A COMPARISON OF THE CLASSICAL BLACK-SCHOLES MODEL AND THE GARCH OPTION PRICING MODEL FOR CURRENCY OPTIONS
Akinyi, Aduda Jane
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This paper 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 Black-Scholes 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.
Department of Statistics and Actuarial Science; Jomo Kenyatta University of Agriculture & TechnologySchool of Mathematics, University of Nairobi
Foreign exchange rates
Risk Neutral Valuation