The Stability Analysis of Predictor-Corrector Method in Solving American Option Pricing Model

In this paper, a new technique is investigated to speed up the order of accuracy for American put option pricing under the Black-Scholes (BS) model. First, we introduce the mathematical modeling of American put option, which leads to a free boundary problem. Then the free boundary is removed by adding a small and continuous penalty term to the BS model that cause American put option problem to be solvable on a fixed domain. In continuation we construct the method of lines (MOL) in space and reach a non-linear problem and we show that the proposed MOL is more stable than the other kinds. To deal with the non-linear problem, an algorithm is used based on the predictor-corrector method which corresponds to two parameters, theta and phi. These parameters are chosen optimally using a rational approximation to determine the order of time convergence. Finally in numerical results a second order convergence is shown in both space and time variables.