Selection of Value-at-Risk models

Value-at-Risk (VaR) is widely used as a tool for measuring the market risk of asset portfolios. However, alternative VaR implementations are known to yield fairly different VaR forecasts. Hence, every use of VaR requires choosing among alternative forecasting models. This paper undertakes two case studies in model selection, for the S&P 500 index and India's NSE-50 index, at the 95% and 99% levels. We employ a two-stage model selection procedure. In the first stage we test a class of models for statistical accuracy. If multiple models survive rejection with the tests, we perform a second stage filtering of the surviving models using subjective loss functions. This two-stage model selection procedure does prove to be useful in choosing a VaR model, while only incompletely addressing the problem. These case studies give us some evidence about the strengths and limitations of present knowledge on estimation and testing for VaR.