On Modelling Extreme Foreign Exchange Volatility Using Copulas

Sammanfattning: The price volatility is an important property to monitor in financial trading. A volatile period implies threats of large losses, but at the same time opportunities of higher gains. This makes accurate volatility prediction models an important part of an algorithmic trading system. This thesis work investigates the extreme value dependence between the Foreign Exchange rate volatility and the rate of change of the offer- and bid volumes present at the market. Each of the currency pairs EURUSD, EURSEK and EURNOK will be analyzed for a one hour period on three different days, where trading volumes and prices are given at several levels at each point in time. The first part of the thesis aims to transform the data into one-dimensional data series, describing the rate of fluctuation of price and volume. These are then subject to time series model fitting in order to remove all forms of autocorrelations in the data. The extreme values of the residual series are then extracted using a block maxima approach, and modelled using the Generalized Extreme Value (GEV) distribution. The quite novel approach of extreme value copulas is then applied as a method of modelling the joint dependence structure between the volume- and price extremes. The results indicate dependence being present, in most cases appropriately described by extreme value copula models. Further research on the topic is suggested.