THE VALUATION OF GNMA MORTGAGE-BACKED SECURITIES: A CONTINUOUS TIME, INTEREST-DEPENDENT CLAIMS APPROACH
Abstract
The Government National Mortgage Association (GNMA) guarantees the timely payment of principal and interest on standardized securities collateralized by a pool of mortgages. Previous studies based on yield comparisons suggest that the market for GNMA securities is characterized by pricing errors. But, a meaningful analysis requires a pricing model which is couched in the context of a model of the term structure of interest rates under uncertainty. This thesis derives a pricing model for GNMA securities by extending the recent theories of the term structure of interest rates, which value long term bonds as a function of the stochastic current interest rate, to include the unique characteristics of the GNMA security. The results of this study should be of interest to (1) investors that own or are considering purchasing GNMA securities, (2) the financial institutions that issue them, (3) the government agencies responsible for regulating this market and supporting housing finance programs, and (4) the financial institutions that create GNMA investment trusts. The pricing model for GNMA securities is logically derived from a well-specified set of assumptions about the characteristics of the capital market and the behavior of individuals. By structuring the problem we are able to identify the characteristics of the GNMA security which have the greatest influence on its value. In particular, given the model of the term structure of interest rates, the examination of the GNMA security shows that the level of the risk-free rate of interest, the prepayment (call) option, the expected rate of non-interest rate dependent prepayments, and the interest rate elasticity of the GNMA security are the most important determinants of its value, risk, and expected return. The pricing model does not have a known analytical solution, therefore, tables of the value of a GNMA security as a function of its time to maturity and the riskless rate of interest are obtained by numerical methods. In addition, the properties of the GNMA pricing model are examined by comparing the numerical solutions for the value of the GNMA security with the numerical solutions for other fixed interest rate securities. These comparisons allow us to examine the magnitude of the effects of the prepayment option, non-interest rate dependent prepayments, and amortization payments on the value of a GNMA security. One of the interesting results of the theoretical and numerical analysis of the GNMA security is that the prepayment option reduces the value, risk, and expected return of the GNMA security relative to an otherwise identical noncallable amortized loan. Intuitively, a GNMA security is a hedged portfolio where one prepayment option is written against each amortized loan in the portfolio. Hence, a GNMA security should be less risky and, therefore, have a lower expected return than an amortized loan. However, the computed yield on a GNMA security will exceed that of an amortized loan because the scheduled cash flows from the two securities are identical while the value of a GNMA security is less than the value of an amortized loan by the value of the call option. Thus, a comparison of the yields on the two securities cannot even correctly identify the security with the largest expected return.
Degree
Ph.D.
Subject Area
Business community
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