This paper studies the option pricing theories on foreign currency option and investigate the empirical studies in pricing currency option. Modern theory of option pricing assumed that the distribution of price changes in underlying securities are log-normal. It means that the price change follows Gauss-Wiener process. The model of currency option is also assumes the same condition that Black-Scholes did in deriving their stock option pricing model. So, I review Black-Scholes and CRR concerning to stock option pricing model and clarify some differences between stock and currency option models.
Most empirical studies are processed based on American options by using European Model, such as Garman-Kohlhagen, Grabbe etc. So, nine out of ten, when its application to option market price, they conclude that naturally market option premium is higher than the model price caused by an early exercise premium in American options, besides some non-synchronization of parameters, like closing exchange rate and spot price of option, or risk free interest rate. So, in this paper to overcome this kind of problem the data for option is european JPY(169 Ea) and DEM(293 Ea) FX Option, unlike previous studies. traded in PHLX during 1997.
In empirical study,
First, for the whole sample, I reject null hypothesis which Garman-Kohlhagen model's Absolute Error or Absolute Percentage Error between G-K model and market price when using three different kinds of historical volatility is near to zero, because above two error is significant by t-test and regression analysis.
Second, I calculate model price by using another volatility, namely implied volatility and then compare this price to that of three kinds of historical volatility one by one. In addition, I divide option samples into three pieces under option conditions, namely in the money, at the money and out of the money.
For the utility of model price, I aiso did t-test by the Absolute Error or Absolute Percentage Error between the option model price and that of real market. The test result also reject null hypothesis that the AE or APE is near to zero.
I conclude that G-K option pricing model is not good enough to calculate market price for replacement. So, afterwards, in my opinion many various studies should be continued to clarify model utility and also market efficiency by different methods.
