Probability of default

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Basel II

Bank for International Settlements
Basel Accord - 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 - 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 a parameter used in the calculation of economic capital or regulatory capital under Basel II for a banking institution. This is an attribute of bank's client.

Contents

[edit] Definition

The probability of default 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 banking) 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, bonds, and options on common stock. The simplist approach, taken by many banks, is to use external ratings agencies such as Egan Jones, Fitch, Moody's Investors Service, or Standard and Poors 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 an euphemism for the default probability which is the true focus of the lender.

[edit] 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 gives 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.

[edit] 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 uncomparable with another estimate at another point-in-time.

In order to overcome these practical and theoretical hurdles it is possibly 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 mulitiplied 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 relatively 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.

[edit] References

  • de Servigny, Arnaud and Olivier Renault (2004). The Standard & Poor's Guide to Measuring and Managing Credit Risk. McGraw-Hill. ISBN13 978-0071417556. 
  • Duffie, Darrell and Kenneth J. Singleton (2003). Credit Risk: Pricing, Measurement, and Management. Princeton University Press. ISBN13 978-0691090467. 

[edit] External links