ESTIMATION OF EXTREME VALUE AT RISK IN RWANDA EXCHANGE RATE

Abstract

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: Exchange rate, EVT approach, Generalized Pareto Distribution, Value at Risk, Maximum Likelihood Estimation, Confidence intervals