The efficient market hypothesis is highly discussed in economic literature. In its strongest form, it states that there are no price trends. When weakening the non-trending assumption to arbitrary short, small, and fully unknown trends, we mathematically prove for a specific class of...

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...

This paper proposes an asymmetric Markov regime-switching (MS) GARCH model to estimate value-at-risk (VaR) for both long and short positions. This model improves on existing VaR methods by taking into account both regime change and skewness or leverage effects. The performance of our MS model...