Analysis Of Pricing European Foreign Currency Option Under The Single-factor Interest Rate Model

The pricing of the financial derivatives is one of the major issues in the financial field. And it is very practical in the real world and also very significant in the academia area. Foreign currency option is one of the most complex financial derivatives. And it is just emerging in our county’s financial market. Now the existing foreign currency options in our county’s financial market are just the simple ones. And we are not that familiar with them. So at this time it is necessary to do some research on the foreign currency options. This paper is one of this research, and is mainly about the pricing of the European foreign currency option under the single-factor interest rate model.Option is one of the financial derivative products. The main idea of pricing a option is as follow:use the partial differential equation as a tool, obtain the mathematical model of the option by applying the theory and methods of the partial differential equation, then calculate the partial differential equation to get the theoretical pricing formula. This paper also follows this line. First, under the single-factor interest rate model, I establish the hypothesis of the European foreign currency option. Then obtain the partial differential equation by using the martinga-le representation theorem. Secondly, I need to solve this partial differential equation. It is very difficult to solve the equation directly because its dimensions are three. So I employ the forward variable transformation to transform the complex three-dimensional form to the ordinary one-dimensional form. Thirdly, I obtain the pricing formula by exploiting the B-S Formula. Finally, I analyze the asensitivity of the factors which affect the price of the foreign currency option by analyzing the solved pricing formula.