New numerical method via RBF approach to the price of fixed-rate mortgages‎

Articles in Press

Document Type : Research Paper

Authors

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

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

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

Abstract

In this paper, we introduce a novel fixed-rate mortgage (FRM) pricing model that overcomes the limitations of existing approaches. Unlike traditional models which rely on deterministic interest rate volatility and thus produce inaccurate valuations in volatile markets, our model incorporates stochastic volatility to more accurately reflect the dynamic nature of interest rate risk. This results in a pricing formula derived from a stochastic volatility framework, providing a strong theoretical basis for understanding volatility’s impact on FRM prices. We use the efficient and accurate Radial Basis Function (RBF) method to solve the resulting partial differential equation (PDE), effectively handling complex boundary conditions. Our numerical experiments demonstrate the model’s practical application and illustrate how FRM prices react to varying volatility across different market conditions. Our findings underscore the critical need for stochastic volatility in FRM valuation and offer valuable insights for improved hedging strategies, ultimately contributing to more realistic and accurate mortgage pricing and enhanced risk management for financial institutions and investors.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 07 May 2025

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History

  • Receive Date: 05 February 2025
  • Revise Date: 30 April 2025
  • Accept Date: 05 May 2025

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