극단치(Extreme Value)이론을 이용한 한국종합주가지수 극단수익률 분포에 관한 실증연구

Abstract

The extreme value distributions have three types known as the Gumbel, Frechet, and Weibull families respectively. Statistical theory states that the asymptotic distribution of extremes has a well-determined form which is independent of the process of returns. This study estimates the asymptotic distributions of daily KOSPI minimal and maximal returns using extreme value theory over the period Jan. 4, 1980 to Apr. 30, 2002. As extreme returns are selected over nonoverlapping periods of varying length from 20 trading days to 200 trading days, estimates of the location parameter, the scale parameter, and the tail index for the distribution of extreme returns are obtained by the maximum likelihood estimation and the least squares estimation. The findings are as follows. The asymptotic distribution of extreme returns is generally a Gumbel distribution for maximal returns and a Frechet distribution for minimal returns by a likelihood ratio test. As extremes are selected over a longer period, the distribution of extremes shifts to the right for maxima and to the left for minima and expands, while the shape of the distribution remains the same. This result could be used to improve our understanding about the whole process of returns.