The Asymptotics of Extreme Returns in the Australian Stock Market

Abstract

Empirical analysis of financial data such as the daily, weekly or monthly prices of assets such as bonds, stocks, currencies and commodities have shown that asset prices approximately follow a martingale process, but the distribution of asset returns tend to be fat-tailed. This paper examines the extreme daily, weekly and monthly returns on the Australian stock market using order statistics and extreme value theory. Using data from the Australian Stock Exchange for the period 1990 to 2001 (11 years), the extreme returns are found to belong to a range of extremevalued family of distributions. The distribution of the underlying returns generating process is found to be conditional on the blocksizes used. The maximal and minimal returns have differing distributions and are correlated indicating a possible bivariate returns generating process. Further, extreme returns are found to be weakly correlated implicating possible volatility clustering of the extreme returns.