Abstract
In this chapter, we build first a univariate and then a multivariate filtered historical simulation (FHS) model for financial risk management. Both the univariate and multivariate methods simulate future returns from a model using historical return innovations. While the former relies on portfolio returns filtered by a dynamic variance model, the latter uses individual or base asset return innovations from dynamic variance and correlation models. The univariate model is suitable for passive risk management or risk measurement whereas the multivariate model is useful for active risk management such as optimal portfolio allocation. Both models are constructed in such a way as to capture the stylized facts in daily asset returns and to be simple to estimate. The FHS approach enables the risk manager to easily compute Value-at-Risk and other risk measures including Expected Shortfall for various investment horizons that are conditional on current market conditions. The chapter also lists various alternatives to the suggested FHS approach.
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References
Andersen, T.G., Bollerslev, T., Christoffersen, P. and Diebold, F.X. (2006a): Volatility and Correlation Forecasting. In: Elliott, G., Granger, C. and Timmermann, A. (Eds.): Handbook of Economic Forecasting. North-Holland, Amsterdam.
Andersen, T.G., Bollerslev, T., Christoffersen, P. and Diebold, F.X. (2006b): Practical Volatility and Correlation Modeling for Financial Market Risk Management. In: Carey, M. and Stulz, R. (Eds.): The Risks of Financial Institutions. University of Chicago Press.
Barone-Adesi, G., Bourgoin, F. and Giannopoulos, K. (1998): Don't Look Back. Risk 11, 100–104.
Bauwens, L., Laurent, S. and Rombouts, J. (2006): Multivariate GARCH Models: a Survey. Journal of Applied Econometrics 21, 79–109.
Bodoukh, J., Richardson, M., and Whitelaw, R. (1998): The Best of Both Worlds. Risk 11, 64–67.
Bollerslev, T. (1986): Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics 31, 307–327.
Bollerslev, T. (1987): A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return. Review of Economics and Statistics 69, 542–547.
Cappiello, L., Engle, R.F. and Sheppard, K. (2004): Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns. Manuscript, Stern School of Business New York University.
Christoffersen, P. (2003): Elements of Financial Risk Management. Academic Press, San Diego.
Christoffersen, P. and Diebold, F. (2000): How Relevant is Volatility Forecasting for Financial Risk Management? Review of Economics and Statistics 82, 1–11.
Christoffersen, P. and Goncalves, S. (2005): Estimation Risk in Financial Risk Management. Journal of Risk 7, 1–28.
Christoffersen, P., Diebold, F. and Schuermann, T. (1998): Horizon Problems and Extreme Events in Financial Risk Management. Economic Policy Review Federal Reserve Bank of New York, October, 109-118.
Demarta, S., and McNeil, A. J. (2005): The t Copula and Related Copulas. International Statistical Review 73, 111–129.
Diebold, F.X., Schuermann, T. and Stroughair, J. (1998): Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management. In: Refenes, A.-P. N., Burgess, A.N. and Moody, J.D. (Eds.): Decision Technologies for Computational Finance, 3-12. Kluwer Academic Publishers, Amsterdam.
Duffie, D. and Pan, J. (1997): An Overview of Value at Risk. Journal of Derivatives 4, 7–49.
Engle, R. (1982): Autoregressive Conditional Heteroskedasticity With Estimates of the Variance of U.K. Inflation. Econometrica 50, 987–1008.
Engle, R. (2002): Dynamic Conditional Correlation - A Simple Class of Multivariate GARCH Models. Journal of Business and Economic Statistics 20, 339–350.
Engle, R. and Manganelli, S. (2004): CAViaR: Conditional Autoregressive Value at Risk by Quantile Regression. Journal of Business and Economic Statistics 22, 367–381.
Engle, R. and Ng, V. (1993): Measuring and Testing the Impact of News on Volatility. Journal of Finance 48, 1749–1778.
Engle, R. F. and Sheppard, K. (2001): Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH. NBER Working Paper 8554.
Gourieroux, C. and Jasiak, J. (2006): Dynamic Quantile Models. Manuscript, University of Toronto.
Hansen, B. (1994): Autoregressive Conditional Density Estimation. International Economic Review 35, 705–730.
Harvey, C.R. and Siddique, A. (1999): Autoregressive Conditional Skewness. Journal of Financial and Quantitative Analysis 34, 465–488.
Hull, J. and Suo, W. (2002): A methodology for assessing model risk and its application to the implied volatility function model. Journal of Financial and Quantitative Analysis 37, 297–318.
Hull, J. and White, A. (1998): Incorporating Volatility Updating into the Historical Simulation Method for VaR. Journal of Risk 1, 5–19.
Joe, H. (1997): Multivariate Models and Dependence Concepts. Chapman Hall, London.
Jondeau, E. and Rockinger, M. (2005): The Copula-GARCH Model of Conditional Dependencies: An International Stock-Market Application. Journal of International Money and Finance forthcoming.
Jorion, P. (2006): Value-at-Risk: The New Benchmark for Managing. Financial Risk. McGraw Hill, New York.
Morgan, J.P. (1996): RiskMetrics – Technical Document 4th Edition. New York.
Lando, D. (2004): Credit Risk Modeling: Theory and Applications Princeton University Press, New Jersey.
Longin, F. and Solnik, B. (2001): Extreme Correlation of International Equity Markets. Journal of Finance 56, 649–676.
Manganelli, S. (2004): Asset Allocation by Variance Sensitivity Analysis. Journal of Financial Econometrics 2, 370–389.
McNeil, A. and Frey, R. (2000): Estimation of Tail-Related Risk Measures for Heteroskedastic Financial Time Series: An Extreme Value Approach. Journal of Empirical Finance 7, 271–300.
Patton, A. (2004): On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation. Journal of Financial Econometrics 2, 130–168.
Patton, A. (2006): Modeling Asymmetric Exchange Rate Dependence. International Economic Review 47, 527–556.
Patton, A.J. and Sheppard, K. (2008): Evaluating volatility and Correlation forecasts. In: Andersen, T.G., Davis, R.A., Kreiss, J.-P. and Mikosch, T. (Eds.): Handbook of Financial Time Series, 801–838. Springer Verlag, New York.
Persaud, A. (2003): Liquidity Black Holes: Understanding, Quantifying and Managing Financial Liquidity Risk. Risk Books, London.
Pesaran, H. and Zaffaroni, P. (2004): Model Averaging and Value-at-Risk based Evaluation of Large Multi Asset Volatility Models for Risk Management. Manuscript, University of Cambridge.
Poon, S.-H., Rockinger, M. and Tawn, J. (2004): Extreme Value Dependence in Financial Markets: Diagnostics, Models and Financial Implications. Review of Financial Studies 17, 581–610.
Pritsker, M. (2001): The Hidden Dangers of Historical Simulation. Finance and Economics Discussion Series 2001–27. Washington: Board of Governors of the Federal Reserve System.
Tse, Y.K. and Tsui, K.C. (2002): A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-varying Correlations. Journal of Business and Economic Statistics 20, 351–362.
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Christoffersen, P. (2009). Value–at–Risk Models. In: Mikosch, T., Kreiß, JP., Davis, R., Andersen, T. (eds) Handbook of Financial Time Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71297-8_33
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DOI: https://doi.org/10.1007/978-3-540-71297-8_33
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