Pricing Foreign Exchange Option Under Fractional Jump-Diffusions

Abstract

Foreign exchange option, as a financial derivative, plays an important role in the financial market. It is of great theoretical and practical significance to study the foreign exchange options, especially its pricing model. In order to more accurately portray the authenticity of foreign exchange market, this paper applies fractional Brown motion in the fractal market hypothesis and combines with jump diffusion process so as to establish the pricing model of foreign exchange option. Moreover, this paper put forward the pricing formulas of European foreign exchange call and put option, as well as their relationships by using the method of insurance actuary pricing. No matter whether the financial market has arbitrage or not, no matter it is complete or not, this conclusion is valid.