Counting Processes for Retail Default Modeling

28 Pages Posted: 16 Jun 2016

See all articles by Nicholas M. Kiefer

Nicholas M. Kiefer

Cornell University - Department of Economics

C. Erik Larson

Promontory Financial Group

Date Written: August 26, 2015


Counting processes provide a very flexible framework for modeling discrete events that occur over time. Estimation and interpretation are easy, and links to more familiar approaches are at hand. The key is to think of data as “event history”, a record of times of switching between states in a discrete state space. In a simple case, the states could be default/nondefault. In other models relevant to credit modeling, the states could be credit scores or payment statuses (30 days past due (dpd), 60 dpd, etc). Here, we focus on the use of stochastic counting processes for mortgage default modeling, using data on high loan-to-value mortgages. Borrowers seeking to finance more than 80% of a house’s value with a mortgage usually either purchase mortgage insurance (MI), allowing a first mortgage greater than 80% from many lenders, or use second mortgages. Are there differences in performance between loans financed by these different methods? We address this question in the counting process framework. In fact, MI is associated with lower default rates for both fixed- and adjustable-rate first mortgages.

Keywords: Survival Analysis, Hazard Functions, Censored Data, Mortgage Insurance, Risk Modeling, Martingales

Suggested Citation

Kiefer, Nicholas M. and Larson, C. Erik, Counting Processes for Retail Default Modeling (August 26, 2015). Journal of Credit Risk, Vol. 11, No. 3, Pages 45–72, 2015, Available at SSRN:

Nicholas M. Kiefer (Contact Author)

Cornell University - Department of Economics ( email )

490 Uris Hall
Ithaca, NY 14853-7601
United States

C. Erik Larson

Promontory Financial Group ( email )

1201 Pennsylvania Avenue, NW
Suite 617
Washington, DC 20004
United States
202-384-1200 (Phone)


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