Model for optimizing lender's decision on dealing with collateral of defaulted mortgage

Shu Ling Chiang and Ming Shann Tsai

Journal of Financial Research, 2025, vol. 48, issue 2, 785-806

Abstract: In this article, we describe a comprehensive model for obtaining a critical gross recovery rate (GRR) for the short sale of a defaulted mortgage. Our model includes the following factors: settlement period, settlement cost, discounted sale/auction price, opportunity cost, failure probability of the short sale, and lender's willingness for the short sale. The results show that using the short sale yields a lower settlement cost, shorter settlement period, but higher loss given default (LGD). The real GRR of a short sale is about 8%–9% less than the critical GRR calculated from our model. This means the lender's willingness for the short sale is high in reality. The sensitivity analyses show that the lender's likelihood of approving a short sale is low if the settlement cost, contract rate, interest rate, and failure probability of the short sale are high. The greater the expected LGD of a foreclosure, the stronger the lender's willingness to approve the short sale. Also, a higher GRR of short sale leads to a lower expected LGD of short sale. This increases the probability of approval for the short sale. Finally, the Home Affordable Foreclosure Alternatives (HAFA) program helped struggling homeowners successfully use a short sale as an alternative to foreclosure, but the HAFA program became less effective as housing prices went up. Our model and analyses should help lenders make the optimal decision about how to efficiently deal with the collateral from a defaulted mortgage to mitigate their LGD.

Date: 2025
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