Institute for Monetary and Economic Studies, Bank of Japan.
    2. Michele Leonardo Bianchi, 2014. "Are the log-returns of Italian open-end mutual funds normally distributed? A risk assessment perspective," Temi di discussione (Economic working papers) 957, Bank of Italy, Economic Research and International Relations Area.

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    More about this item

    Keywords

    Value at Risk; Expected Shortfall; Fat-Tailed Distribution; Truncated Stable Distribution; Numerical Simulation;
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