Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-808812420221222PRICING PERPETUAL AMERICAN OPTIONS UNDER
REGIME SWITCHING JUMP DIFFUSION MODELSPRICING PERPETUAL AMERICAN OPTIONS UNDER
REGIME SWITCHING JUMP DIFFUSION MODELS4774931793710.22055/jamm.2022.39634.1999FASagharHeidariFaculty of Mathematical Sciences, Department of Actuarial Science, Shahid Beheshti University, Tehran , Iran0000-0002-1639-1726HosseinAzariFaculty of Mathematical Sciences, Department of Applied Mathematics, Shahid Beheshti University, Tehran, Iran0000-0002-8669-3535Journal Article20220224In this article, we examine the issue of pricing 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 problems and then discretize by using the finite difference method. We use linear interpolation to approximate the<br /><br />integral term. The discrete maximum principle is applied to the linear complementarity<br /><br />problems to obtain the error estimates. We also illustrate some numerical results in order<br /><br />to demonstrate and compare the accuracy of the method for our problem.In this article, we examine the issue of pricing 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 problems and then discretize by using the finite difference method. We use linear interpolation to approximate the<br /><br />integral term. The discrete maximum principle is applied to the linear complementarity<br /><br />problems to obtain the error estimates. We also illustrate some numerical results in order<br /><br />to demonstrate and compare the accuracy of the method for our problem.https://jamm.scu.ac.ir/article_17937_98dbe87004e38c0329c24fac60a382ab.pdf