Siegel's paradox and the pricing of currency options

Abstract

It is an important property of a currency option that its value does not depend on whose point of view is taken, that of the domestic or foreign investor. Option values obtained from the Garman-Kohlhagen model do satisfy this property. The Merton jump-diffusion model has been proposed as a more realistic currency option model, to eliminate pricing biases inherent in the Garman-Kohlhagen model. The jump-diffusion model assumes that the jump risk is non-priced, ie, can be diversified away. If both the domestic and foreign investor make that assumption, then the jump-diffusion model produces option values which are different for the two investors, thus violating the law of one price. This is an instance of the Siegel paradox. The extent to which computed option values may differ between the two investors is indicated through numerical examples.