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

Jalili, Rahele; Neisy, Abdolsadeh; Vahidi, Alireza

doi:10.22034/cmde.2025.65809.3045

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	New numerical method via RBF approach to the price of fixed-rate mortgages
Computational Methods for Differential Equations
مقاله 7، دوره 14، شماره 3، مهر 2026، صفحه 1103-1111 اصل مقاله (690.31 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.65809.3045
نویسندگان
Rahele Jalili¹؛ Abdolsadeh Neisy^* ²؛ Alireza Vahidi³
¹Department of Mathematics, Science and Research branch, Islamic Azad University, Tehran, Iran.
²Department of Mathematics, Faculty of Mathematics Science and Computer, Allameh Tabataba’i University (ATU), Tehran, Iran.
³Department of Mathematics, Shahr-e-rey branch, Islamic Azad University, Tehran, Iran.
چکیده
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 yields 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.
کلیدواژه‌ها
Fixed-rate mortgages؛ Stochastic volatility؛ Stochastic interest rate؛ Heston model؛ Radial Basis Function

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