Performance of fat-tailed Value-at-risk : A comparison using backtesting on the OMXS30

Detta är en Magister-uppsats från Högskolan i Jönköping/IHH, Economics, Finance and Statistics; Högskolan i Jönköping/IHH, Economics, Finance and Statistics

Sammanfattning:

The aim of this thesis is to test if the application of fat tailed distributions in value-at-risk models is of better use for risk managers than the Normal distribution. Value-at-risk is a regulatory tool used in Basel regulations. Basel II and III regulate capital required by banks according to value-at-risk backtest results. Value-at-risk is therefore of great importance for financial institutions and banks. The models used for the value-at-risk estimation are rolling ARMA(1,1)-GARCH(1,1) models with Normal, Student’s t, and Generalized hyperbolic distributed errors. The performance of the value-at-risk models was estimated using backtest forecasting on a thousand day out-of-sample window, based on the OMXS30 index. Results reveal that the normal value-at-risk model performs worse compared to the non-normal value-at-risk models. Density forecasts show that value-at-risk estimates directly benefit from including parameters of kurtosis. However, evaluation tests show that none of the models underestimate value-at-risk, and therefore the rejection of the Normal distribution in value-at-risk estimation is not sufficiently justified.

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