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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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    1. Kurtz, Thomas G. & Xiong, Jie, 1999. "Particle representations for a class of nonlinear SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 103-126, September.
    2. 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.
    3. Kau, James B, et al, 1992. "A Generalized Valuation Model for Fixed-Rate Residential Mortgages," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 24(3), pages 279-299, August.
    4. Yevgeny Goncharov, 2006. "An Intensity-Based Approach To The Valuation Of Mortgage Contracts And Computation Of The Endogenous Mortgage Rate," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 889-914.
    5. 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.
    6. Green, Jerry & Shoven, John B, 1986. "The Effects of Interest Rates on Mortgage Prepayments," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 18(1), pages 41-59, February.
    7. Dunn, Kenneth B & McConnell, John J, 1981. "Valuation of GNMA Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 36(3), pages 599-616, June.
    8. Metzler, Adam, 2010. "On the first passage problem for correlated Brownian motion," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 277-284, March.
    9. Niels Rom-Poulsen, 2007. "Semi-analytical MBS Pricing," The Journal of Real Estate Finance and Economics, Springer, vol. 34(4), pages 463-498, May.
    10. Campbell, Tim S & Dietrich, J Kimball, 1983. "The Determinants of Default on Insured Conventional Residential Mortgage Loans," Journal of Finance, American Finance Association, vol. 38(5), pages 1569-1581, December.
    11. Cunningham, Donald F & Capone, Charles A, Jr, 1990. "The Relative Termination Experience of Adjustable to Fixed-Rate Mortgages," Journal of Finance, American Finance Association, vol. 45(5), pages 1687-1703, December.
    12. Schwartz, Eduardo S & Torous, Walter N, 1989. " Prepayment and the Valuation of Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 44(2), pages 375-392, June.
    13. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers, 2011. "Default clustering in large portfolios: Typical events," Papers 1104.1773, arXiv.org, revised Feb 2013.
    14. Stanton, Richard, 1995. "Rational Prepayment and the Valuation Mortgage-Backed Securities," Review of Financial Studies, Society for Financial Studies, vol. 8(3), pages 677-708.
    15. Kau, James B. & Keenan, Donald C. & Muller III, Walter J. & Epperson, James F., 1995. "The Valuation at Origination of Fixed-Rate Mortgages with Default and Prepayment," The Journal of Real Estate Finance and Economics, Springer, vol. 11(1), pages 5-36, July.
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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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