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

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 (ADE) 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.