Modelling Indonesian stock indices using variance gamma

Abstract

In this paper we discuss a class of Levy process which is called variance gamma (VG) to model the dynamics of Indonesian Stock Indices. There are some stock indices listed in Indonesia Stock Exchange (ISE), but in this paper we choose two of them, Jakarta Composit Index (JCI) and Jakarta Islamic Index (JII). JCI compose of all stocks traded in ISE and an important indicator for the stock price dynamics in the ISE. JII, on the other hand only consist of 30 stocks based on syariah in order to develop the syariah stock market in Indonesia. It is well known that the dynamics of stock indices can be modelled using stochastic models such as a well known Geometric Brownian Motion (GBM). In this paper we will use VG model to describe the dynamics of those two indices and compare the performance of the model with a GBM model. We found that the VG model gives a better performance than GBM model based on some criteria in modelling the dynamics of the JCI and JII Index