Optimal Mortgage Loan Diversification | Kourosh Marjani Rasmussen, Stavros A. Zenios
| | Abstract | 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. | | Keywords | Mortgage loans products, CVaR modeling, stochastic programming. | | Type | Journal paper [Submitted] | | Journal | Quantitative Finance. | | Year | 2007 Month November | | Electronic version(s) | [pdf] | | BibTeX data | [bibtex] | | IMM Group(s) | Operations Research |
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