MODELLING THE VOLATILITY OF EXCHANGE RATES IN RWANDESE MARKETS (Published)
This work applied Generalized Autoregressive Conditional Heteroskedasticity (GARCH) approach to modelling volatility in Rwanda Exchange rate returns. The Autoregressive (AR) model with GARCH errors was fitted to the daily exchange rate returns using Quasi-Maximum Likelihood Estimation (Q-MLE) method to get the current volatility. Asymptotic consistency and asymptotic normality of estimated parameters were given. Akaike Information criterion was used for appropriate GARCH model selection while Jarque Bera test used for normality testing revealed that both returns and residuals have fat tails behaviour. It was shown that the estimated model fits Rwanda exchange rate returns data well.
Keywords: Exchange Rate, GARCH model, Model, Quasi Maximum Likelihood, Volatility
ESTIMATION OF EXTREME VALUE AT RISK IN RWANDA EXCHANGE RATE (Published)
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