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A Steady State Solution to a Mortgage Pricing Problem

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  • Dejun Xie

Abstract

This paper considers a mortgage contract where the borrower pays a fixed mortgage rate and has the choice of making prepayment. Assume the market interest follows the CIR model, a free boundary problem is formulated. Here we focus on the infinite horizon problem. Using variational method, we obtain an analytical solution to the problem, where the free boundary is implicitly given by a transcendental algebraic equation.

Suggested Citation

  • Dejun Xie, 2009. "A Steady State Solution to a Mortgage Pricing Problem," Papers 0909.5389, arXiv.org.
  • Handle: RePEc:arx:papers:0909.5389
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    File URL: http://arxiv.org/pdf/0909.5389
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    1. Xinfu Chen & John Chadam & Lishang Jiang & Weian Zheng, 2008. "Convexity Of The Exercise Boundary Of The American Put Option On A Zero Dividend Asset," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 185-197.
    2. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    3. James F. Epperson & James B. Kau & Donald C. Keenan & Walter J. Muller, 1985. "Pricing Default Risk in Mortgages," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 13(3), pages 261-272.
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