Estimating default and loss parameters
Probability of default, loss given default and exposure at default are estimated from internal and external histories, with margins of conservatism where data are thin or do not cover a downturn.
GRA · Banking Nexus
Spatial financeWhere capital meets hazard, exposure and transition
Statistics for bank risk measurement
Probability and statistics underlie every credit, market and operational risk measure in banking. Default probabilities, loss distributions, value at risk and stress losses all rest on estimation from limited and often unrepresentative data, and the discipline makes the uncertainty in those estimates explicit for the people who rely on them.
01Qeyd
Statistics for bank risk measurement on the record.
Method recordSTEM method
- RêbazÎhtîmal û statîstîk
- ParêzvanZanista pergalan û modelkirin
- Applied inBanking Nexus
- Dane4 inputs
- Checks4 validation steps
- Canonical pageSTEM Commons
02Serlêdan
What probability and statistics does here.
Probability and statistics provide the mathematical framework for describing uncertainty and learning from data. They underpin estimation, testing and prediction in every risk discipline. In financial stability, capital markets and investment and climate and hazards, statistical methods quantify the likelihood and uncertainty of losses across interconnected pergalan. They make the evidence behind risk decisions explicit and reproducible. The canonical description is on the STEM Commons.
Operational loss modelling
The frequency and severity of operational losses are modelled from internal, external and scenario data, with heavy tails treated explicitly rather than smoothed away.
Back-testing and calibration
Predicted default rates and value at risk are compared with outcomes using binomial and traffic-light tests, and calibration is reviewed when realised values diverge.
03Stress test
How a shock to assets becomes a system loss.
The equity the system loses after interbank contagion, against the initial hit, as leverage, interconnection and recovery rates change, the core of a macroprudential Testa zextê. Teaching model with stated illustrative values, not a prediction.
Kontrol
- Fall in external assets
- 2.0%
- Leverage (assets over equity)
- 10 times
- Interbank share of assets
- 10%
- Recovery on interbank claims
- 40%
- Banks in the system
- 20
- Core banks
- 20% of banks
Xwendin
- Equity lost to the initial shock
- 18.0%
- Equity lost after contagion
- 45.0%
- Added by contagion (DebtRank)
- 27.0 points
- Banks in default
- 0
Jimar, rêbaz û çavkanî
| Round | System equity lost (%) | Banks in default |
|---|---|---|
| 0 | 18.00 | 0 |
| 1 | 28.80 | 0 |
| 2 | 35.28 | 0 |
| 3 | 39.17 | 0 |
| 4 | 41.50 | 0 |
| 5 | 42.90 | 0 |
| 6 | 43.74 | 0 |
| 7 | 44.24 | 0 |
| 8 | 44.55 | 0 |
| 9 | 44.73 | 0 |
| 10 | 44.84 | 0 |
| 11 | 44.90 | 0 |
| 12 | 44.94 | 0 |
| 13 | 44.96 | 0 |
| 14 | 44.98 | 0 |
| 15 | 44.99 | 0 |
| 16 | 44.99 | 0 |
| 17 | 45.00 | 0 |
| 18 | 45.00 | 0 |
| 19 | 45.00 | 0 |
| 20 | 45.00 | 0 |
| 21 | 45.00 | 0 |
| 22 | 45.00 | 0 |
| 23 | 45.00 | 0 |
| 24 | 45.00 | 0 |
| 25 | 45.00 | 0 |
| 26 | 45.00 | 0 |
| 27 | 45.00 | 0 |
| 28 | 45.00 | 0 |
| 29 | 45.00 | 0 |
| 30 | 45.00 | 0 |
Rêbaz
- DebtRank Battiston and others (2012), Scientific Reports 2:541
- Differential DebtRank Bardoscia and others (2015), PLOS ONE 10
- Contagion in financial networks Gai and Kapadia (2010), Proc. R. Soc. A 466
- Clearing in financial networks Eisenberg and Noe (2001), Management Science 47
- Pankeya nediyarîyê (Monte Carlo ya parametreyan) Spiegelhalter, Pearson and Short (2011), Visualising uncertainty about the future, Science 333
- Hesasiyeta yek-yek (tornado) Saltelli and others (2008), Global Sensitivity Analysis: The Primer, Wiley
Dane
No observed data enters this model: it runs on the teaching values set by the controls, to be replaced with a programme’s own evidence.
Li seranserê şeş stûnan, bi pêşengiya Nexus Consortium
- Ceribandin Labs
- Hatiye avakirin di Banking Nexus in Foundry
- Tê ceribandin li Banking Nexus in Universe
- Hatiye kodkirin di Darayî, sîgorta û aborî di Standards de
- Hatiye weşandin di Banking Nexus in Reports
- Tê de tê dayîn Fakulteya Darayî û Aborî di Academy de
04Dane
What the method consumes.
Datasets and records used by probability and statistics on this platform, with the role each plays and the label its values carry. Sources are listed in the source register.
| Dane | Rol | Nîşan |
|---|---|---|
| Internal default and recovery histories | Parameter estimation | ÇAVDÊRÎKIRÎ |
| Rating agency default studies | External benchmark | REPORTED |
| Operational loss databases | Frequency and severity fitting | REPORTED |
| Market price series | Value at risk and back-testing | ÇAVDÊRÎKIRÎ |
05Exposure, loss and capital
What statistics for bank risk measurement means for exposure, loss and capital.
The exposure, loss, scenario and capital views a risk officer, supervisor or ministry of finance would ask for, with the frameworks they report against. Structures follow supervisory and actuarial practice. Values are illustrative: never prices, ratings or advice.
Scenario pathways
How statistics for bank risk measurement could be stressed under the scenario families central banks and supervisors use.
| Scenario family | Transition risk | Physical risk | What a stress test asks |
|---|---|---|---|
| Orderly | Early, gradual policy | Kêmtir | Can the book absorb a steady repricing? |
| Disorderly | Late, abrupt policy | Lower to medium | What breaks under a sudden repricing and credit migration? |
| Hot house world | Limited policy | High and rising | Where do physical losses concentrate in collateral and insurance? |
NGFS climate scenarios · Network for Greening the Financial SystemIFRS S2 Climate-related Disclosures · ISSBTCFD recommendations · Financial Stability Board TCFDPrinciples for the effective management of climate-related financial risks · Basel Committee on Banking Supervision
06Erêkirin
How results are checked.
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
| Kontrol bikin | How it is done |
|---|---|
| Out-of-time validation | Models are tested on periods not used in estimation, including a stressed period where one is available |
| Low-default portfolio treatment | Where defaults are rare, conservative estimators and expert overlays are documented and challenged |
| Tail diagnostics | Fitted distributions are checked in the tail, not only on average fit |
| Sensitivity reporting | Key parameter changes and their effect on capital and provisions are reported to decision-makers |
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
08Stewardship
Who maintains the method.
Zanista pergalan û modelkirin stewards probability and statistics for the Consortium and reviews how it is applied across platforms.
09Girêdayî
Ev rûpel li ser Konsorsiyûmê te ber bi kû ve dibe.
10Pirs
Pirs û bersiv.
What are the limits of probability and statistics in this field?
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
How are results checked?
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
Are the values on this page real?
The data names, roles and checks are real descriptions of practice. The canvas shows a design of the method’s use, not a run; no result is reported here.
Where else is this method applied?
Çavdêrxaneya canonical method page lists every platform that applies it.
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