The Historical Simulation Method for Value-at-Risk: A Research Based Evaluation of the Industry Favorite

Abstract

This paper surveys the literature relating to the historical simulation method of calculating VaR. The historical simulation method is the most popular method for VaR calculation in the banking industry. Thirty Eight papers are surveyed to understand the performance measures for VaR methods and the comparative performance of Historical Simulation VaR methods. The performance measures are broadly divided into unconditional coverage and conditional coverage measures. While regulatory requirements are limited to unconditional coverage measures, conditional coverage measures have been developed to spot the phenomenon of exception clustering. The performance of historical simulation - the basic and modified methods - in comparison with other methods is surveyed through available studies. The historical simulation approach is found to provide superior unconditional coverage among a wide variety of alternate methods ranging from the simple variance covariance approach to the sophisticated GARCH, explaining its popularity in the industry. This superiority translates into lesser likelihood of regulatory penalties since the regulatory back testing framework is based on unconditional coverage. The advantage of superior performance by historical simulation is lost when it is measured on conditional coverage measures (joint tests of unconditional coverage and independence). However, the sophisticated conditional volatility models like GARCH are not much better than the historical simulation in conditional coverage. A modification to the historical simulation method, the filtered historical simulation method emerges as the best performer using conditional coverage criteria. This study has an important contribution to make to available research. First it compiles the performance measures of VaR methods. Second it surveys the modifications to the historical simulation approach. Third and most important it presents a comparative picture of the most popular approach vis a vis other methods on a variety of performance parameters.