Why standard risk models failed in the subprime crisis? An approach based on Extreme Value Theory as a measure to quantify market risk of equity securities and portfolios

Abstract

The assessment of risk is an important and complex task with which market regulators and financial institutions are faced, especially after the last subprime crisis. It is argued that since market data is endogenous to market behaviour, statistical analysis made in times of stability does not provide much guidance in times of crisis. It is well known that the use of Gaussian models to assess financial risk leads to an underestimation of risk. The reason is because these models are unable to capture some important facts such as heavy tails which indicate the presence of large fluctuations in returns. This thesis provides an overview of the role of extreme value theory in risk management, as a method for modelling and measuring extreme risks. In this empirical study, the performance of different models in estimating value at risk and expected tail loss, using historical data, are compared. Daily returns of nine popular indices (PSI20, CAC40, DAX, Nikkei225, FTSE100, S&P500, Nasdaq, Dow Jones and Sensex) and seven stock market firms (Apple, Microsoft, Lehman Brothers, BES, BCP, General Electric and Goldman Sachs), during the period from 1999 to 2009, are modelled with empirical (or historical), Gaussian and generalized Pareto (peaks over threshold technique of extreme value theory). It is shown that the generalized Pareto distribution fits well to the extreme values using pre-crisis data. The results support the assumption of fat-tailed distributions of asset returns. As expected, the backtesting results show that extreme value theory, in both value at risk and expected tail loss estimation, outperform other models with normality assumption in all tests. Additionally, the results of the generalized Pareto distribution model are not significantly different from the empirical model. Further topics of interest, including software for extreme value theory to compute a tail risk measure, such as Matlab, are also presented.