Semi-parametric Method for Estimating Tail Related Risk Measures in the Stock Market
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The generalized Pareto distribution (GPD) approach for estimating the Value-at-Risk (VaR) and the expected shortfall (ES) is compared to other methods for evaluating extreme risk with normally distributed returns. When the market index returns have a fat-tailed distribution, the risk measures computed from the normal distribution underestimate the tail-related risk. We also compare the computation results of the VaR based on the GPD approximations to those based on the RiskMetrics methodology and GARCH model estimation. The estimates of the VaR are robust to a variety of threshold values. Contrary to this, the VaR values based on the RiskMetrics methodology and the GARCH model are extremely volatile. From a risk manager’s perspective, it would be difficult to adjust capital requirement of a financial institution to conditional market risk. Due to concerns raised for practical and statistical reasons, we can conclude that the GPD method for measuring unconditional market risk is more appropriate for measuring and managing the tail-related risk.
Abstract
The generalized Pareto distribution (GPD) approach for estimating the Value-at-Risk (VaR) and the expected shortfall (ES) is compared to other methods for evaluating extreme risk with normally distributed returns. When the market index returns have a fat-tailed distribution, the risk measures computed from the normal distribution underestimate the tail-related risk. We also compare the computation results of the VaR based on the GPD approximations to those based on the RiskMetrics methodology and GARCH model estimation. The estimates of the VaR are robust to a variety of threshold values. Contrary to this, the VaR values based on the RiskMetrics methodology and the GARCH model are extremely volatile. From a risk manager’s perspective, it would be difficult to adjust capital requirement of a financial institution to conditional market risk. Due to concerns raised for practical and statistical reasons, we can conclude that the GPD method for measuring unconditional market risk is more appropriate for measuring and managing the tail-related risk.
참고문헌 (34)
- Akgiray, V., "Distribution Properties of Latin American Black Market Exchange Rates", Journal of International Money and Finance, 71(1), pp.37~48 (1988)
- Ang, A., "Asymmetric Correlations of Equity Portfolios", Journal of Financial Economics, 63(3), pp.443~494 (2002)
- Booth, G. G., "Prudent Margin Levels in the Finnish Stock Index Futures Market", Management Science, 43(8), pp.1177~1188 (1997)
- Carmona, R., "Statistical Analysis of Financial Data in S-PLUS" (2004), Springer-Verlag
- Heavy Tails and Copulas with Evanesce, "Carmona, R.", Princeton University, ~ (2001)
- Coles, S., "An Introduction to Statistical Modeling of Extreme Values" (2001), Spring-Verlag
- Dacorogna, M. M., "Extremal Forex Returns in Extremely Large Data Sets", Extremes, 4(2), pp.105~127 (2001)
- Danielsson, J., "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation", Journal of Multivariate Analysis, 76, pp.226~248 (2001)
- Value-at-Risk and Extreme Returns, "Danielsson, J.", Financial Markets Group, London School of Economics, ~, pp.FMGDiscussion Paper No. 273 (1997)
- Beyond the Sample : Extreme Quantile and Probability Estimation with Applications to Financial Data, "Danielsson, J.", Tinbergen Institute, ~, pp.Discussion paper, TI98- 016 (1998), 2
- Danielsson, J., "Fat Tails, VaR and Subadditivity", Journal of Econometrics, 172(2), pp.283~291 (2013)
- Diebold, F. X., "Pitfalls and Opportunities in the use of Extreme Value Theory in Risk Management", Advances in Computational Management Science, 2(1), pp.3~12 (1997)
- Embrechts, P., "Modelling Extremal Events" (1997), Springer-Verlag
- Embrechts, P., "Risk Management: Value at Risk and Beyond" (2000), Cambridge University Press
- Fisher, R., "Limiting forms of the Frequency Distribution of the Largest or Smallest Member of a Sample", Proceedings of the Cambridge Philosophical Society, 24(2), pp.180~190 (1928)
- Goldie, C., "Slow Variation with Reminder : Theory and Applications", Quarterly Journal of Mathematics, Oxford 2nd Series, 38, pp.45~71 (1987)
- Hall, P., "Using the Bootstrap to Estimate Mean Square Error and Select Smoothing Parameter in Nonparametric Problem", Journal of Multivariate Analysis, 32, pp.177~203 (1990)
- Hols, M., "The Limiting Distribution of Extremal Exchange Rate Returns", Journal of Applied Econometrics, 6(3), pp.287~302 (1991)
- Hsu, C-P., "Effectiveness of Copula-extreme Value Theory in Estimating Value-at-risk : Empirical Evidence from Asian Emerging Markets", Review of Quantitative Finance and Accounting, 39(4), pp.447~468 (2012)
- Jansen, D., "On the Frequency of Large Stock Returns : Putting Booms and Busts into Perspective", Review of Economics and Statistics, 73(1), pp.18~24 (1991)
- Kearns, P., "Estimating the Density Tail Index for Financial Time Series", Review of Economics and Statistics, 79(2), pp.171~175 (1997)
- Koedijk, K. G., "The Tail Index of Exchange Rate Returns", Journal of International Economics, 29(1), pp.93~108 (1990)
- Loretan, M., "Testing the Covariance Stationarity of Heavytailed Time Series", Journal Empirical Finance, 1(2), pp.211~248 (1994)
- Longin, F. M., "The Asymptotic Distribution of Extreme Stock Market Returns", Journal of Business, 63(3), pp.383~408 (1996)
- Longin, F. M., "From Value-at-Risk to Stress Testing : The Extreme Value Approach", Journal of Banking and Finance, 24, pp.1097~1130 (2000)
- Longin, F. M., "Extreme Correlation of International Equity Markets", Journal of Finance, 56(2), pp.649~676 (2001)
- "Calculating Quantile Risk Measures for Financial Return Series using Extreme Value Theory" (1998)[URL]
- McNeil, A. J., "Internal Modelling and CAD II", pp.93~113 (1999), RISK Books
- McNeil, A. J., "Estimation of Tail-related Risk Measures for Heteroskedastic Financial Time Series : An Extreme Value Approach", Journal of Empirical Finance, 7, pp.271~300 (2000)
- The Peaks over Thresholds Method for Estimating High Quantiles of Loss Distributions, "McNeil A. J.", Department of Mathematics, ETH Zentrum, ~ (1997)
- McNeil A. J., "Extremes and Integrated Risk Management" (2000), RISK Books
- 오세경, "극단치이론(Extreme Value Theory)과 Value-at-Risk: GPD모형을 중심으로", 금융연구, 19(1), pp.69~112 (2005), 한국금융연구원
- Tastan, H., "Estimating Time-varying Conditional Correlations between Stock and Foreign Exchange Markets", Physica A : Statistical Mechanics and its Applications, 360(2), pp.445~458 (2006)
- Zivot, E., "Modeling Financial Time Series with S-PLUS" (2006), Springer