Value-at-Risk and Extreme Events

Abstract: The purpose of this thesis is to test the risk-measure Value-at-Riskand techniques for calculating it on data from the Financial Crisis of2007–2010. Different “pre-Financial Crisis” approaches to calculatingValue-at-Risk are considered, and tested on data from the period ofthe Financial Crisis. Also combinations of different approaches aretested. Estimation of Value-at-Risk is done using the two different frame-works: Historical simulation (regular and the Hybrid approach) andparametric (conditional heteroscedastic) models. The conditional heteroscedastic models considered are the EGARCHand the APARCH, calibrated using QMLE-methods. They are applied to the normal and Student’s t-distributions, Generalized ErrorDistribution and a non-parametric distribution. Consequently, a semi-parametric approach consisting of a non-parametric distribution alongwith an ARCH model is considered. Quantile regression as by Koenker (1978) is used for the parameterestimation of the Historical simulation models used. The Value-at Risk models are validated using Christoffersen’s con-ditional coverage test.Four stock indices (NIKKEI 225, NASDAQ 100, FTSE 100 andISEQ-overall) are evaluated, selected based on location and the re-gional effect of the Financial Crisis. Models are calibrated based ondata from before the Financial Crisis of 2007–2010, as the crisis isknown at present (April 2010). It is found that the present approach to Value-at-Risk estimationcan not be considered redundant due to the extreme events of theFinancial Crisis.