Document Type : Research Article

**Authors**

Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran

**Abstract**

In this paper, we first present a nonlinear structural model for pricing mortgage-backed securities. These derivatives are considered to be the primary cause of the 2008 financial crisis that was raised in the United States. We focus our work on pass-through mortgages, which pay both the principal and interest to the investors. We begin our work by introducing the factors that affect the market of mortgage-backed securities. Then, by applying some assumptions and conditions to the parameters of the initial model, and without the loss of generality, we show that this model can be greatly simplified. We focus our attention on how the change in interest rates can affect the value of mortgage-backed securities. Various numerical methods can be used to solve the reduced model that is achieved. We adapt the mesh-less method of radial basis functions to solve the reduced model. The numerical results indicate that the method that we have used can capture the market trends in a specific interval.

**Keywords**

pp. 1033-1050.

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