Extreme daily changes in U.S. Dollar London inter-bank offer rates

The likelihood of extreme daily changes in London Interbank Offer rates are estimated using the peaks-over-threshold method developed from extreme value theory. Value at risk and expected shortfall for high quantiles are produced for the left and right tails of the distributions for each maturity. The Generalized Pareto distribution of the peaks-over-threshold method is found to be unsuitable for modeling exceedances above a high threshold for samples of simple daily changes in the LIBOR. When the series are transformed to logarithmic daily changes, extreme value analysis proceeds smoothly and yields useful information about the relative frequency or magnitudes of extreme events. The main consequence of this is that the risk statistics associated with a given change in the LIBOR depend on the initial rate level; at higher (lower) interest rates, changes of a given size are more (less) likely to occur.