Value-at-risk for the long and short trading position with the Pearson type-IV distribution

We examine the value-at-risk where the volatility and returns are modelled via a typical GARCH(1,1) model and the innovations process is the Pearson type-IV distribution. As case studies, we examine the NASDAQ and FTSE100 indices from 12-Dec-1984 to 21-Dec-2000. The model is fitted to the data via maximisation of the logarithm of the maximum likelihood estimator. In sample backtesting is performed by the success-failure ratio, the Kupiec p-test, the Christoffersen tests, the expected shortfall, and the DQ test of Engle and Manganelli. The results indicate that the Pearson type-IV distribution gives better results compared with the skewed student distribution.