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The Journal of Structured Finance

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Automatic Spline Knot Selection in Modeling Mortgage Loan Default Using Shape Constrained Regression

Guangning Xu, Geng Deng, Xindong Wang and Ken Fu
The Journal of Structured Finance Summer 2021, jsf.2021.1.123; DOI: https://doi.org/10.3905/jsf.2021.1.123
Guangning Xu
is a vice president at Wells Fargo & Company in Charlotte, NC
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Geng Deng
is a senior vice president at Wells Fargo & Company in McLean, VA
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Xindong Wang
is a senior vice president at Wells Fargo & Company in McLean, VA
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Ken Fu
is a managing director at Wells Fargo & Company in McLean, VA
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Abstract

In mortgage default modeling, many of the key variables, such as loan age, FICO score, Debt-to-Income ratio (DTI), and Loan-to-House-Value ratio (LTV), have nonlinear relationships with the target default rates. Experienced modelers generally apply a spline transformation with knots to the individual variables. In this article, we introduce the Quantile-based Shape Constrained Maximum Likelihood Estimator (QSC-MLE), which features an automatic spline knot selection in a mortgage default model. QSC-MLE is an enhanced variant of SC-MLE (Chen and Samworth 2016) used in combination with a quantile-based knots set, to effectively process large datasets. QSC-MLE requires generic shape information of the inputs, for example, the monotonicity or convexity of the FICO score, DTI, and LTV to capture any nonlinear effects. We show that the new default model considerably improves the accuracy of the out-of-sample prediction in comparison with the logistic regression and the Cox proportional hazards model. Moreover, the model conveniently generates component-wise spline functions, which facilitates the interpretation of the default rate response to the input variables.

TOPICS: MBS and residential mortgage loans, quantitative methods, statistical methods, credit risk management, performance measurement

Key Findings

  • ▪ A mortgage default model using the Quantile-based Shape Constrained Maximum Likelihood Estimator (QSC-MLE), which features automatic spline knot selection.

  • ▪ QSC-MLE constructs shape-constrained spline functions to capture nonlinear effects of model inputs.

  • ▪ The new default model considerably improves the accuracy of the out-of-sample prediction.

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The Journal of Structured Finance: 28 (1)
The Journal of Structured Finance
Vol. 28, Issue 1
Spring 2022
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Automatic Spline Knot Selection in Modeling Mortgage Loan Default Using Shape Constrained Regression
Guangning Xu, Geng Deng, Xindong Wang, Ken Fu
The Journal of Structured Finance Jun 2021, jsf.2021.1.123; DOI: 10.3905/jsf.2021.1.123

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Automatic Spline Knot Selection in Modeling Mortgage Loan Default Using Shape Constrained Regression
Guangning Xu, Geng Deng, Xindong Wang, Ken Fu
The Journal of Structured Finance Jun 2021, jsf.2021.1.123; DOI: 10.3905/jsf.2021.1.123
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  • Article
    • Abstract
    • MODEL MORTGAGE DEFAULT RATE
    • LOAN-LEVEL DATA DESCRIPTION
    • DATA PROCESSING
    • AUTOMATIC KNOT SELECTION WITH QSC-MLE
    • CONNECTING THE COXPH MODEL WITH THE LOGISTIC REGRESSION
    • MORTGAGE DEFAULT MODEL USING QSC-MLE
    • CONCLUSION
    • APPENDIX
    • ENDNOTES
    • REFERENCES
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  • PDF (Subscribers Only)

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