| Non-normality, namely, asymmetry and/or leptokurtosis, has been a stylized fact for financial asset return distributions in the finance literature. Fat-tailedness, in particular, can have significant impact on the accuracy in computing value at risk (VaR), which became popular from the mid-1990s as a primary measure of market risks arising from the trading activities of banks.; The normal VaR method might seriously underestimate VaR in the presence of fatter tails than predicted by a normal distribution. Its main variant, the normal GARCH method, based on conditional volatility, achieved some degree of success, but the problem of fat-tailedness still remains, though it is mitigated, after modeling volatilities using GARCH. On the other hand, the historical simulation method has gained popularity in practice because it is free from the non-normality problem, but it has the limitation of requiring a large amount of data to ensure reliable VaR estimation.; The primary purpose of this study is to develop a new methodology of VaR estimation to better handle skewness and fat-tailedness than the existing analytical VaR approaches, while at the same time being more flexible than the historical simulation approaches. The new approach adopts the g-and-h distribution and, hence, it is named the g-and-h VaR method. The proposed methodology permits greater simplicity and flexibility in accommodating non-normality and combines the merits of the normal and the historical simulation methods.; To validate the accuracy of the g-and-h VaR method, the empirical analysis is conducted, for several data sets of interest and foreign exchange rates, by comparing the frequency of exceedances with that of the normal method. The method is extended to compute VaR for portfolios. The results from backtesting show that the performance of both methods is equally satisfactory at the 95% confidence level, but at the 99% or higher levels the g-and-h method significantly outperforms the normal method. In addition, the procedure for decomposing portfolio VaR into its individual components is developed for the g-and-h method to examine the contribution of each constituent to total VaR. |
