A Value at Risk Efficiency Test Under Different Scenarios: Historical Simulation and MOnte Carlo Simulation Approaches

This dissertation work represent an efficiency test of Historical Simulation and Monte Carlo Simulation approaches in Value at Risk calculation using randomly generated numbers as an underlying data series. The data series contain 250, 500, 1000 and 10000 observations and they follow two specified distributions, which are Student-t and normal distributions with zero mean and 0.02 standard deviation. The generated data series are analysed thoroughly utilising unit root test, serial correlation test, and test for ARCH effects. Based on the test results, VaR measures for Historical Simulation and Monte Carlo Simulation methods are obtained and compared with the true VaR measures from the set distributions. The outcomes show that Monte Carlo Simulation methods provide with better values when sample size is small (less than 500 observations), whereas Historical Simulation method proved to be robust when data series contain 1000 or more observations, regardless of distribution type. Moreover, the VaR results from Student-t distribution are more volatile than the VaR outcomes from normal distribution. In addition, as confidence level increases, the less precise the VaR estimates become