Arbitrage-Free Pricing of Reverse Mortgages using Neural Stochastic Differential Equations

Working paper

Bai, D.; Wang, C.-W.; Zhang, J.; Zhu, W.

Working paper · 2025

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Abstract

Reverse mortgages play a critical role in financing retirement consumption and managing longevity risk for aging homeowners, yet their valuation is inherently challenging due to joint exposure to mortality risks, interest rates, and housing market conditions over long horizons. This paper develops an arbitrage-free valuation framework based on neural stochastic differential equations (Neural SDEs) to jointly model these risks. The Neural SDEs relax restrictive parametric assumptions while preserving the structure required for pricing and simulation, and are estimated using a likelihood-based approach that targets the full conditional distribution. Extensive empirical results show that Neural SDEs consistently outperform conventional benchmark models in both one-step forecasting and full-path simulation. Building on these improved dynamics, we develop a Monte Carlo pricing engine for reverse mortgages with tenure payments. These dynamics imply higher tail risk and more conservative, economically prudent valuations, highlighting the economic relevance of flexible, state-dependent modeling for long-dated retirement products.

Keywords: Reverse mortgage, neural stochastic differential equations (SDE), deep learning, longevity risk, Monte Carlo

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