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A stochastic partial differential equation model for the pricing of mortgage-backed securities

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  • Ahmad, F.
  • Hambly, B.M.
  • Ledger, S.

Abstract

We develop a dynamic structural model for the wealth of individual mortgagors in a mortgage pool. We model the process of default and prepayment and, by taking a limit as the pool size goes to infinity, derive a stochastic partial differential equation (SPDE) which can be used to describe the evolution of the loss process from the pool. We prove existence and uniqueness of solutions to this SPDE and show how our model is able to capture, in a flexible way, the prices of credit risky tranches of mortgage-backed securities under different market conditions.

Suggested Citation

  • Ahmad, F. & Hambly, B.M. & Ledger, S., 2018. "A stochastic partial differential equation model for the pricing of mortgage-backed securities," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3778-3806.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:11:p:3778-3806
    DOI: 10.1016/j.spa.2017.12.002
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    References listed on IDEAS

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    6. Deng, Yongheng, 1997. "Mortgage Termination: An Empirical Hazard Model with a Stochastic Term Structure," The Journal of Real Estate Finance and Economics, Springer, vol. 14(3), pages 309-331, May.
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    11. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers, 2011. "Default clustering in large portfolios: Typical events," Papers 1104.1773, arXiv.org, revised Feb 2013.
    12. Vyacheslav Gorovoy & Vadim Linetsky, 2007. "Intensity‐Based Valuation Of Residential Mortgages: An Analytically Tractable Model," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 541-573, October.
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    Cited by:

    1. Ben Hambly & Nikolaos Kolliopoulos, 2019. "Stochastic PDEs for large portfolios with general mean-reverting volatility processes," Papers 1906.05898, arXiv.org, revised Mar 2024.
    2. Emanuele Casamassima & Lech A. Grzelak & Frank A. Mulder & Cornelis W. Oosterlee, 2021. "Pricing and Hedging Prepayment Risk in a Mortgage Portfolio," Papers 2109.14977, arXiv.org, revised Oct 2021.

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