Testing Expected Shortfall Models for Derivative Positions

In this paper we test several risk management models for computing expected shortfall for one-period hedge errors of hedged derivatives positions. Contrary to value-at-risk, expected shortfall cannot be tested using the standard binomial test, since we need information of the distribution in the tail. As derivatives positions change characteristics and thereby the size of risk exposures over time one cannot apply the standard tests based on stationarity. To overcome this problem, we present a transformation procedure. For comparison purposes the tests are also performed for value-at-risk.