Optimal Recursive Refinancing and the Valuation of Mortgage-Backed Securities

We study the optimal recursive refinancing problem where a borrower minimizes his lifetime mortgage costs by repeatedly refinancing when rates drop sufficiently. Key factors affecting the optimal decision are the cost of refinancing and the possibility that the mortgagor may have to refinance at a premium rate because of his credit. The optimal recursive strategy often results in prepayment being delayed significantly relative to traditional models. Furthermore, mortgage values can exceed par by much more than the cost of refinancing. Applying the recursive model to an extensive sample of mortgage-backed security prices, we find that the implied credit spreads that match these prices closely parallel borrowers’ actual spreads at the origination of the mortgage. These results suggest that optimal recursive models may provide a promising alternative to the reduced-form prepayment models widely used in practice.