Mortgage Modification and the Decision to Strategically Default: A Game Theoretic Approach

By Collins, Andrew J.; Harrison, David M. et al. | The Journal of Real Estate Research, July 1, 2015 | Go to article overview

Mortgage Modification and the Decision to Strategically Default: A Game Theoretic Approach


Collins, Andrew J., Harrison, David M., Seiler, Michael J., The Journal of Real Estate Research


(ProQuest: ... denotes formulae omitted.)

Various stakeholders across the United States continue to express frustration and mounting confusion as to why the residential real estate credit market remains stagnant long after the initial housing crisis of September 2008. Evidence of the continuing tightness within this market is readily observable by examining mortgage origination statistics. For example, the Mortgage Bankers Association (2012) reports that while total U.S. mortgage originations averaged over $3 trillion per year from 2002 to 2007, since 2008 they have failed to reach the $2 trillion threshold in any single year. While this decline in origination volume is clearly observable, a complete understanding of the underlying root causes is not.

One emerging thematic question throughout the continuing analysis of this housing crisis is whether, and to what extent, issues of strategic default materially influence housing market outcomes. For example, Wyman (2010), FICO (2011), and Guiso, Sapienza, and Zingales (2013) all document that strategic mortgage default, the decision of the borrower to exercise his put option (stop paying his mortgage) even though he has the financial means to maintain his payments, continues to rise. Interestingly, at the same time, lenders appear to be unwilling to modify loans, a decision that has also caused much consternation among both policymakers and market participants.1 Despite such governmental program efforts as the Home Affordable Modification Program (HAMP) and the Home Affordable Refinance Program (HARP), all efforts to date remain unsuccessful in stimulating the flow of funds through the mortgage markets and improving loan performance outcomes. In fact, a July 2013 SigTarp Report states that almost half of all HAMP loan modifications have re-defaulted. The report further suggests the ''Treasury should conduct in-depth analysis and research to determine the causes of redefault of HAMP permanent mortgage modifications and the characteristics of loans or the homeowner that may be more at risk for redefault.''2

Recognizing that the decision of the borrower to strategically default on his mortgage and the lender's decision of whether or not to modify a loan are extremely complex and inter-related, we take an entirely new approach. Specifically, we construct a game theoretic model that identifies both the economic and behavioral incentives for borrowers and lenders to act in their own best interests. Researchers have generally examined only the economic incentives of default, implicitly assuming wealth is the only materially relevant incentive of the borrower.3 However, more recently, Seiler, Seiler, Lane, and Harrison (2012), Guiso, Sapienza, and Zingales (2013), and Seiler (2014a, 2014b) document myriad emotional considerations as well.

From a game theoretic perspective, we also make a contribution in that most game theory models are designed in a very simplistic fashion (using, for example, a 2^2 normal-form design) in which the reader is asked to accept the assumption that the over simplified game can be applied to understand real world phenomenon. We take a different approach. Our game theoretic model is far more complex, built based on a robust set of variables (and their relations) found in previous studies to influence borrower and lender decision-making. Using a backward inductive approach, the resulting subgame perfect equilibrium strategies we achieve are thus based on the specific value inputs from past studies. To learn how sensitive our model is to the results from these past studies, we then focus on the key inputs of our model and conduct a Latin hypercube sampling (LHS) sensitivity analysis.

The central contribution of this investigation is our finding that it is Pareto optimal for the lender to modify a mortgage only in rare instances. This result is surprising in the sense that many people fault lenders for not modifying more loans, but is likely not surprising to those in the lending industry since they appear to have reached the same conclusion as we do. …

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