Estimating the probability of rare and extreme events is a crucial issue in the risk estimation of exchange rate returns. Extreme Value Theory (EVT) is a well-developed theory in the field of probability that studies the distribution of extreme realizations of a given distribution function, or of a stochastic process, satisfying certain assumptions. This work has fitted the Generalized Pareto Distribution (GPD) to the excess returns assuming the residuals are independent and identically distributed. The results are used to estimate extreme Value at Risk (VaR) in Rwanda exchange rate process.
Keywords: Confidence intervals, EVT approach, Exchange Rate, Generalized Pareto Distribution, Maximum Likelihood Estimation, Value at Risk
