The valuation of foreign currency options in Kenya under stochastic volatility

Abstract

The main objective of this research project is to show how foreign currency options can be valued in Kenya under stochastic volatility and also to come up with a model for predicting variance and volatility of exchange rates. First the research sought to develop a model for predicting variance based on the USD and Kenya Shillings exchange rates in Kenya for a period of five years between 2008-2012.The research also sought to show how foreign currency options would be priced information from the available data. This research used descriptive research design and the Garman Kohlhagen model for valuation of foreign currency options. The research uses Garch (1, 1) model to fit the variance regression line which was used to predict variance and subsequently the volatility that together with other variables isplugged into the Garman Kohlhagen model. to price the foreign currency options. The research gave findings that were consistent with research done in the area of valuation of foreign currency options. The research shown that foreign currency options can be valued in Kenya by use of a Garch (1, 1) framework which was a good fit for the actual data as the coefficients of the model were within the model constraints of ( + 0.98) <1 for using Garch (1, 1) .The research found out that for call options when the spot exchange rate is below the strike price the option has statistically zero value and when above strike price the option has a positive value. On the other hand the price of a put currency option is positive when the spot exchange rate is below the strike price and statistically zero when the spot exchange rates are above the strike prices and the further away from the strike price the spot exchange rate is the higher the value of the option.