Essays on value at risk

Abstract

Value-at-Risk (VaR) is a measure of the market risk of a portfolio. It quantifies, newlinein monetary terms, the exposure of a portfolio to market fluctuations at certain newlineconfidence level. The financial community all over the world has accepted VaR as a newlinetool for market risk management. newlineThis thesis deals with some statistical aspects of VaR with special emphasis on Indian newlineequity market. In particular, it addresses the issues of model selection, power of newlinestatistical tests and the use of extreme value theory in VaR implementation. newlineThe thesis defines a two stage VaR model selection procedure based on the dual newlinecriteria of statistical accuracy and minimisation of the cost of risk management. In newlinethis two stage approach, statistical accuracy is considered as the necessary condition newlinefor an good VaR model. If multiple models survive the test of statistical accuracy, we newlinedo a second stage filtering of the surviving models using subjective loss functions. In newlinethe second stage, certain loss functions reflecting the risk management problem are newlinedefined and the VaR models are judged by how well they are able to minimise the newlineloss functions. We apply this two stage methodology to a class of 15 models of VaR newlineestimation for India s prominent equity index, the Nifty index. We find that for 95% newlineVaR estimation, a statistically appropriate model could be chosen in the first stage newlineitself, while at 99% level, three models were accepted in the first stage and we applied the second stage of filtering to the three competing models, by using the loss functions newlinereflecting the risk management problems of a regulator and a firm. The differences in newlineloss functions between different economic agents - a clearing corporation or a finance newlinecompany are economically significant insofar as they lead to different judgments for newlinemodel selection. newlineA Monte carlo investigation into the statistical tests of VaR models reveals that the newlineexisting tests do not possess adequate statistical power to reject false VaR models. newlineOften the power is found to be even less than the no