A Copula Approach to Modeling Extreme Values of Exchange Rates

Abstract: In this thesis we consider a general approach to modeling dependence in extreme values of exchange rates by using copulas. As specific examples the following pairs of currencies are analyzed: Swedish krona to U.S. dollar (SEK/USD), Swedish krona to Euro (SEK/EUR), Swedish krona to British pound (SEK/GBP), Swedish krona to Japanese Yen (SEK/JPY), Swedish krona to Danish krone (SEK/DKK) and Swedish krona to Norwegian krone (SEK/NOK). The daily log-return series are first modeled individually using ARMA-GARCH models. In some cases, when it is statistically significant, we also use three month Stockholm Interbank Offered Rate (STIBOR) as a covariate in our models. After the models have been fitted to the datasets the residuals are considered for further analysis. We fit several bivariate copula models to the residual series and use different measures of goodness-of fit to choose one between competing models. We demonstrate the flexibility of the approach by repeating our analysis both for the original residuals as well as the monthly and quarterly extreme values of the series. Keywords. GARCH, EGARCH, copula, extreme values, exchange rates, modelling