In this thesis we have explored the very high prices that sometimes occurs in the Nord Pool electricity market Elspot. By applying AR-GARCH time series models, extreme value theory, and ACER estimation techniques, we have sought to estimate the probabilities of threshold exceedances related to electricity prices. Of particular concern was the heavy-tailed Fréchet distribution, which was the asymptotic distribution assumed in the ACER estimation.We have found that with extreme value theory we are better equipped to deal with the very high quantiles in the time series we have analyzed. We have also described a method that can give an assessment of the probability of exceeding a selected level in the electricity price.