In this study, we construct a compartmental model that tracks the different states and their respective hazards for typical mortgage loans. We consider that an active mortgage loan could become delinquent in light of either common systemic risks or idiosyncratic risks in the job market. These two groups of employment-related perils jeopardize the sources of income underlying the mortgage monthly payments to lenders and could hurt the ability of mortgage loan borrowers to retire their debt. We also contemplate ongoing risks of a collapse in the housing market, which might transform the mortgage loan to be "underwater" and consequently diminish borrowers' incentives to service the outstanding balance. We develop the necessary derivations, illustrate the functionality of the model over several hypothetical simulations and sensitivity analyses, suggest variable estimation specific guidelines, conclude, and discuss potential extensions for the proposed model.
Keywords: Differential equations; Failure risks; Mortgage loans; Simulations; States of nature.
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