Estymacja ryzyka rynkowego w oparciu o modele Garch i Teorię wartości ekstremalnych

Abstract

This paper discusses estimation of two measures of market risk: Value at Risk and Expected Shortfall. Presented here approach is based on the use of GARCH models and extreme value theory. GARCH models with different innovation distributions were used to estimate the current volatility, while extreme value theory was used to model the tail of the innovation distribution of the GARCH model. This approach enabled to estimate separately the volatilty of the financial market and the tails of the log return distribution , which led up to more precise estimation of heaviness of the tails. Backtesting enabled to compare the results of the proposed method with other standard approaches used in market risk estimation. Analysis was co nducted for log returns of WIG20 index from 9 years period.