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Comparing Value-at-Risk Methodologies

Comparing Value-at-Risk Methodologies. Breno Néri New York University breno.neri@nyu.edu http://homepages.nyu.edu/ ~bpn207 With Luiz Lima Financial Economics Workshop November 12 th , 2007. 1987: Black Monday - 23% drop in value 1995: Mexico 1997: Asia 1998: Russia and Latin America

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Comparing Value-at-Risk Methodologies

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  1. Comparing Value-at-Risk Methodologies Breno Néri New York University breno.neri@nyu.edu http://homepages.nyu.edu/~bpn207 With Luiz Lima Financial Economics Workshop November 12th, 2007

  2. 1987: Black Monday - 23% drop in value 1995: Mexico 1997: Asia 1998: Russia and Latin America 1998: Long-Term Capital Management Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Market Risk Exposure Oliver Linton Value-at-Risk Breno Néri

  3. Market Risk Exposure Efficiency 1996: amendment to the 1988 Basle Capital Accord 1998: adopted by U.S. bank regulatory agencies Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Measures of Market Risk Lopez (JR, 1999) Value-at-Risk Breno Néri

  4. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application VaR(p) Value-at-Risk Breno Néri

  5. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application VaR(p) Value-at-Risk Breno Néri

  6. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework Giot and Laurent (JEF, 2004) Value-at-Risk Breno Néri

  7. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework • Conditional Mean: OLS • Lags and/or other Conditioning Variables • Information Criteria: • Akaike: AIC • Schwarz (Bayesian): BIC • Shibata • Hannan-Quinn Value-at-Risk Breno Néri

  8. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework • RiskMetrics • Gaussian GARCH • Skewed-t APARCH • ARCH Quantile Value-at-Risk Breno Néri

  9. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework ARCH(p) • RiskMetrics • Gaussian GARCH • Skewed-t APARCH • ARCH Quantile Engle (EC’A, 1982) Value-at-Risk Breno Néri

  10. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework GARCH(p,q) • RiskMetrics • Gaussian GARCH • Skewed-t APARCH • ARCH Quantile Bollerslev (JE, 1986) Value-at-Risk Breno Néri

  11. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework APARCH(p,q) • RiskMetrics • Gaussian GARCH • Skewed-t APARCH • ARCH Quantile Ding, Granger and Engle (JEF, 1993) He and Teräsvirta (1999a,b) Value-at-Risk Breno Néri

  12. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework Skewed Student-t Fernández and Steel (JASA,1998) Lambert and Laurent (2001) Value-at-Risk Breno Néri

  13. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework • RiskMetrics • Gaussian GARCH • Skewed-t APARCH • ARCH Quantile J.P. Morgan (1996) Value-at-Risk Breno Néri

  14. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework • RiskMetrics • Gaussian GARCH • Skewed-t APARCH • ARCH Quantile Value-at-Risk Breno Néri

  15. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework • RiskMetrics • Gaussian GARCH • Skewed-t APARCH • ARCH Quantile Value-at-Risk Breno Néri

  16. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework • RiskMetrics • Gaussian GARCH • Skewed-t APARCH • ARCH Quantile Value-at-Risk Breno Néri

  17. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework • RiskMetrics • Gaussian GARCH • Skewed-t APARCH • ARCH Quantile Giot (JFM, 2003) Giot and Laurent (JAE, 2003) Value-at-Risk Breno Néri

  18. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application General Framework • RiskMetrics • Gaussian GARCH • Skewed-t APARCH • ARCH Quantile Value-at-Risk Breno Néri

  19. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Exponential Power Function Value-at-Risk Breno Néri

  20. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Exponential Power Function Value-at-Risk Breno Néri

  21. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Exponential Power Function Value-at-Risk Breno Néri

  22. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Skewed Exponential Power Function: Skewed Gaussian Skewed Student-t Exponential Power Function Value-at-Risk Breno Néri

  23. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Minimum/Maximum Extremum Estimators M-Estimators Huber (1964, 1965, 1982, 1981) Wooldridge / Green / Davidson and Mackinnon Value-at-Risk Breno Néri

  24. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimators Wooldridge Value-at-Risk Breno Néri

  25. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Uniform Weak Law of Large Numbers M-Estimators Wooldridge Value-at-Risk Breno Néri

  26. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Uniform Weak Law of Large Numbers M-Estimators Wooldridge Value-at-Risk Breno Néri

  27. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimators Value-at-Risk Breno Néri

  28. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimators Value-at-Risk Breno Néri

  29. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimators Value-at-Risk Breno Néri

  30. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimators Value-at-Risk Breno Néri

  31. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimators: FOC Value-at-Risk Breno Néri

  32. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimators: Examples Value-at-Risk Breno Néri

  33. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimators: Examples Value-at-Risk Breno Néri

  34. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimators: Examples Value-at-Risk Breno Néri

  35. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimator: Quantile Regression Value-at-Risk Breno Néri

  36. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimator: Quantile Regression Value-at-Risk Breno Néri

  37. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimator: Quantile Regression Value-at-Risk Breno Néri

  38. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimator: Quantile Regression Value-at-Risk Breno Néri

  39. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application M-Estimator: Quantile Regression Value-at-Risk Breno Néri

  40. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Quantile Regression: Equivariance Koenker and Portnoy (BSA, 1996) Value-at-Risk Breno Néri

  41. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Quantile Regression Koenker and Portnoy (BSA, 1996) Value-at-Risk Breno Néri

  42. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application ARCH Quantile VaR • RiskMetrics • Gaussian GARCH • Skewed-t APARCH • ARCH Quantile Wu and Xiao (JR, 2002) Value-at-Risk Breno Néri

  43. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application ARCH Quantile VaR Wu and Xiao (JR, 2002) Value-at-Risk Breno Néri

  44. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application ARCH Quantile VaR Value-at-Risk Breno Néri

  45. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application More on Quantile Regression • Original Paper: • Koenker and Basset (Econometrica, 1978) • Goodness of Fit: • Koenker and Machado (JASA, 1999) • Inference on Quantile Regression Process: • Koenker and Xiao (Econometrica, 2002) • Quantile AutoRegressive Model, QAR(p): • Koenker and Xiao (2004a) • Unit Root Test for each quantile in a QAR(p): • Koenker and Xiao (JASA, 2004b) Value-at-Risk Breno Néri

  46. Unconditional Coverage Point Estimator for p Independence Conditional Coverage Dynamic Quantile Magnitude Loss Function Other Backtests Time Until First Failure Duration Based Approach Mixed Test CD-Test Scale CD-Method Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Backtests Value-at-Risk Breno Néri

  47. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Unconditional Coverage Point Estimator for p Independence Conditional Coverage Dynamic Quantile Magnitude Loss Function Other Backtests Time Until First Failure Duration Based Approach Mixed Test CD-Test Scale CD-Method Backtests Kupiec (JD, 1995) Value-at-Risk Breno Néri

  48. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Unconditional Coverage Point Estimator for p Independence Conditional Coverage Dynamic Quantile Magnitude Loss Function Other Backtests Time Until First Failure Duration Based Approach Mixed Test CD-Test Scale CD-Method Backtests Haas (2001) Value-at-Risk Breno Néri

  49. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Unconditional Coverage Point Estimator for p Independence Conditional Coverage Dynamic Quantile Magnitude Loss Function Other Backtests Time Until First Failure Duration Based Approach Mixed Test CD-Test Scale CD-Method Backtests Christoffersen (IER, 1998) Value-at-Risk Breno Néri

  50. Value-at-Risk Quantile Regression Backtest Monte Carlo Empirical Application Unconditional Coverage Point Estimator for p Independence Conditional Coverage Dynamic Quantile Magnitude Loss Function Other Backtests Time Until First Failure Duration Based Approach Mixed Test CD-Test Scale CD-Method Backtests Christoffersen (IER, 1998) Value-at-Risk Breno Néri

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