Daily stock prices prediction using variance gamma model

Abstract

The Black-Scholes-Merton model is often used for modeling company assets, which requires normally distributed data. The company's asset price fluctuates greatly, causing the form of data distribution to allow for heavy tails, asymmetry and excess kurtosis. Therefore we need a model that can capture this phenomenon. The model is the Variance Gamma model, abbreviated as VG. The assumption of normality in the Black-Sholes-Merton theory is unable to capture the heavy tail and the asymmetry that exists in the log returns asset. This form of density usually that is too high compared to normal density is known as excess kurtosis. The additional parameters in the VG process can overcome heavy tail, asymmetry and excess kurtosis. These parameters can control the kurtosis, asymmetry, and adjust the slope of the log asset density. The VG process can be obtained from two approaches. First, the VG process as a change in Brownian motion to Gamma time, abbreviated as VG1. Second, the VG process is obtained by the difference of the two Gamma processes, abbreviated as VG2. In this study we applied the VG model to predict the daily stock price of PT Bank Negara Indonesia (Persero) Tbk. The results obtained show that the VG model provides accurate daily stock price prediction results.