ADI method of credit spread option pricing based on jump-diffusion model

Document Type : Research Article

Authors

• R. Mohamadinejad ¹
• A. Neisy ²
• J. Biazar ¹

¹ Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

² Department of Mathematics, Faculty of Mathematics Science and Computer, Allameh Tabataba’i University, Tehran, Iran

10.22067/ijnao.2021.11333.0

Abstract

As the main contribution of this article, we establish an option on a credit spread under a stochastic interest rate. The intense volatilities in financial markets cause interest rates to change greatly; thus, we consider a jump term in addition to a diffusion term in our interest rate model. However, this decision leads us to a partial integral differential equation. Since the integral part might bring some difficulties, we put forward a fairly new numerical scheme based on the alternating direction implicit method. In the remainder of the article, we discuss consistency, stability, and convergence of the proposed approach. As the final step, with the help of the MATLAB program, we provide numerical results of implementing our method on the governing equation.

Keywords

• Interest rate
• Option pricing
• Jump-diffusion models
• Alternating direction implicit, Convergence

20.1001.1.24236977.2021.11.1.10.7

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