VALUE AT RISK ANALYSIS BY MIXTURE OF THE MULTIVARIATE NORMAL DISTRIBUTIONS IN THE BIST TECHNOLOGY INDEX

Abstract

The purpose of this study is to use the mixture distribution approach in the computation of the value at risk (VaR) by parametric method which is one of the financial risk calculation methods when the financial data is non-normal distribution. In the study, VaR was calculated based on the mixture of multivariate normal distributions. The EM algorithm for the maximum likelihood estimates of the mixture distribution parameters is given. The number of components for the mixture distribution model is determined by Akaike and Bayesian information criteria. In the calculation of VaR for the portfolio which is created by giving equal weight to stocks, classical and mixture distribution approaches are compared. As a result of the comparison, in the statistical modeling of financial assets, modeling based on the mixture of multivariate normal distributions was found to be more successful.