Probability of default
Encyclopedia
Probability of default (PD) is a parameter used in the calculation of economic capital
or regulatory capital under Basel II
for a banking institution. This is an attribute of a bank's client.
) or for a portfolio of clients with similar attributes (for retail banking
). The credit history of the counterparty / portfolio and nature of the investment are taken into account to calculate the PD.
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, bond
s, and option
s 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.
In order to overcome these practical and theoretical hurdles it is possible to convert pure PIT estimated PD's to TTC or Long-Term PD's by following some simple steps:
As most Practitioners have little data on PD's compared to data on losses, this method provides a way of overcoming practical challenges. Furthermore, the method takes into consideration existing default definitions (and changing default definitions) and cyclical effects caused by macroeconomic forces as represented in Loss Frequency Data. One crucial assumption, however, is the belief that the segment/obligor type has remained relatively constant over the time period the time-series has been created for.
' (formerly Moody's KMV) public firm model, a structural credit risk model originally based on the work of Stephen Kealhofer, John McQuown, and Oldrich Vasicek
. The public firm EDFTM model reflects numerous theoretical and empirical variations on the traditional Black-Scholes-Merton structural model, and is probably the best-known commercial implementation of the structural modeling framework. Although often associated with a one-year time horizon, a term structure of EDFTM credit measures from one to five years is calculated.
In June 2011 Moody's Analytics introduced Through-the-Cycle EDF credit measures to the market. Through-the-Cycle EDF (TTC EDF) credit measures are probabilities of default that are largely free of the effect of the aggregate credit cycle, primarily reflecting a firm’s enduring, long-run credit risk trend. TTC EDF measures are derived from Moody’s Analytics’ public firm EDF model through a filtering technique that separates the underlying components of EDF measures that correspond to the observed frequency of the credit cycle. According to the Moody's Analytics' TTC EDF model, the key difference between point-in-time and through-the-cycle credit measures lies in their information content: a PIT measure incorporates all relevant credit trend information in estimating a firm’s creditworthiness, whereas a TTC measure moves primarily in response to a firm’s underlying, long-run credit quality trend, tuning out changes attributed to cyclical variation that is likely to be reversed with the passage of time.
Economic capital
-Finance and Economics:In financial services firms, economic capital can be thought of as the capital level shareholders would choose in absence of capital regulation....
or regulatory capital under Basel II
Basel II
Basel II is the second of the Basel Accords, which are recommendations on banking laws and regulations issued by the Basel Committee on Banking Supervision...
for a banking institution. This is an attribute of a bank's client.
Definition
The probability of default (also call Expected default frequency) is the likelihood that a loan will not be repaid and will fall into default. PD is calculated for each client who has a loan (for wholesale bankingWholesale banking
Wholesale banking is the provision of services by banks to the likes of large corporate clients, mid-sized companies, real estate developers and investors, international trade finance...
) or for a portfolio of clients with similar attributes (for retail banking
Retail banking
Retail banking is banking in which banking institutions execute transactions directly with consumers, rather than corporations or other banks. Services offered include: savings and transactional accounts, mortgages, personal loans, debit cards, credit cards, and so forth.-Types of...
). The credit history of the counterparty / portfolio and nature of the investment are taken into account to calculate the PD.
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
Logistic regression
In statistics, logistic regression is used for prediction of the probability of occurrence of an event by fitting data to a logit function logistic curve. It is a generalized linear model used for binomial regression...
. Default probabilities may also be estimated from the observable prices of credit default swaps, bond
Bond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...
s, and option
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...
s on common stock. The simplest approach, taken by many banks, is to use external ratings agencies such as Standard and Poors, Fitch
Fitch Ratings
The Fitch Group is a majority-owned subsidiary of FIMALAC, headquartered in Paris. Fitch Ratings, Fitch Solutions and Algorithmics, are part of the Fitch Group....
or Moody's Investors Service for estimating PDs from historical default experience. For small business default probability estimation, logistic regression
Logistic regression
In statistics, logistic regression is used for prediction of the probability of occurrence of an event by fitting data to a logit function logistic curve. It is a generalized linear model used for binomial 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.
How to calculate the probability of default
The following steps are commonly used:- Analyse the credit risk aspects of the counterparty / portfolio;
- Map the counterparty to an internal risk grade which has an associated PD: and
- Determine the facility specific PD. This last step will give a weighted Probability of Default for facilities that are subject to a guarantee or protected by a credit derivative. The weighting takes account of the PD of the guarantor or seller of the credit derivative.
- Once the probability of default has been estimated, the related credit spread and valuation of the loan or bond is the next step. A popular approach to this critical element of credit risk analysis is the "reduced form" modeling approach of the Jarrow-Turnbull model.
How to calculate Through-The-Cycle probability of default
Through-the-Cycle (TTC) PD's are long-run probabilities of default which take into consideration upturns and downturns in the economy. Conceptually, it is the simple average, median or equilibrium of Point-In-Time (PIT) PD's (PD's which are calculated for very short horizons) over a long period of time where several economic cycles have played out. Usually, the simple regulatory formula is to take the long-term average of PIT PD's. This is, however, impractical as long-term data is often limited for any obligor/portfolio making calculations cumbersome. Furthermore, it is theoretically incorrect as obligor/portfolio characteristics tend to metamorphisize over time making one estimation of PD at one point-in-time incomparable with another estimate at another point-in-time.In order to overcome these practical and theoretical hurdles it is possible to convert pure PIT estimated PD's to TTC or Long-Term PD's by following some simple steps:
- Calculation of at least 1 PIT PD. This PD will be composed of defaults with and without losses (i.e. LGD < 100%).
- Find the percentage of customers for the same obligor/portfolio (for which the PD has been calculated) where there have been losses. This is often referred to as 'Loss Frequencies' and these data are often recorded far back into time. Alternatively, use public data on bankruptcies as a proxy.
- Take the ratio between the average of PIT PD's and the Average of Loss Frequencies in overlapping years.
- Loss Frequency Averages are then multiplied with the found ratio. These are referred to as 'Estimated PIT PD's'.
- Create a Time-Series with PD's and Estimated PIT PD's, where Estimated PIT PD's are used to compliment existing PD's
- Last step is to calculate Long-Term Averages or Equilibriums based upon regression techniques and steady-state macroeconomic data.
As most Practitioners have little data on PD's compared to data on losses, this method provides a way of overcoming practical challenges. Furthermore, the method takes into consideration existing default definitions (and changing default definitions) and cyclical effects caused by macroeconomic forces as represented in Loss Frequency Data. One crucial assumption, however, is the belief that the segment/obligor type has remained relatively constant over the time period the time-series has been created for.
Expected Default Frequency(EDFTM)
Expected Default Frequency (EDFTM) is a trademarked term for the probability of default derived from Moody's AnalyticsMoody's Analytics
Moody’s Analytics provides capital markets and risk management professionals with credit analysis, economic research, financial risk management software, and advisory services...
' (formerly Moody's KMV) public firm model, a structural credit risk model originally based on the work of Stephen Kealhofer, John McQuown, and Oldrich Vasicek
Oldrich Vasicek
Oldrich Alfons Vasicek a Czech mathematician, received his master's degree in math from the Czech Technical University, 1964, and a doctorate in probability theory from Charles University four years later....
. The public firm EDFTM model reflects numerous theoretical and empirical variations on the traditional Black-Scholes-Merton structural model, and is probably the best-known commercial implementation of the structural modeling framework. Although often associated with a one-year time horizon, a term structure of EDFTM credit measures from one to five years is calculated.
In June 2011 Moody's Analytics introduced Through-the-Cycle EDF credit measures to the market. Through-the-Cycle EDF (TTC EDF) credit measures are probabilities of default that are largely free of the effect of the aggregate credit cycle, primarily reflecting a firm’s enduring, long-run credit risk trend. TTC EDF measures are derived from Moody’s Analytics’ public firm EDF model through a filtering technique that separates the underlying components of EDF measures that correspond to the observed frequency of the credit cycle. According to the Moody's Analytics' TTC EDF model, the key difference between point-in-time and through-the-cycle credit measures lies in their information content: a PIT measure incorporates all relevant credit trend information in estimating a firm’s creditworthiness, whereas a TTC measure moves primarily in response to a firm’s underlying, long-run credit quality trend, tuning out changes attributed to cyclical variation that is likely to be reversed with the passage of time.
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.moodysanalytics.com Moody's Analytics
- 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)