점프확산모델을 이용한 KOSPI 수익률의 분석

Abstract

본 논문에서는 KOSPI 지수의 Log-return값에 대한 점프확산모델의 매개변수를 일정한 값을 가진다고 가정하고, 각 점프확산모델별로 매개변수 값을 estimation한다. 이때 사용되는 estimation은 Multinomial maximum likelihood estimation이다. 이렇게 구해진 매개변수로 만들어진 점프확산모델을 Kolmogorov, Cramer-von Mises, Anderson-Darling 통계치로 실제 data값과이 적합도를 측정한다.

The jump-diffusion model has been proposed to complement shortcomings of the Black-Scholes model. We consider five models for jump size distribution in the jump-diffusion model

there are known in literature, two are new. The theoretical densities of these jump-diffusion models are fit to empirical log-returns of KOSPI index data.We use Kolmogorov, Cramer-von Mises and Anderson-Darling statistics for goodness of fit test. We observe that the double exponential's skewness and the double triangle's kurtosis are the closest to the empirical value. In statistical test, the double exponential model turned out to be the best. However, the double triangle model is more realistic since the jump rate of this model is smaller than other two models. In tail part, the asymmetric normal model is closer to empirical data than the normal model.