Pricing of Currency Options: A comparison of Garman Kohlhagen and GARCH Option Pricing Model

This paper aims at comparing the accuracy and pricing performance of two popular and widely used currency option pricing models, Garman Kohlhagen (1983) and Duan (1995) GARCH option pricing model. In order to accomplish analysis, historical data on European type of options on $/GBP are used, which were trading on Philadelphia Stock Exchange (PHLX) in the year 1996. A wide range of call and put options are considered, with lots of variety in the quotes, Time to Maturity and Moneyness. It was observed that the key difference between both models and its theoretical price is volatility. GK assumes constant or historical volatility and Duan’s GARCH option pricing model uses future volatility. In this paper, Bollerslev (1986) GARCH (1, 1) volatility is estimated and used in Duan’s GARCH option pricing model i.e. in Monte Carlo Simulation process. The three performance measures, RMSE, MAPE and Average Percentage Difference, used in this paper to evaluate the efficiency, categorically declares Duan’s GARCH option pricing model, as a superior model overall than Garman Kohlhagen, but the pricing efficiency of the models varies across moneyness and time to maturity. Keywords: Option Pricing; Currency Options; Garman-Kohlhagen; GARCH; Volatility