Probability of default


Probability of default is a financial
term describing the likelihood of a default over a particular time horizon.
It provides an estimate of the likelihood that a borrower will be
unable to meet its debt obligations. PD is used in a variety of credit
analyses and risk management frameworks. Under Basel II, it is a key parameter
used in the calculation of economic capital or regulatory capital for a
banking institution. Overview
The probability of default is an estimate of the likelihood that the
default event will occur. It applies to a particular assessment horizon, usually
one year. Credit scores, such as FICO for
consumers or bond ratings from S&P, Fitch or Moodys for corporations or
governments, typically imply a certain probability of default.
For group of obligors sharing similar credit risk characteristics such as a
RMBS or pool of loans, a PD may be derived for a group of assets that is
representative of the typical obligor of the group. In comparison, a PD for a
bond or commercial loan, are typically determined for a single entity.
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
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, number of times
delinquent in the past six months, 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 economy. 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 or point-in-time 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. Credit default swap-implied
probabilities of default are based upon the market prices of credit default
swaps. Like equity prices, their prices contain all information available to the
market as a whole. As such, the probabliity of default can be inferred
by the price. CDS implied PD’s can be used with EDF credit measures to improve
accuracy. Deriving Point-in-Time(PIT) and
Through-the-cycle(TTC) PDs There are alternative approaches for
deriving and estimating PIT and TTC PDs. One such framework involves
distinguishing PIT and TTC PDs by means of systematic predictable fluctuations
in credit conditions, i.e. by means of a “credit cycle”. This framework,
involving the selective use of either PIT or TTC PDs for different purposes,
has been successfully implemented in large UK banks with BASEL II AIRB
status. As a first step this framework makes use
of Merton approach in which leverage and volatility are used to create a PD
model. As a second step, this framework assumes
existence of systematic factor(s) similar to Asymptotic Risk Factor Model.
As a third step, this framework makes use of predictability of credit cycles.
This means that if the default rate in a sector is near historic high then one
would assume it to fall and if the default rate in a sector is near
historic low then one would assume it to rise. In contrast to other approaches
which assumes the systematic factor to be completely random, this framework
quantifies the predictable component of the systematic factor which results in
more accurate prediction of default rates.
As per this framework, the term PIT applies to PDs that move over time in
tandem with realized, default rates, increasing as general credit conditions
deteriorate and decreasing as conditions improve. The term TTC applies to PDs
that exhibit no such fluctuations, remaining fixed overall even as general
credit conditions wax and wane. The TTC PDs of different entities will change,
but the overall average across all entities won’t. The greater accuracy of
PIT PDs makes them the preferred choice in such current, risk applications as
pricing or portfolio management. The overall stability of TTC PDs makes them
attractive in such applications as determining Basel II/II RWA.
The above framework provides a method to quantify credit cycles, their systematic
and random components and resulting PIT and TTC PDs. This is accomplished for
wholesale credit by summarizing, for each of several industries or regions,
MKMV EDFs, Kamakura Default Probabilities, or some other,
comprehensive set of PIT PDs or DRs. After that, one transforms these factors
into convenient units and expressed them as deviations from their respective,
long-run-average values. The unit transformation typically involves the
application of the inverse-normal distribution function, thereby
converting measures of median or average PDs into measures of median or average
“default distance”. At this point, one has a set of indices measuring the
distance between current and long-run-average DD in each of a
selected set of sectors. Depending on data availability and portfolio
requirements, such indices can be created for various industries and
regions with 20+ years covering multiple recessions.
After developing these indices, one can calculate both PIT and TTC PDs for
counterparties within each of the covered sectors. To obtain PIT PDs, one
introduces the relevant indices into the relevant default models, re-calibrate
the models to defaults, and apply the models with current and projected
changes in indices as inputs. If a PD model weren’t otherwise PIT, the
introduction of the indices will make it PIT. The specific model formulation
depends on the features important to each, distinguished class of
counterparties and data constraints. Some common approaches include:
Factor Ratio Model: Calibration of financial/non-financial factors and
credit-cycle indices to defaults. This approach works well with large number of
defaults, e.g. SME portfolios or large-corporate portfolios calibrated to
external default samples. Scorecard model: Calibration of score
and credit-cycle indices calibrated to observed internal or external defaults.
This approach works with smaller number of defaults where there is not enough
data to develop a ratio model. E.g. Funds portfolio
Agency Direct model: Calibration of ECAI grades and credit indices to ECAI
defaults and applying it to Agency and internal co-rated entities. This
approach works well where there is a large co-rated dataset but not enough
internal defaults e.g. Insurance portfolio
Agency Replication model: Calibrate financial/non-financial
factors/scorecard score to PDs estimated from the Agency Direct model. This
approach works well where there is a large, co-rated dataset but a small
sample of internal defaults—e.g. Insurance portfolio
External vendor model: Use of models such as MKMV EDF model with credit cycle
indices. At this point, to determine a TTC PD,
one follows three steps: Converting the PIT PD to PIT DD
Subtracting the credit cycle index from the PIT DD, thereby obtaining the TTC
DD; and Converting the TTC DD to TTC PD.
In addition to PD models, this framework can also be used to develop PIT and TTC
variants of LGD, EAD and Stress Testing models.
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 See also
Expected loss and its three factors Loss given default magnitude of likely
loss on the exposure, expressed as a percentage of the exposure
Probability of default probability of default of a borrower
Exposure at default amount to which the bank was exposed to the borrower at the
time of default, measured in currency For the effects of correlation between
PD and LGD see Expected loss References
^ Bankopedia:PD Definition ^ FT Lexicon:Probability of default
^ Introduction:Issues in the credit risk modelling of retail markets
^ Basel II Comprehensive Version, Pg 100 ^ a b BIS:Studies on the Validation of
Internal Rating Systems ^ Slides 5 and 6:The Distinction between
PIT and TTC Credit Measures it-Measures-and-Fair-Value-Spreads.ashx>
1/aguais_et_al_basel_handbook2_jan07.pdf ^ Aguais, S. D., et al, 2004,
“Point-in-Time versus Through-the-Cycle Ratings”, in M. Ong, The Basel Handbook:
A Guide for Financial Practitioners ^ Merton, Robert C., “On the Pricing of
Corporate Debt: The Risk Structure of Interest Rates”, Journal of Finance,
Vol. 29, No. 2,, pp. 449-470 ^ Gordy, M. B. A risk-factor model
foundation for ratings-based bank capital rules. Journal of Financial
Intermediation 12, 199 – 232. ^ http:www.bis.orgirbriskweight.pdf
^ The Basel II Risk Parameters Reading
de Servigny, Arnaud and Olivier Renault. The Standard & Poor’s Guide to Measuring
and Managing Credit Risk. McGraw-Hill. ISBN 978-0-07-141755-6.
Duffie, Darrell and Kenneth J. Singleton. Credit Risk: Pricing,
Measurement, and Management. Princeton University Press. ISBN
978-0-691-09046-7. External links
Implied Default Probability from CDS – QuantCalc, Online Financial Math
Calculator ode282731.pdf?abstractid=1921419&mirid=1
Through-the-Cycle EDF Credit Measures methodology paper
http:www.bis.orgbcbsca.htm Basel II: Revised international capital framework
http:www.bis.orgbcbs107.htm Basel II: International Convergence of Capital
Measurement and Capital Standards: a Revised Framework
http:www.bis.orgbcbs118.htm Basel II: International Convergence of Capital
Measurement and Capital Standards: a Revised Framework
http:www.bis.orgbcbs128.pdf Basel II: International Convergence of Capital
Measurement and Capital Standards: a Revised Framework, Comprehensive Version

2 comments on “Probability of default”

  1. rahuul rahuul says:

    just reciting everything from wikipedia

  2. Julian Rey Odyssey Hernandez says:

    fuck this bot

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