| Abstrakt: |
In this article, we examine the issue of pricing the perpetual American option with a differential equation approach with free boundary properties. To describe the underlying asset dynamics in these options, we use the feature of jump-diffusion models under regime-switching. In pricing these perpetual options, due to the possibility of early application, we need to solve the ordinary integro-differential equation with a free boundary. For this purpose, we write the equation created from this model first as a linear complementarity problem and then discretize it by using the finite difference method. We use linear interpolation to approximate the integral term. The discrete maximum principle is applied to the linear complementarity problems to obtain the error estimates. We also illustrate some numerical results to demonstrate and compare the accuracy of the method for our problem. [ABSTRACT FROM AUTHOR] |
