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Fixed rate mortgage valuation using a contingent claims approach
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In this thesis a methodology based on the Cox, Ingersoll and Ross (1985a) equilibrium model is developed in order to evaluate British fixed rate mortgage contracts. The spot interest rate and the house price are used as state variables and it is assumed that the borrowers' decision making process is driven by a purely economic rationale. In other words, the framework can be classified as a frictionless model. Both, repayment and ("without profits") endowment mortgages, with specifications based on the common provisions inhert in the British mortgage market," are evaluated. The model also provides values for mortgage indemnity guarantees, the corresponding coinsurance, the embedded options to tenninate the loan through prepayment or default and the bond·type annuity corresponding to the mortgage monthly payments.
As the partial differential equation that gives the values of the different features of the mortgage contracts does not have a closed·form solution, an explicit finite difference method was used to solve. the problem. Numerical results for the value of the different components of the mortgage contracts were detennined under different economic scenarios. The relationship between the evolution of the parameters used to characterise the economic environment and the value of the different mortgagere· lated assets is in line with the underlying economic intuition.
The comparison between repayment and endowment mortgages leads to the conclusion that the value of the prepayment option tends to be higher in the latter case.
This implies that, ceteris paribus, the borrower needs to pay more in order to reach an equilibrium combination in "without profits" endowment mortgage contracts.
Changes in the contractual features inherent to the specification of the mortgage products lead to different equilibrium coupon rates and different values for the mortgage-related assets. Consequently, studies that do not take into account fundamental features embedded in mortgage contracts, like the prepayment and the default options or the early redemption penalty, tend to produce biases that might lead
to misleading conclusions.
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Pereira, José António de Azevedo (1997). " Fixed rate mortgage valuation using a contingent claims approach". Tese de Doutoramento. Manchester Business Scholl.