Evaluating Value-at-Risk Methodologies: Accuracy versus Computational Time

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Abstract
Recent research has shown that different methods of computing Value at Risk (VAR) generate widely varying results, suggesting the choice of VAR method is very important. This paper examines six VAR methods, and compares their computational time requirements and their accuracy when the sole source of inaccuracy is errors in approximating nonlinearity. Simulations using portfolios of foreign exchange options showed fairly wide variation in accuracy and unsurprisingly wide variation in computational time. When the computational time and accuracy of the methods were examined together, four methods were superior to the others. The paper also presents a new method for using order statistics to create confidence intervals for the errors and errors as a percent of true value at risk for each VAR method. This makes it possible to easily interpret the implications of VAR errors for the size of shortfalls or surpluses in a firm's risk based capital. This paper was presented at the Financial Institutions Center's October 1996 conference on "
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