Pricing On Two Barriers Options With Compensation Factor

It is difficult to conform a tree and to supply the demand that the boundary points should accompany to the barrier points in the solution of barrier options. And it is complex to find the probability of the option have not been knock out before the expiry date and the probability of the underlying assets first arriving the barrier lines in the pricing of double barrier options. This paper try to find a conciseness way to price double barriers options with compensation factor.This paper discuss how to price double barriers options with compensation factor. Applying many times the variable substitution on the system of partial differential equation. And adopt Fourier expansion to solve it, and get the expression in infinite-term series. Then using the finite terms as the exact solution. The method avoids conforming a tree and seeking density of probability and make the solution conciseness.Applying further the central difference method basing on the model of Hoggord, Whal-ley &Wilmott, and prove the existence and uniqueness of the solution and find out stability conditions, which is simpler and more clear than the method of conforming a tree, Monte Carlo Method and quasi-Monte Carlo method. This paper prices gold derivatives as a example and discuss how volatility and risk-free rate of interest influence on the price of the option. It finds out the property of the pricing model of the European call option with transaction costs, and discusses how transaction costs and volatility influence on the price of the option.