Moving boundary transformation for American call options with transaction cost: finite difference methods and computing

作者：Egorova V N^*; Tan S H; Lai C H; Company R; Jodar L

来源：International Journal of Computer Mathematics, 2017, 94(2): 345-362.

DOI：10.1080/00207160.2015.1108409

• Nonlinear PDE
• free boundary
• transformation
• finite difference methods
• Newton-likemethod
• alternating direction explicit method
• 60G40
• 65N06
• 65N12

The pricing of American call option with transaction cost is a free boundary problem. Using a new transformation method the boundary is made to follow a certain known trajectory in time. The new transformed problem is solved by various finite difference methods, such as explicit and implicit schemes. Broyden's and Schubert's methods are applied as a modification to Newton's method in the case of nonlinearity in the equation. An alternating direction explicit method with second-order accuracy in time is used as an example in this paper to demonstrate the technique. Numerical results demonstrate the efficiency and the rate of convergence of the methods.

• 出版日期2017