Evaluating the Forecasts of Risk Models

The forecast evaluation literature has traditionally focused on methods for assessing point-forecasts. However, in the context of risk models, interest centers on more than just a single point of the forecast distribution. For example, value-at-risk (VaR) models which are currently in extremely wide use form interval forecasts. Many other important financial calculations also involve estimates not summarized by a point-forecast. Although some techniques are currently available for assessing interval and density forecasts, none are suitable for sample sizes typically available. This paper suggests an new approach to evaluating such forecasts. It requires evaluation of the entire forecast distribution, rather than a value-at-risk quantity. The information content of forecast distributions combined with ex post loss realizations is enough to construct a powerful test even with sample sizes as small as 100.

[1]  Jose A. Lopez.  Regulatory Evaluation of Value-at-Risk Models , 1996 .

[2]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[3]  Philippe Jorion.  Value at risk: the new benchmark for controlling market risk , 1996 .

[4]  S. Durlauf.  Spectral Based Testing of the Martingale Hypothesis , 1991 .

[5]  S. Heston.  A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[6]  David S. Bates.  Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options , 1998 .

[7]  P. Kupiec.  The performance of S&P 500 futures product margins under the SPAN margining system , 1994 .

[8]  Testing backtesting : an evaluation of the Basle guidelines for backtesting internal risk management models of banks , 1998 .

[9]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[10]  Paul H. Kupiec,et al.  Techniques for Verifying the Accuracy of Risk Measurement Models , 1995 .

[11]  Richard Courant.  Differential and Integral Calculus (Volume II) , 1936 .

[12]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1974 .

[13]  A R Forrest,et al.  Quality control. , 1978, British medical journal.

[14]  Milton C. Chew.  Distributions in Statistics: Continuous Univariate Distributions-1 and 2 , 1971 .

[15]  Chris Chatfield,et al.  Calculating Interval Forecasts , 1993 .

[16]  Jeremy Berkowitz,et al.  Generalized Spectral Estimation , 1996 .

[17]  F. Diebold,et al.  Forecast Evaluation and Combination , 1996 .

[18]  M. Pritsker.  Evaluating Value at Risk Methodologies: Accuracy versus Computational Time , 1996 .

[19]  David S. Bates.  Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Thephlx Deutschemark Options , 1993 .

[20]  Anthony S. Tay,et al.  Evaluating Density Forecasts , 1997 .