Risk and Dependence Analysis of Australian Stock Market - The Case of Extreme Value Theory

Abstract

The quantification of risk and dependence are major components of financial risk modelling. Financial risk modelling frequenty uses the assumption of a normal distribution when considereing the return series which makes modelling easy but is inefficient if the data is not normally distributed or if it exhibits extreme tails. When dealing with extreme financial events to quantify extreme market risk, Extreme Value Theory (EVT) proves to be a natural statistical modelling technique of interest. Estimation of tail dependence between financial assets plays a vital role in various aspects of financial risk modelling including portfolio theory and hedging amongst applications. Extreme Value Theory (EVT) provides well established methods for considering univariate and multivariate tail distributions which are useful for forecasting financial risk or modelling the tail dependence of risky assets. In this paper we focus on the extreme risk and dependence analysis of the ASX-All Ordinaries (Australian) stock market using using univariate and multivariate EVT based methods. The empirical evidence shows that EVT can be successfully applied to financial market return series for predicting daily VaR using a GARCH(1,1) and EVT based dynamic approach. We also use nonparametric measures based on bivariate EVT to investigate asymptotic dependence and estimate the degree of tail dependence of the ASX-All Ordinaries daily returns with four other international markets, viz., the S&P-500, Nikkei-225, DAX-30 and Heng-Seng for both right and left tails of the return distribution in extreme quantiles. It is investigated whether the asymptotic dependence between these markets is related to the heteroskedasticity present in the logarithmic return series using GARCH filters. The empirical evidence from bivariate EVT methods show that the asymptotic dependence between the extreme tails of the stock markets does not necessarily exist and rather can be associated with the heteroskedasticity present in the financial time series of the various stock markets.