This article shows that, in the presence of transaction costs payable by borrowers on refinancing, it is possible to construct a separating equilibrium in which borrowers with differing mobility select fixed rate mortgages (FRMs) with different combinations of coupon rate and points. We also show that, in the absence of such costs, no such equilibrium is possible. This provides a possible explanation for the large menus of FRMs typically encountered by potential borrowers, and suggests that the menu available at the time of origination should be an important predictor of future prepayment. We numerically implement the model, developing the first contingent claims mortgage valuation algorithm that can quantify the effect of self-selection on real contracts in a realistic interest rate setting. The algorithm allows investors to account for self-selection when valuing mortgages and mortgage-backed securities. It also, for the first time, allows lenders to determine the optimal points/coupon rate schedule to offer to a specified set of potential borrowers, given the current level of interest rates.