Pricing the default and prepayment risks of mortgages: An option pricing theoretic approach and an empirical hazard rate analysis

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




James R. Follain


Pricing, Default, Prepayment risks, Mortgages, Option pricing, Hazard rate

Subject Categories

Business | Economics | Finance and Financial Management


This study proposes a theoretic interpolation-based lattice model to price the prepayment and default option values of a fixed-rate mortgage, and uses a hazard model to empirically investigate the prepayment and default behavior of FHA insured multifamily loans.

A "pure" option-pricing model is used to price the value of prepayment and default options. Prepayment is treated as an American call option and default as a put option. An interpolation-based lattice model is used to solve backward the prepayment and default option values. Unlike the traditional lattice methods, in which the total number of nodes grows geometrically with time steps when stochastic volatility is present, the number of nodes in this model grows linearly with each variable dimension. The common problem of "non-recombination" is handled through interpolation. This approach can easily accommodate early exercise of option, which is one of the important features of mortgage termination. Another advantage of this approach is that it does not require transformation of the original processes. Therefore, alternative underlying processes can be easily adapted to this model. Finally, numerical results are presented and compared with the results of another lattice approach to demonstrate the accuracy and efficiency of the model.

Research under the empirical investigation is to examine the prepayment and default behavior of FHA insured multifamily mortgages. In most literature, analyses of prepayment and default are conducted separately. However, default and prepayment are clearly not statistically independent, and may actually be related. Given the competing nature of prepayment and default risks, a competing risk hazard model is employed to estimate the conditional prepayment and claim rates for multifamily mortgages simultaneously. Furthermore, the risk preferences and idiosyncrasies across borrowers vary widely. This study presents a competing risk hazard model that accounts for the unobserved heterogeneity among borrowers and estimates the unobserved heterogeneity simultaneously with the parameters of the prepayment and default functions. Finally, the study compares and tests the practical importance of incorporating the competing risk feature and the unobserved heterogeneity in the estimation. The data set used in this study includes one of the largest FHA insured multifamily mortgages: the market rate 221d(4) New Constructions and Substantial Rehabilitation program (OMI). The data set includes information on OMI loans originating from 1965 to 1995. Maximum likelihood estimation is used to estimate the hazard model.


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