Multiquadratic-Radial Basis Functions Method for Mortgage valuation under jump-diffusion model

Document Type : Original Article

Authors

1 Department of Applied Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Mathematics, Faculty of Mathematical Science, Allameh Tabataba’i University (ATU), Tehran, Iran.

3 Department of Mathematics, Shahr-e-rey branch, Islamic Azad University, Tehran, Iran.

Abstract

Given the significant benefits of the Radial Basis Function (RBF) approach, here in this paper, we tried to exploit and adopt this method for the Fixed-Rate Mortgage (FRM) models. In the real world, a jump occurs due to an unknown reason and perhaps better reflects the evolution of real estate prices during bubbles and crises in the real estate markets. For the house price evolution, the jump- diffusion models are used which would lead to a Partial-Integro Differential Equation (PIDE) model. The main concentration is on the difficulty of projecting the pricing of FRM that deals with contracts in where the underlying stochastic factors are the house price and the interest rate. Utilizing the stochastic house-price and stochastic interest-rate models, we were able to develop a reliable mortgage valuation. The identified Partial-Integro Differential Equation (PIDE) from the FRM pricing model, solved by RBF considering the fact that a closed-form solution is usually unavailable. Further, to display the expected behaviour of the contract, the possible applications of the suggested method applied to UK fixed-rate mortgages. Based on available resources, a set of economic parameters was determined for the mortgage to provide an instance to show the applicability of the proposed approach.

Keywords

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