MODELLING EXTREME EVENTS: APPLICATION TO ZAGREB STOCK EXCHANGE

In the paper we analyse the performance of Value at Risk (VaR) models at extreme quantiles: 0.99, 0.995 and 0.999 for both long and short positions in Croatian, Zagreb stock exchange index – CROBEX. Backtesting shows that none of the usually employed VaR models correctly forecasts the risk during the ongoing global and domestic financial crisis. The only exceptions are the extreme value based models which correctly forecast the true level of upside and downside risk. We also investigate the closeness of fit of theoretical distributions to the extreme tails of CROBEX returns. Results show that generalised Pareto distribution, which has a sound theoretical foundation, provides the best fit to both tails of CROBEX returns. We find that distribution tails differ signifi cantly, with the right tail having a higher tail index,indicative of more extreme events.