Generalized Empirical Distribution Function

Abstract

One way to produce Value at Risk (VAR) for financial institution is to apply previously observed movements of the market underlying parameters (interest rates, for example) to their current values in order to obtain starting point of the analysis. This way multiple starting points can be created. For each starting point change in the value of the portfolio can be measured using some acceptable valuation technique. If the definition of VAR is 99th percentile, then 99% in the sorted sequence of value changes is declared to represent VAR. In this article we are trying to give answer to the following questions: what is the appropriate confidence interval for the value of VAR obtained this way. The problem with the traditional treatment using empirical distribution function or non parametric approach is that all observed values did not come from the same distribution and they were not measured with the same precision. So the second question that we address is: what is the most efficient way to improve precision. The article addresses both questions and gives tools for the optimal resource allocation for the precision improvement.