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Optimal Exercise of Mortgage Options: Default and Refinancing

We are the first to provide closed-form analytic solutions for the joint problem of mortgage refinancing and default. Our solution takes into account reduction in mortgage interest rates and the "cash-out" motive for refinancing. The model predicts how long the households are likely to wait before defaulting, even if default is costless, when their mortgage goes "underwater" and we also derive the optimal default strategy under costly default. Our solutions for default are generally consistent with empirical works on mortgage default. Although our refinancing results are comparable to other closed-form solutions and numerical models, we offer additional results for "cash-out" refinancing.