Optimal Mortgage Loan Diversification

Kourosh Marjani Rasmussen, Stavros A. Zenios

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    Homebuyers in several countries may finance the purchase of their properties using different variants of either adjustable-rate mortgages (ARMs) or fixed-rate mortgages (FRMs). The variety and complexity of these loan products poses a risk management task for mortgage bank advisors to recommend the right mortgage loan strategy for the individual mortgagor; almost all mortgage banks advise their customers to take a single loan product. This argument is often justified by the fact that trade frictions make it unattractive to hold a portfolio of loans as a private home owner. Even with transaction costs, however, we show in this paper that most mortgagors with some degree of risk aversion benefit from holding a mortgage portfolio. To do so we develop a multistage Mean--Conditional Value at Risk (MCVaR) model to consider the risk of the mortgage payment frequency function explicitly using a coherent risk measure. In addition to the diversification benefits we also show that the multistage model produces superior results as compared to single period models and that the solutions are robust with regards to changes in uncertainty parameters in particular for risk averse mortgagors. Finally, we show how the model can be used to calculate fair premia for adjustable rate mortgages with interest rate guarantees (caps) which are becoming increasingly popular as a hybrid product between the existing ARM and FRM mortgages.
    Original languageEnglish
    JournalQuantitative Finance.
    Publication statusSubmitted - 2008


    • Mortgage loans products
    • stochastic programming
    • CVaR modeling


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