Abstract
This study makes use of different statistical techniques to estimate unconditional and conditional market risk measures. The unconditional measures are calculated by using three traditional Value at Risk techniques namely the Historical Simulation (HS), Variance-Covariance (VC) and Monte Carlo simulation (MCS). However, for the conditional market risk measure, this study employs a novel technique known as the Generalized Autoregressive Score (GAS) model. This technique allows us to overcome the unrealistic assumption often used in empirical studies that argue that the score of the empirical distribution when computing the conditional Value at Risk measures; is constant over time. The technique used in this study allows us to relax this assumption and let the score of the empirical distribution to evolve over time. The study begins by removing the effect of autocorrelation and heteroskedasticity in the returns series by applying an Autoregressive Moving Average Generalized Autoregressive Conditional Heteroscedasticity (ARMA-GARCH) process. Thereafter, the filtered returns are fitted to a GAS process in order to estimate the evolving score of the empirical distribution of the returns to be used in the conditional Value at Risk computation. The study uses a sample data of daily log returns of four stock market indices: - the South African ALSI, the UK FTSE 100, the Chinese Hang Seng and the U.S. S&P 500 spanning from the 22 September 2003 to 5 November 2019. Firstly, the results of the unconditional Value at Risk measures are found to be around 3%, 5% and 2% for the HS, VC and (MCS) techniques, respectively. Secondly the estimated parameters of all the specified ARIMA-GARCH models used to filter the return series were found to be statistically significant including the leverage which suggests that bad news have a higher volatility than good news in the respective stock markets. Finally, the resulting standardized residuals were used to estimate the evolving score (parameters) of the GAS process. The estimated parameters from the GAS model show that the scores of the empirical distribution are significant and that the current score of the empirical distribution are explained by their previous score values. The market risk measures obtained with the GAS model are found to be more reliable than the ones obtained with traditional conditional Value at Risk model that assume constant score. To validate our results, the study implements three back test techniques namely, the unconditional coverage test, the conditional coverage test and the three zone test. The results support our abovementioned findings.
M.Com. (Financial Economics)