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This study used extreme value theory to establish if the volatility witnessed in the exchange rate of the Kenya Shilling against the U.S. dollar in the period 1999 to 2013 could have been predicted and also determine if the long-term stability in the exchange rate was violated in the period. The peak over threshold model is applied to the tail of the volatility process of exchange rate returns of the Kenya Shilling against the U.S. dollar. The results showed that despite episodes of extreme volatility, the long-term stability of the exchange rate was maintained during the period. However, implementation of policies that will increase and sustain the level of foreign exchange inflows into the country is necessary to mitigate the vulnerability of the exchange rate to external and domestic shocks. Specifically, policies to promote the export sector and those to increase the level of foreign exchange reserves held by the Central Bank of Kenya should be encouraged. The comparably extreme volatility witnessed in the period 2008 to 2010 showed that political stability is a key component of foreign exchange market stability in Kenya.         Key words: Volatility, Extreme Value Theory, Peaks over Threshold model, GARCH model

Modelling extreme volatility in the daily exchange rates of the Kenya shilling against the U.S. dollar