# PRICING PERPETUAL AMERICAN OPTIONS UNDER REGIME SWITCHING JUMP DIFFUSION MODELS

Document Type : Original Paper

Authors

1 Faculty of Mathematical Sciences, Department of Actuarial Science, Shahid Beheshti University, Tehran , Iran

2 Faculty of Mathematical Sciences, Department of Applied Mathematics, Shahid Beheshti University, Tehran, Iran

Abstract

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

integral term. The discrete maximum principle is applied to the linear complementarity

problems to obtain the error estimates. We also illustrate some numerical results in order

to demonstrate and compare the accuracy of the method for our problem.

Keywords

Main Subjects

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### History

• Receive Date: 24 February 2022
• Revise Date: 14 June 2022
• Accept Date: 21 August 2022