A study on the accuracy of reduced-form VaR methods.

摘要

Value at Risk (VaR) has become the standard tool used across the financial industry both to estimate market risk and to issue regulation. Most commonly, VaR is defined as the maximum dollar value that a portfolio might lose over a certain time horizon, at a given probability level. Although VaR is most appealing for its conceptual simplicity as an aggregate measure of risk, its estimation poses very challenging statistical problems. So far, the focus in the VaR literature has been on model development rather than model comparison. The few studies comparing VaR modeling approaches are limited in three respects: the scope of models included, the quality of data employed (mainly simulated portfolios and data obtained using Monte Carlo techniques), and the nature of the model effectiveness measures (mainly the coverage rate and various bias measures). This dissertation attempts to correct these shortcomings by including the most commonly used modeling approaches and their implementation methods for each of the three categories of approaches: parametric, nonparametric and semiparametric. VaR is estimated daily at the 5 percent and the 1 percent level for 15 real-life data series of returns over 5 relevant asset classes, such as equities, fixed-income, commodities, foreign exchange and hedge funds. Statistical tests are employed in order to assess coverage accuracy, independence of VaR hits, and overall model goodness. Finally, methods are ranked using several criteria: number of assets for which the overall goodness test is passed in the whole sample, the variation of coverage rates observed across subsample years, measured both in absolute terms (standard deviation and range) and relative to the true coverage rate, as well as the tendency to systematically misestimate VaR. The study identifies a couple of methods that are able to deliver superior results, consistent both across time and asset classes.