[Andrew Davidson Co] The Relationship Between the Yield Curve and Mortgage Current Coupon.pdf

April 2001Q UA NT IT AT IV E PE RS PE CT IV ES .. THE RELATIONSHIP BETWEEN THE YIELD CURVE MORTGAGE CURRENT COUPON By Eknath Belbase, PhD Dan Szakallas QUANTITATIVE PERSPECTIVES .. Introduction A dynamic prepayment model is an integral component of an option- adjusted valuation and risk management framework. Such a model typically requires a forecast of future mortgage rates and possibly index rates such as prime and COFI. Term structure models are used to forecast rates of various maturities on the Libor/Swap yield curve or on the Treasury yield curve. It is therefore necessary to model mortgage rates as functions of these yield curve rates. In this article we discuss the Andrew Davidson Co., Inc. approach to forecasting mortgage current coupon as a function of either Treasury or swap rates. Along the way, we compare several statistical approaches to the problem and discuss software implementation issues. In addition, we examine the relative performance of using a single Treasury rate, two Treasury rates or two swap rates to forecast mortgage current coupon rates. The current coupon is the semi-annual equivalent of the parity-price interpolated coupon, based upon the two bonds whose price brackets the parity price. The mortgage current coupon rates used were based on month-end closing prices. The types used are Fannie Mae 7, 15 and 30 year, Ginnie Mae I 15 and 30 year, and Freddie Mac 5, 7, 15 and 30 year. These rates can be viewed on Bloomberg, e.g. MTGE FNCL Index for the FNMA 30 rate. APRIL 2001 THE RELATIONSHIP BETWEEN THE YIELD CURVE MORTGAGE CURRENT COUPON By E. Belbase, PhD D. Szakallas Data 2The Treasury rates used were month-end closing par bond-equivalent yields for the two and ten-year on-the-run Treasuries (GT2 govt and GT10 govt) or the two and ten-year zero coupon Treasuries (STRP02Ygovt and STRP10Ygovt). The swap rates used were either the two and ten-year Libor rates (USSWAP2 index and USSWAP10 index) or the two and ten-year zero coupon Libo