Application of an evolutionary algorithm for VaR calculations

The Value-at-Risk (VaR) approach has been extensively used for measuring and controlling of market risks in financial institutions during the last decade. The risk control and management systems required in the new banking industry are based on the Banks for International Settlements' (BIS) suggestions. Financial asset returns are traditionally modeled as being distributed according to the normal or lognormal distributions. However the VaR estimations, calculated in this way, usually involve a systematic error because the density of the returns' occurrences is not distributed normally. The leptokurtic distribution of financial asset returns can be defined more realistically with a t -distribution. The aim of this study is to estimate the parameters of t -distribution through Maximum Likelihood Estimation (MLE) using an Evolutionary Algorithm (EA) approach. Experimental results show that successful VaR calculations at high confidence levels can be done using the t -distribution with the parameter setting found by the EA.