Validating market risk models using realized PIT values
Lok, Hsiao Yen
MetadataShow full item record
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.