Probability of default (PD) is the estimated likelihood that a borrower will fail to meet its debt obligations within a given period, most often one year. It is expressed as a percentage, so a PD of 1.5% means that out of a large group of similar borrowers, about 15 in every 1,000 are expected to default over the year. Banks, rating agencies, bond investors and fintech lenders use PD to price loans, set limits and measure credit risk.
PD answers only the question of whether default happens. How much is lost when it does is measured by loss given default, and how much is owed at that moment by exposure at default. Multiplied together the three give expected credit loss. PD is closely tied to a credit rating or internal grade, since each grade on a bank's scale is mapped to a PD band.
Probability of default in plain terms
A weather forecast that says "30% chance of rain tomorrow" does not mean it will rain for 30% of the day. It means that on days that look like tomorrow, rain falls about three times in ten. Probability of default works the same way for borrowers.
A lender looks at a borrower's income, debts, payment history and industry, and compares it with thousands of earlier borrowers who looked similar. If two in every hundred of those earlier borrowers stopped paying within a year, the new borrower is given a PD of about 2%. Nobody knows whether this particular borrower will default; the number simply describes the odds for someone in their position.
Defining default
A PD is only meaningful once "default" is defined. Under the Basel framework a default occurs when the obligor is more than 90 days past due on a material obligation, or when the bank considers the obligor unlikely to pay in full without recourse to actions such as selling collateral. Signs of unlikeliness to pay include a distressed debt restructuring, a bankruptcy filing, or a large specific provision. Rating agencies use their own definitions, which focus on missed payments and distressed exchanges, so agency default rates and bank PDs are not always directly comparable. A broader treatment of the event itself is in the entry on default.
How PD is estimated
The simplest estimate is the observed default rate for a pool of similar borrowers:
If a grade contains 4,000 performing borrowers on 1 January and 60 of them default by 31 December, the one-year default rate is , or 1.5%. Banks average such rates over many years to set the PD for each grade. Other methods include:
- Scorecards. Logistic regression or machine-learning models built on application and behaviour data, widely used in retail lending and linked to the credit score.
- Structural models. Following the Merton approach, a firm defaults when the value of its assets falls below its debt, so PD can be derived from equity prices and volatility.
- Market-implied PD. Derived from bond credit spreads or credit default swap prices, using the rough relation that spread is about PD times LGD. These reflect risk premiums as well as default risk, so they usually exceed historical PDs.
Point-in-time and through-the-cycle PD
A point-in-time (PIT) PD reflects current economic conditions and moves with the business cycle; it rises quickly in a recession. A through-the-cycle (TTC) PD is an average over a full cycle and changes only when the borrower's underlying quality changes. Accounting under IFRS 9 and CECL requires forward-looking PIT estimates, adjusted for macroeconomic scenarios. Regulatory capital under the Basel internal ratings-based (IRB) approach favours long-run averages to stop capital swinging with the economy. Many banks therefore keep one rating model and convert between the two views.
PD in Basel capital rules
Under the IRB approach of Basel III, banks estimate PD for each obligor grade and feed it into a supervisory formula that sets risk-weighted assets. Under the foundation IRB approach banks supply only PD, while supervisory values are used for LGD and exposure. To limit very low estimates, the Basel framework sets a PD floor of 0.05% for most non-sovereign exposures, up from 0.03% under Basel II. Supervisors require at least five years of data for PD estimation and regular back-testing, comparing predicted PDs with actual default rates.
Limitations
PD estimates are only as good as the data behind them. Low-default portfolios, such as lending to large banks or sovereigns, have too few defaults for a reliable rate. Models trained in benign years can underestimate risk before a crisis, as many mortgage models did before 2008. Defaults are also correlated: in a downturn many borrowers fail together, which a single PD per borrower does not show. Portfolio models and stress tests are used alongside PD to capture this concentration risk.