Valuation of currency options with stochastic volatility

Abstract

Currency options have gained acceptance as invaluable tools in managing foreign exchange risk. They are extensively used and bring a much wider range of hedging alternatives as a result of their unique nature. Options are fundamentally different from forward contracts, as whereas the parties are committed or ‘locked-in’ to a future transaction in a forward contract, the buyer (holder) of an option contract has the right, but not the obligation to complete the transaction at some time in the future. Options are attractive financial instruments to portfolio managers and corporate treasuries because of this flexibility. This research study sought 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. The study focuses on developing 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 and show how foreign currency options would be priced 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 is plugged 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 shows that foreign currency options can be valued in Kenya by use of a Garch framework which was a good fit for the actual data as the coefficients of the model were within the model constraints of 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