Abstract
This paper presents a reduced-form barrier model for the optimal principal reset in a loan modification, thereby maximizing the loan value to the lender bank and minimizing the likelihood of foreclosure by the homeowner. Reducing the loan-to-value (LTV) ratio will reduce the present value of future payments on the loan, but will also reduce the probability of default, thereby saving foreclosure losses. The optimal trade-off of these two countervailing effects will pinpoint the optimal LTV at which the loan must be reset. We present a reduced-form barrier option decomposition of the loan value that makes the optimization of LTV easy to implement. An extension of the model is shown to account for varying growth rate assumptions about house prices. The model in this paper accounts for the homeowner's ability to pay and willingness to pay, and uses the framework to model shared-appreciation mortgages (SAMs).
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