Abstract:
This paper makes use of two types of extreme value distributions, namely: the generalised
extreme value distribution often referred to as the block of maxima method (BMM), and the
peak-over-threshold method (POT) of the extreme value distributions, to model the financial
tail risks associated with the empirical daily log-return distributions of the Dow Jones Islamic
market (DJIM), the U.S. S&P 500, the S&P Europe (SPEU), and the Asian S&P (SPAS50)
indexes during the period between 01/01/1998 and 16/09/2015. Using both the maximum
likelihood (ML) method and the bootstrap simulations to estimate the parameters of these
extreme value distributions in the left and right tails separately, we find that the empirical
distributions of conventional stock markets are characterized by a fat-left tail behaviour,
which implies high probability of price drops during a financial crisis, and by a right-tail
characterised by a truncation. This finding implies the existence of an upper bound on
possible profit during an extreme event. The empirical distribution of the Islamic market is
characterised by a thin-left tail behaviour, implying moderately low probability of price drops
during a financial crisis, and by a right-tail without truncation implying large probability of
positive returns during an extreme event. We divide our sample period into three equal subperiods
in order avoid the impact of outliers and structural breaks. The results in each subperiod
remain the same and also suggest that for all stock returns the BMM method performs better than the POT method, and that the Islamic stock market is less risky than the
conventional stock markets during extreme events.
