A comparison of the classical black-scholes model and the Garch option pricing model for currency options.

Abstract

This study looks at the consequences of introducing heteroscedasticity in option pricing. The analysis shows that introducing heteroscedasticity results in a better fitting of the empirical distribution of foreign exchange rates than in the Brownian model. In the BlackScholes world the assumption is that the variance is constant, which is definitely not the case when looking at financial time series data. In this study we therefore price a European call option under a Garch model Framework using the Locally Risk Neutral Valuation Relationship. Option prices for different spot prices are calculated using simulations. We use the non-linear in mean Garch model in analyzing the Kenyan foreign exchange market.