The mortgage market in the United States is broadly based and vertically deep. From the most general perspective, we can separate the primary mortgage market from the secondary market. The primary mortgage market originates loans to borrowers (the “mortgagors”) and sells the loans into the secondary market for securitization. Not all mortgage loans are sold into the secondary market for securitization. In this case, banks or financial institutions in general, are direct investors in these mortgage loans.

The traditional 30 year fixed rate mortgages contain a call option to prepay without penalty and the put option to default. Mortgage lenders are selling embedded American straddles (combined call and put options) to the mortgagors. However, the mortgagors do not exercise these options efficiently, and, moreover, their behavior is heterogeneous and cannot be represented by a typical mortgagor. The average refinancing and defaulting behavior of a portfolio of mortgages has to be described in terms of the age of the mortgage, seasonality, burnout level, underwriting standards, and credit scores in order to value the mortgages. Such risks have to be priced into the valuation of the mortgage. Therefore, the option adjusted spread has to be estimated to determine the market pricing of the risks embedded in these mortgage loans. In sum, valuation of mortgage loans must take into consideration three salient features: the embedded options, inefficiency in exercising the options, and the market price of mortgage loan risks.

Despite the importance of the subject, scant research papers address all three salient features. Chen (1996), Levin(2005), Cheyette (1996), and Longstaff (2002) determine the call option by the optimal exercise rule, incorporating a measure of refinancing inefficiency. However, these papers fail to model aging, seasonality and other salient features of the mortgagors’ heterogeneous behavior into account. While Schwartz and Torous (1989, 1992, 1993), Boudoukh et al (1997), and Hayre (2001) use econometrically estimated prepayment models to capture the factors affecting the mortgagors' behavior in prepayment, they ignore defaults. They fail to identify default and prepayment as separate events, thus missing the insights into the mortgagors’ behavior that provide a more accurate valuation model, even for mortgage securities with full credit guarantees.

Incorporating default risk in mortgages is challenging. There is voluminous literature on valuing defaultable bonds, yet sparse literature on mortgages. Credit risk literature on bonds uses the structural model and the reduced form models to value the default risk. However, such approaches cannot be adapted to value mortgage loans because of the complex interactions of the prepayment and default risks with the mortgagors’ heterogeneous behavior. In addition, underwriting requirements and the borrower’s behavior in the case of mortgage loans are strictly different than corporate bonds.

A second genre of mortgage termination research is inferential (and normative) in nature. It attempts to take the perspective of the borrower toward asking the question, 'why do borrowers default or prepay their mortgage? For example, there is a growing literature in modeling the competing prepayment and default risks. Downing et al. (2002) focuses on the housing index to specify the structural model in default risk. Calhoun and Deng (2002), Deng, Quigley and Van Order (2000), and Dunsky and Pennington-Cross (2003) present a method to estimate the mortgagors’ behavior with these competing options. However, these papers fail to consider the question of mortgage valuation.

One contribution of this paper is that we model the termination risks from the borrowers' perspective and use the model to value the mortgages. We propose a valuation model of 30 year fixed rate mortgage loans, which uses a multinomial logit model to specify the mortgagors’ behavior and a two factor arbitrage-free interest rate model to specify the interest rate movements. The model also specifies the determinants of the option adjusted spread for mortgage loans using the mortgage origination information.

Another contribution of the paper is to provide insights into the question: given the conceptual structure of the econometric model, what factors account for the default event and the prepayment event? At the borrower level of investigation, we cannot overlook the competing risks of the nature of the default and prepayment events. In particular, during each month of themortgage, the borrower must choose between making their scheduled mortgage payment, prepaying their mortgage (owing to refinance, or move) or failing to make the scheduled payment. The default and prepayment events are mutually exclusive in that the borrower is unable to default on a prepaid loan or prepay on a defaulted loan.

The main empirical results based on our sample data and valuation model are as follows. While the mortgage age, seasonality, burn-out factor, and credit score at origination are important factors affecting both the prepayment and default experiences, their impacts are different. The results highlight the competing nature of the two options, and the importance of separating the conditional default rate from the conditional prepayment rate. The model can provide reasonable explanatory power for both the conditional prepayment rate and the conditional default rate. The prepayment model is shown to be reasonable in fitting the historical prepayment and default experiences.

The valuation model is then analyzed with the following three main results. The option adjusted spreads vary significantly across the loans, suggesting that the market price of mortgage loan risk is not necessarily cohort or pool specific, but rather borrower/loan specific. Our results show that if the recovery ratio is between 90%-95%, the OAS at origination would not tighten or widen with the FICO scores above 700. However, for lower FICO scores, the option adjusted spread is sensitive to the assumed recovery ratio in the valuation. This result is important to determine the value of a mortgage loan where there is no active securities market to provide the market price. The OAS model can be used instead.

The economic cost of guaranteeing the default risk depends primarily on the principal amount borrowed, the loan to value ratio and the FICO score. The guarantee price elasticities to the original loan size and the FICO scores are -0.44 and -11.89 respectively. The guarantee model is useful for any financial institutions which provides credit risk guarantees and for banks to hedge their credit positions. And the duration of a mortgage loan is then studied over a range of recovery rates. Our findings indicate that high OLTV loans originated to low credit score borrowers will have shorter duration relative to all other mortgages when fully guaranteed. However, for an investor in whole loans with an expected recovery rate of 80%, this result does not hold. This result has broad implications to banks and asset management in managing the interest rate risks of a risky mortgage portfolio.

The paper proceeds in five sections. The next section describes the empirical implementation of the model. Section 3 describes the empirical results of the prepayment/default model. Section 4 provides the results of valuing the mortgage loans. And section 5 contains the implications and conclusions.

Download
PDF Ebook Valuing Fixed Rate Mortgage Loans with Default and Prepayment Options