Probability of default

Basel II
Bank for International Settlements Basel Accords Basel I Basel II
Background
Banking Monetary policy Central bank Risk Risk management Regulatory capital Tier 1 Tier 2
Pillar 1: Regulatory Capital
Credit risk Standardized IRB Approach F-IRB A-IRB PD LGD EAD Operational risk Basic Standardized AMA Market risk Duration Value at risk
Pillar 2: Supervisory Review
Economic capital Liquidity risk Legal risk
Pillar 3: Market Disclosure
Disclosure
Business and Economics Portal

Probability of default (PD) is the likelihood of a default over a particular time horizon. It provides an estimate of the likelihood that a client of a financial institution will be unable to meet its debt obligations. PD is a key parameter used in the calculation of economic capital or regulatory capital under Basel II for a banking institution.

Overview

Under Basel II, a default event on a debt obligation is said to have occurred if

• it is unlikely that the obligor will be able to repay its debt to the bank without giving up any pledged collateral
• the obligor is more than 90 days past due on a material credit obligation

The PD is an estimate of the likelihood that the default event will occur over a fixed assessment horizon, usually taken to be one year. The PD can be estimated for a particular obligor which is the usual practice in wholesale banking, or for a segment of obligors sharing similar credit risk characteristics which is the usual practice in retail banking.

Stressed and Unstressed PD

The PD of an obligor not only depends on the risk characteristics of that particular obligor but also the economic environment and the degree to which it affects the obligor. Thus, the information available to estimate PD can be divided into two broad categories -

• Macroeconomic information like house price indices, unemployment, GDP growth rates, etc. - this information remains the same for multiple obligors
• Obligor specific information like revenue growth (wholesale), number of times delinquent in the past six months (retail), etc. - this information is specific to a single obligor and can be either static or dynamic in nature. Examples of static characteristics are industry for wholesale loans and origination "loan to value ratio" for retail loans.

An unstressed PD is an estimate that the obligor will default over a particular time horizon considering the current macroeconomic as well as obligor specific information. This implies that if the macroeconomic conditions deteriorate, the PD of an obligor will tend to increase while it will tend to decrease if economic conditions improve.

A stressed PD is an estimate that the obligor will default over a particular time horizon considering the current obligor specific information, but considering "stressed" macroeconomic factors irrespective of the current state of the economoy. The stressed PD of an obligor changes over time depending on the risk characteristics of the obligor, but is not heavily affected by changes in the economic cycle as adverse economic conditions are already factored into the estimate.

For a more detailed conceptual explanation of stressed and unstressed PD, refer .

Through-the-cycle(TTC) and Point-in-Time(PIT)

Closely related to the concept of stressed and unstressed PD's, the terms through-the-cycle (TTC) or point-in-time (PIT) can be used both in the context of PD as well as rating system. In the context of PD, the stressed PD defined above usually denotes the TTC PD of an obligor whereas the unstressed PD denotes the PIT PD. In the context of rating systems, a PIT rating system assigns each obligor to a bucket such that all obligors in a bucket share similar unstressed PDs while all obligors in a risk bucket assigned by a TTC rating system share similar stressed PDs .

PD Estimation

There are many alternatives for estimating the probability of default. Default probabilities may be estimated from a historical data base of actual defaults using modern techniques like logistic regression. Default probabilities may also be estimated from the observable prices of credit default swaps, bonds, and options on common stock. The simplest approach, taken by many banks, is to use external ratings agencies such as Standard and Poors, Fitch or Moody's Investors Service for estimating PDs from historical default experience. For small business default probability estimation, logistic regression is again the most common technique for estimating the drivers of default for a small business based on a historical data base of defaults. These models are both developed internally and supplied by third parties. A similar approach is taken to retail default, using the term "credit score" as a euphemism for the default probability which is the true focus of the lender.

Some of the popular statistical methods which have been used to model probability of default are listed below .

• Linear Regression
• Discriminant analysis
• Logit and Probit Models
• Panel models
• Cox proportional hazards model
• Neural Networks
• Classification Trees

Reading

• de Servigny, Arnaud and Olivier Renault (2004). The Standard & Poor's Guide to Measuring and Managing Credit Risk. McGraw-Hill. ISBN 978-0071417556. 
• Duffie, Darrell and Kenneth J. Singleton (2003). Credit Risk: Pricing, Measurement, and Management. Princeton University Press. ISBN 978-0691090467. 

External links

• http://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1921419_code282731.pdf?abstractid=1921419&mirid=1 Through-the-Cycle EDF Credit Measures methodology paper
• http://www.bis.org/publ/bcbsca.htm Basel II: Revised international capital framework (BCBS)
• http://www.bis.org/publ/bcbs107.htm Basel II: International Convergence of Capital Measurement and Capital Standards: a Revised Framework (BCBS)
• http://www.bis.org/publ/bcbs118.htm Basel II: International Convergence of Capital Measurement and Capital Standards: a Revised Framework (BCBS) (November 2005 Revision)
• http://www.bis.org/publ/bcbs128.pdf Basel II: International Convergence of Capital Measurement and Capital Standards: a Revised Framework, Comprehensive Version (BCBS) (June 2006 Revision)