Validating market risk models using realized PIT values

Abstract

The aim of this thesis is to propose new tests for validating market risk models for financial losses using realized probability-integral transform (PIT) values. We introduce a flexible framework for testing Value-at-Risk (VaR) exceptions at multiple levels based on a weighted transformation of the realized PIT values, where the weight function reflects the risk objectives of the modeller. This framework can be extended to perform tests using multiple different weight functions. We show that this extended framework either nests or is closely related to many of the traditional VaR and realized PIT tests in existing literature. This approach to model validation is preferable to likelihood-ratio based testing, which can be shown to be a test that is based on a set of specific weight functions that may not reflect the modeller’s risk objectives. A further advantage of this framework is that it can be easily be extended to explicitly tests for serial independence of the realized PIT values. We do this using the idea of blocking, as well as exploiting the martingale difference (MD) property. In the empirical studies, we have also found that tests based on VaR exceptions have great difficulty in detecting poorly calibrated historical simulation (HS) models. We will see how tests based on elicitability theory and proper scoring rule complement the tests based on VaR exceptions to detect poorly calibrated HS models.