Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates

In emerging countries, such as Kenya, the foreign exchange market is an important aspect in the economic development of a country. The currency exchange rate market, like the rest of the world's financial markets, has been marked by considerable instabilities over the last decade. The objective of this paper is to model the volatility of the KSH/USD exchange rate prices using and calculate the VaR using the GARCH-EVT model. In particular, this article uses the two-stage GARCH-EVT approach to estimate the value at risk of the Kenyan Shilling against the US dollar., particularly the one-day ahead Value-at-Risk forecast in risk control. The conditional and unconditional coverage test are used to back test the model. We compare the performance of the GARCH-EVT with the daily log returns of key currency in addition to modelling the value at risk in the Kenyan Foreign Exchange market (US dollar) foreign currencies from the period November 2004 – June 2021 for trading days with the exception of holidays and weekends. The mean equation that was best fitting for the data was ARMA (4,2). The optimal GARCH model for the returns of the KSH/USD exchange rate is the GARCH (1,3) with student-t innovations. The results of the backtesting show that GARCH-EVT can be utilized to estimate and forecast VaR at both 5% and 1% level of significance.