A two-factor, stochastic programming model of Danish mortgage-backed securities

Søren S. Nielsen, Rolf Poulsen

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    Danish mortgage loans have several features that make them interesting: Short-term revolving adjustable-rate mortgages are available, as well as fixed-rate, 10-, 20- or 30-year annuities that contain embedded options (call and delivery options). The decisions faced by a mortgagor are therefore non-trivial, both in terms of deciding on an initial mortgage, and in terms of managing (rebalancing) it optimally.We propose a two-factor, arbitrage-free interest-rate model, calibrated to observable security prices, and implement on top of it a multi-stage, stochastic optimization program with the purpose of optimally composing and managing a typical mortgage loan. We model accurately both fixed and proportional transaction costs as well as tax effects. Risk attitudes are addressed through utility functions and through worst-case (min-max) optimization. The model is solved in up to 9 stages, having 19,683 scenarios. Numerical results, which were obtained using standard soft- and hardware, indicate that the primary determinant in choosing between adjustable-rate and fixed-rate loans is the short-long interest rate differential (i.e., term structure steepness), but volatility also matters. Refinancing activity is influenced by volatility and, of course, transaction costs.
    Original languageEnglish
    JournalJournal of Economic Dynamics and Control
    Volume28
    Issue number7
    Pages (from-to)1267-1289
    ISSN0165-1889
    Publication statusPublished - 2004

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