A Comparison of Alternative Models for Pricing GNMA Mortgage‐Backed Securities

Abstract

SINCE THE ISSUANCE OF the first Government National Mortgage Association (GNMA) mortgage-backed pass-through security in February 1970, the total amount of GNMAs issued has grown to over $105 billion. In terms of their trading volume, GNMA securities are the most actively-traded class of long-term fixedrate instruments. However, this gross volume statistic masks the fact that GNMAs are not homogeneous securities. They differ by coupon interest rate and remaining term to maturity. There is also a widely-held belief [12] and some evidence [7] that GNMAs differ according to their expected prepayment rates. The bulk of the trading volume in GNMAs is comprised of newly-issued securities. New securities are generally issued at the Federal Housing Administration (FHA) maximum interest rate and have terms to maturity of 30 years. While most GNMA trading is comprised of new issues, the bulk of the outstanding securities is comprised of old securities whose coupon rates may differ from the current FHA ceiling and whose remaining terms to maturity are less than 30 years. This raises a pricing problem for GNMA security dealers, portfolio managers, financial institutions that hold large portfolios of GNMA securities, and other potential GNMA investors. Up-to-date market price quotes are available for new issues, but quotes for old ones are not so readily available. Thus, potential traders confront the problem of pricing these infrequently traded securities. The problem of pricing GNMA securities was initially addressed by Curley and Guttentag [5]. They presented a model for the pricing of GNMAs that was an imaginative and important extension of the then widely-used average life procedure. The particular innovation of their model was to incorporate estimates of the prepayment probabilities to determine expected future cash flows. Through simulation and sensitivity analysis, Curley and Guttentag (hereafter C & G) compared prices generated by their model with those generated by the traditional average life procedure. In his discussion of the C & G paper, Brealey [1] encouraged the authors to extend their model to incorporate uncertainty and to value explicitly the call options attached to the underlying mortgage loans. In a previous paper [6], we