Competing Risks in Mortgage PD: Prepayment vs Default

Naive mortgage default rates understate credit risk because most mortgages leave the portfolio through prepayment long before they could default. If you divide defaults by the full cohort, loans that already left in good standing get counted as if they were still at risk. This is the competing risks problem, and correcting for it is the baseline expectation for any defensible mortgage PD modeling work.

The four ways a mortgage's life ends

A mortgage's life ends in one of a small number of ways. Naming them is the first step toward seeing why naive PD calculations get into trouble.

• Prepayment. The loan pays off without a credit event. Here that includes refinance (the borrower takes out a new loan on better terms and pays off the old one), sale (the borrower sells the home and pays off the loan from the proceeds), voluntary curtailment to zero (the borrower pays extra principal until the balance reaches zero, which is rare but possible) and maturity, where the borrower makes every scheduled payment and the loan ends on its contractual date.
• Default. In this framework a loan defaults when its current delinquency status reaches 6, meaning 180 or more days past due, or when its zero balance code falls in the FNC set of disposition codes. The loan ends with a credit event, and the LGD data fields populate at the disposition month.
• Modification. A loss mitigation action changes the loan's terms, such as the interest rate, the remaining term, the principal balance or a combination. The loan continues, but for credit risk modeling it has effectively restarted. The pre-modification spell ends and a new spell with different parameters begins.
• Still active. The observation window closes while the loan is still paying under its original terms. These loans are right censored. We know they have not defaulted yet, but we do not know what they will eventually do.

In any month, the next-period probabilities of these outcomes add up to one. The outcomes compete. Once one of them happens, the loan leaves the at-risk population for the others. The competing risks framework exists to handle exactly this structure.

Why prepayment dominates

In U.S. mortgages, prepayment is by a wide margin the dominant competing risk. Two structural drivers fuel it.

1. Rate-driven refinancing. When market rates fall well below the borrower's contract rate, the borrower has an economic reason to refinance. How strongly they respond depends on the size of the incentive and the cost of refinancing. Prepayment modeling for mortgage-backed security pricing is a separate discipline in its own right.
2. Life-driven prepayment. Moves, job changes, family changes, retirement or death can lead to a home sale whatever rates are doing. This has a fairly stable baseline frequency that varies with demographic mix and macro mobility conditions.

Together, these drivers mean a typical 30-year mortgage pool sees something like half of its loans prepay within the first 7 to 10 years. The share is sometimes higher during low-rate refinance waves and sometimes lower when rates are high. In any reasonable mortgage cohort, prepayments outnumber defaults many times over.

A worked example on 10,000 loans

Take 10,000 California loans from the 2019 Q1 cohort, with performance tracked through September 2025. This cohort lived through the 2020 to 2021 low-rate refinance wave, so its prepayment rate is high. The terminal outcomes are:

• Prepaid: 7,806 loans (78.06%)
• FNC default: 303 loans (3.03%)
• Modified without a later FNC default: 3 loans (0.03%)
• Still active at the cutoff: 1,888 loans (18.88%)

The buckets don't overlap by construction. FNC takes precedence, so a loan that defaulted and later prepaid counts as defaulted. Prepayment takes precedence over modification, so a loan that was modified and then prepaid counts as prepaid. Prepayments outnumber defaults roughly 25 to 1.

The naive PD is 303 divided by 10,000, or about 3%. The arithmetic is correct, but the result is misleading. Most of those 10,000 loans were no longer able to default by the time the window closed because they had already prepaid.

A simple at-risk correction keeps only loans that stayed available to default, meaning the 303 defaults plus the 1,888 loans still active. With the same numerator and this smaller denominator, the rate jumps to almost 14%, roughly five times the naive figure.

The two numbers answer different questions. If you want the probability that a representative loan from the cohort hit FNC default before the cutoff, the naive denominator is the right one. If you want the probability that a loan still at risk will go on to default, the naive number misleads, because it averages over loans that already left.

The simple at-risk correction shows the direction of the bias. It is not a PD estimate. It overcorrects, because some loans that prepaid would have prepaid before reaching 180 or more days past due even if every loan had been observed over its full potential life.

How survival analysis fixes the denominator

Competing risks survival analysis is statistical machinery built for this problem. Its core ideas are:

• Person time. Each loan adds to the at-risk population only for as long as it actually stays at risk. A loan observed for three years before prepaying adds three years of exposure. The naive calculation treats every loan as if it added the same exposure.
• Censoring. A loan that prepays at month 36 is censored at month 36 and drops out of the at-risk denominator after that point. A loan still active at the cutoff is right censored at the cutoff month. Censoring is what removes the prepayment and still-active bias.
• Monthly hazards. Instead of cohort-level rates, the framework asks how likely a loan that is still at risk this month is to default next month. It then integrates those hazards into cumulative probabilities. The Kaplan-Meier estimator weights each loan's contribution by the time it actually spent at risk.
• Two competing risks frameworks. Cause-specific hazards model each outcome's hazard separately and treat exits through the other outcomes as censored. Subdistribution hazards, the Fine-Gray framework, model the cumulative incidence of each outcome directly and account for the competing outcomes inside the model.

The bias always points the same way. Naive PDs understate risk, and competing-risks-corrected PDs are larger, sometimes much larger.

Modification complicates the picture

Modification is less common than prepayment, but it raises modeling issues that prepayment does not. The most common modifications cut the interest rate, extend the term, or forgive or defer part of the principal, which usually lowers the monthly payment. A modified loan is structurally a different loan, and the borrower's behavior under the original terms does not directly predict their behavior under the new ones.

There are two broad ways to treat it. One censors the loan at the modification month and brings it back as a fresh observation, using the modification month as its new origination date. The other treats modification as an outcome state alongside default and prepayment and continues modeling from the modified state. Each approach has tradeoffs.

In the 2019 cohort, modifications were very rare because most stressed loans either self-cured during the COVID forbearance window or rode out the stress. In a portfolio that includes crisis-era cohorts such as 2007 to 2009, modification rates would be much higher.

Why the bias matters for validation, capital and CECL

• Validation. When a model risk management team reviews a PD scorecard, one of the first methodology questions is how prepayment was handled in the calibration sample. A model trained on naive cohort default rates gives PD estimates that are biased downward.
• Capital. Basel IRB capital formulas take PD estimates as direct inputs, so a downward-biased PD produces a downward-biased capital requirement.
• CECL reserves. The CECL standard requires lifetime expected credit losses, measured on a pooled basis for loans that share similar risk characteristics. Because lifetime losses add up PD estimates over the loan's remaining life, any PD bias compounds over that horizon.
• Benchmarks. A substantial part of the academic mortgage default literature, notably Deng, Quigley and Van Order (2000), treats default and prepayment as competing risks in a survival framework. Comparing a naive rate against them is an apples-to-oranges comparison.

Sample size matters too. About 300 defaults are enough to show the direction of the bias, but not enough to fit a properly calibrated PD model or survival regression. That calls for a larger multi-vintage sample weighted toward crisis vintages, where defaults are dense.

A reading habit worth building

Whenever you read a mortgage default rate in a research paper, regulatory report, vendor pitch deck or internal validation document, first ask how prepayment was handled. If the document doesn't say, the treatment is almost always naive, and the implied default rate is almost always too low compared with what survival analysis would produce.

Key takeaways

• A mortgage can prepay, default or be modified, and loans still active at the cutoff are right censored.
• Prepayment dominates. In a 10,000-loan 2019 cohort, 7,806 loans prepaid and 303 defaulted, roughly 25 to 1.
• Dividing defaults by total cohort size understates the default rate for loans that stayed at risk.
• A back-of-the-envelope at-risk correction raised the rate from about 3% to almost 14%. It shows the bias direction but overcorrects, so it is not a PD estimate.
• Survival analysis with censoring, cause-specific hazards or Fine-Gray is the proper correction.
• Competing risks treatment matters for validation, Basel IRB capital, CECL reserves and benchmark comparisons.