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Testing and Comparing Value-at-Risk Measures

Author

Listed:
  • Peter Christoffersen
  • Jinyong Hahn
  • Atsushi Inoue

Abstract

Value-at-Risk (VaR) has emerged as the standard tool for measuring and reporting financial market risk. Currently, more than eighty commercial vendors offer enterprise or trading risk management systems which report VaR-like measures. Risk managers are therefore often left with the daunting task of having to choose from this plethora of risk models. Accordingly, this paper develops a framework for asking, first, how a risk manager can test that the VaR measure at hand is properly specified. And second, given two different VaR measures, how can the risk manager compare the two and pick the best in a statistically meaningful way? In the application, competing VaR measures are calculated from either historical or option-price based volatility measures, and the VaRs are tested and compared. La valeur exposée au risque (value at risk - VaR) est devenue un outil standard de mesure et de communication des risques associés aux marchés financiers. Plus de quatre-vingts fournisseurs commerciaux proposent actuellement des systèmes de gestion d'entreprise ou de gestion des risques commerciaux fournissant des mesures de type VaR. C'est donc souvent aux gestionnaires des risques qu'incombe la tâche difficile d'opérer un choix parmi cette pléthore de modèles de risques. Cet article propose un cadre utile pour déterminer par quel moyen le gestionnaire des risques peut s'assurer que la mesure de VaR dont il dispose est bien définie, et, dans un deuxième temps, comparer deux mesures de VaR différentes et choisir la meilleure en s'appuyant sur des données statistiques utiles. Dans l'application, différentes mesures de VaR sont calculées à partir soit de mesures de volatilité historiques ou de mesures de volatilité implicites dans le prix des options; les VaR sont également vérifiées et comparées.

Suggested Citation

  • Peter Christoffersen & Jinyong Hahn & Atsushi Inoue, 2001. "Testing and Comparing Value-at-Risk Measures," CIRANO Working Papers 2001s-03, CIRANO.
    • Handle: RePEc:cir:cirwor:2001s-03
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    References listed on IDEAS

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    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Economic Policy Review, Federal Reserve Bank of New York, vol. 2(Apr), pages 39-69.
    4. Wagster, John D, 1996. "Impact of the 1988 Basle Accord on International Banks," Journal of Finance, American Finance Association, vol. 51(4), pages 1321-1346, September.
    5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," Center for Financial Institutions Working Papers 99-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
    6. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    7. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    8. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    11. Dimson, Elroy & Marsh, Paul, 1995. "Capital Requirements for Securities Firms," Journal of Finance, American Finance Association, vol. 50(3), pages 821-851, July.
    12. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    13. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    14. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    15. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    16. Jorion, Philippe, 1995. "Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-528, June.
    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. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    19. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    More about this item

    Keywords

    Risk management; volatility; nonnested testing; options; model risk; Gestion des risques; volatilité; tests non emboîtés; options; risque modèle;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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