Mortgage-Backed Securities: Products, Structuring, and Analytical Techniques, 2nd Edition

APPENDIX

An Option-Theoretic Approach to Valuing MBS^*

Throughout this book, the importance of understanding the underpinnings of prepayment behavior has been emphasized as well as their effects on mortgage-backed security valuations. Prepayment speeds are the dominant consideration in MBS analysis. The evolving nature of borrower behavior was first described in Chapter 4. In Chapters 10 through 12, how prepayment projections are taken into account in valuation, relative value, and risk models was examined. Most prepayment models in current use are econometric models that have been calibrated to historical prepayment data. Although the right to refinance a mortgage is widely recognized as a call option granted by the lender to the homeowner, option-theoretic models are not currently used in prepayment modeling despite their use for valuing corporate bonds and agency debentures with embedded option. There are two reasons often cited for not employing option-theoretic models to value an MBS: (1) Most borrowers do not exercise the option optimally; and (2) empirically it has been found that option-based models are not able to explain observed prices of MBS.

In this appendix, we describe a relatively new approach for valuing MBS developed by Kalotay, Yang, and Fabozzi (KYF hereafter)¹ and show how it can be used to value pools of mortgages and MBS issued by Ginnie Mae, Fannie Mae, and Freddie Mac (i.e., high-grade pools, where neither the credit risk of the homeowner nor that of the ...