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Mortgages and Markov Chains: A Simplified Evaluation Model

Author

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  • Paul Zipkin

    (Graduate School of Business, Columbia University, New York, New York 10027)

Abstract

This paper has two purposes. The first is purely expository: to introduce stochastic interest-rate models and security-evaluation methods in a simple mathematical setting. Specifically, we assume the uncertainties in the model are represented by a discrete-time, finite-state Markov chain. Second, using this framework, we present a relatively simple model for the evaluation of mortgage-backed securities.

Suggested Citation

  • Paul Zipkin, 1993. "Mortgages and Markov Chains: A Simplified Evaluation Model," Management Science, INFORMS, vol. 39(6), pages 683-691, June.
    • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:6:p:683-691
    DOI: 10.1287/mnsc.39.6.683
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    Cited by:

    1. Lee, Pei-Ting & Rosenfield, Donald B., 2005. "When to refinance a mortgage: A dynamic programming approach," European Journal of Operational Research, Elsevier, vol. 166(1), pages 266-277, October.
    2. John Board & Charles Sutcliffe & William T. Ziemba, 2003. "Applying Operations Research Techniques to Financial Markets," Interfaces, INFORMS, vol. 33(2), pages 12-24, April.
    3. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    4. David Landriault, 2008. "On a generalization of the expected discounted penalty function in a discrete‐time insurance risk model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(6), pages 525-539, November.
    5. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    6. Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1689-1718, November.
    7. L. Douglas Smith & Canser Bilir & Vega W. Huang & Kuo-yao Hung & Mark Kaplan, 2005. "Citibank Models Credit Risk on Hybrid Mortgage Loans in Taiwan," Interfaces, INFORMS, vol. 35(3), pages 215-229, June.
    8. Johnson, Michael P. & Solak, Senay & Drew, Rachel Bogardus & Keisler, Jeffrey, 2013. "Property value impacts of foreclosed housing acquisitions under uncertainty," Socio-Economic Planning Sciences, Elsevier, vol. 47(4), pages 292-308.

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    Keywords

    finance; stochastic models;

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