American Journal of Theoretical and Applied Statistics 2015; 4(6): 426-431 Published online September 25, 2015 (http://www.sciencepublishinggroup.com/j/ajtas) doi: 10.11648/j.ajtas.20150406.12 ISSN: 2326-8999 (Print); ISSN: 2326-9006 (Online) Modelling the Volatility of Exchange Rates in Rwandese Markets Jean de Dieu Ntawihebasenga 1 , Joseph Kyalor Mung’atu 2 , Peter Nyamuhanga Mwita 3 1 Mahatma Gandhi University-Rwanda, Faculty of Science, Department of Mathematics, Kigali-Rwanda 2 Jomo Kenyatta University of Agriculture and Technology, Faculty of Applied Science, Department of Statistics and Actuarial Science, Kisumu-Kenya 3 Jomo Kenyatta University of Agriculture and Technology, Faculty of Applied Science, Department of Statistics and Actuarial Science, Nairobi-Kenya Email address: jsenga2015@gmail.com (J. D. Ntawihebasenga), jmungatu@fsc.jkuat.ac.ke (J. K. Mung’atu), petermwita@fsc.jkuat.ac.ke (P. N. Mwita) To cite this article: Jean de Dieu Ntawihebasenga, Joseph Kyalor Mung’atu, Peter Nyamuhanga Mwita. Modelling the Volatility of Exchange Rates in Rwandese Markets. American Journal of Theoretical and Applied Statistics. Vol. 4, No. 6, 2015, pp. 426-431. doi: 10.11648/j.ajtas.20150406.12 Abstract: This work applied Generalized Autoregressive Conditional Heteroskedasticity (GARCH) approachto 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.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: Model, Volatility, ExchangeRate, Quasi Maximum Likelihood, GARCH Model 1. Introduction Exchange rates are a challenging concept due to the fact that one has to deal with foreign exchange rates whenever he/she travels to a foreign country. Exchange rates markets are world decentralized marketplaces that determine the relative values of different currencies. Volatility refers to the spread of all likely outcomes of an uncertain variable. Statistically, volatility is often measured as the sample standard deviation. Volatility is related to but not exactly the same as risk. Risk is related with undesirable results, but volatility can be defined as a measurement of the change in price over a given period of time. The conditional volatility in exchange rate returns is considered as the origin of exchange rates risk and has certain significances on the volume of international trade. Exchange rate volatility is a measure of the fluctuations in exchange rate markets. The risk in foreign exchange can be defined as exposure to uncertainty and it cannot be dismissed in exchange rate markets since both importers and exporters of goods and services are affected by exchange rates fluctuations. Exchange rate risk also known as Foreign exchange risk or currency risk refers to a financial risk posed by an exposure to unanticipated changes in the exchange rate between two currencies. It may also be defined as the variability of a portfolio’s value caused by uncertain fluctuations in the exchange rates. A value of any currency fluctuates as its demand and supply fluctuates, this means that if demand decrease or supply increase this can cause depreciation of the currency’s value. On other hand if supply decreases and demand increases, this can cause appreciation of the value of currency(Madura, 1989).When volatility in exchange rates increases itleads to uncertainty in pricing and this hurts importers who spend more for the same quantity.The volatility in prices has implications on the profits and survival of business enterprises (Smith et al, 1990). Recently, researchers and academics have estimated conditional volatility of exchange rates return using different techniques.Maanaet al (2010) modeled exchange rate volatility of Kenya exchange rate markets using GARCH (1, 1) model. They found that the importers and exporters of goods and services are both affected by exchange rate fluctuations.Ghysels and Jasiak (1996) estimated the volatility as non-constant and non-symmetric with left fat tail. Some researchers argue that the true volatility cannot be estimated because there is no relationship between prior, current, and future volatilities for financial assets (Sandmann