A Comparison of the Classical Black-Scholes Model and the GARCH Option Pricing Model for Currency Options

Citation:
Aduda JA. "A Comparison of the Classical Black-Scholes Model and the GARCH Option Pricing Model for Currency Options." ICASTOR Journal of Mathematical Sciences. 2011;5(2):267-284.

Abstract:

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.

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