Losses and dependence
Distributions, correlations and tail risk.
RISK METHODS / INTERACTIVE DEMONSTRATORS
Risk methods that clarify a decision.
Illustrative methods connect exposure, distribution, horizon, liquidity, credit and capital. They make assumptions and limitations visible; they are neither prudential requirements nor recommendations.
MARKET RISKPORTFOLIO RISKCREDIT & COUNTERPARTYLIQUIDITY & CAPITAL
Scope and decision framework
Why this laboratory?
A risk measure needs an exposure, a horizon and explicit assumptions. This laboratory connects loss distributions, liquidity, credit and controls to examine which decisions an indicator can support. It complements valuation with an examination of vulnerabilities.
Ambition with discipline
Scenarios do not cover every possible event and do not constitute prudential requirements. Operational, systemic and systematic risks remain distinct. Decisions require suitable data quality, justified scenarios and review of model limitations.
Credit and liquidity
Default, recovery and funding constraints.
Controls and resilience
Stress scenarios, responsibilities and limitations.
All methods and sections
Related methods and sections
Systemic risk concerns financial-system disruption and transmission. Systematic risk concerns common-factor exposure. Operational failures may trigger systemic disruption, but these categories are not interchangeable.
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VaR, Expected Shortfall & stress
VaR—
Expected Shortfall—
Stress VaR—
Sensitivity curve: confidence rises from 50.1% to 99.9% along the horizontal axis; the vertical axis is Gaussian VaR in euros. This is not a sampled loss distribution. Zero mean, constant volatility and square-root-of-time scaling; illustrative inputs.
Comprendre le modèle et ses limites
Mesure delta-normale ; la normalité et la linéarité sont des hypothèses fortes.
Model and method references
Gaussian market-risk framework; stress inputs and numerical conventions are defined by this calculator.
J.P. Morgan / Reuters (1996). RiskMetrics — Technical Document, fourth edition.
Perte attendue & capital économique
EL—
UL—
EC—
Comprendre le modèle et ses limites
EL = EAD×PD×LGD ; capital asymptotique mono-facteur.
Model and method references
Credit-factor model reference; this tool uses the explicitly displayed homogeneous-pool approximation.
O. Vasicek (2002). Loan portfolio value. Risk, December.
Exposition de contrepartie & CVA
CVA—
PD cumulée—
Exposure × 1.96—
Comprendre le modèle et ses limites
Intégration EPE × défaut marginal × LGD ; hypothèses très simplifiées.
Model and method references
Reduced-form credit references; exposure approximation is defined by this calculator.
ROBERT A. JARROW, STUART M. TURNBULL (1995). Pricing Derivatives on Financial Securities Subject to Credit Risk. The Journal of Finance 50(1), 53-85.
Darrell Duffie, Kenneth J. Singleton (1999). Modeling Term Structures of Defaultable Bonds. Review of Financial Studies 12(4), 687-720.
METHODOLOGY / SOURCES
Référentiel et périmètre
Les horizons de liquidité renvoient au cadre de Bâle ; les calculs restent des démonstrateurs à valider.
RISK GOVERNANCE / CHALLENGE
Du chiffre à la décision
Qualité et traçabilité.
Hypothèses et benchmark.
Limites et escalade.
Attribution et décisions.
18 energy risk scenarios
Interactive research · Synthetic scenarios
Counterparty and concentration
DECISION FRAMEWORK
A scenario range is not a confidence interval
Uncertainty about a conditional mean differs from uncertainty about a future individual outcome: the latter also includes the unobserved disturbance. Likewise, a grid of user-selected shocks is a scenario range, not a statistically estimated interval. Heteroskedasticity-robust inference changes standard-error estimation under its assumptions; it does not repair omitted-variable bias or validate a forecasting model. With time-ordered data, dependence and stability also matter. Label the object being measured, the observation window and the assumptions behind any interval before comparing it with a stress scenario.
Decision, data and controls
Separate stress range, mean uncertainty and outcome uncertainty; retain sample dates and error assumptions; avoid attaching statistical coverage to an illustrative 3D surface.
Scope, limitations and source
No confidence or prediction interval is estimated by this companion. Robust standard errors require an appropriate estimator for the data structure.
Wooldridge (7th ed., 2020), §6-4a, printed pp.201–204 / PDF224–227; §8-2 printed pp.263–267 / PDF286–290; §11-1 printed pp.367–370 / PDF390–393.
EVIDENCE AND CONTROLS
Exposure includes orders that may still fill
Filled positions are only part of an automated trading system’s exposure. An accepted resting order, an order awaiting acknowledgement and a strategy committed to send another leg can create additional positions. A control design should explain which pending states consume a limit and how cancellations release it. For a conservative buying scenario, assume relevant buy orders fill while offsetting sell orders do not; document that convention rather than treating it as a universal margin rule. Reconcile order and trade events so that position limits refer to the same state of the system.
Decision, data and controls
Define filled and potential exposure separately; retain acknowledgements and cancellation states; check limit release against event reconciliation.
Scope, limitations and source
Control-design lesson from a historical market-specific account. The website is not an order-management or pre-trade risk system, and current venue rules must be verified independently.
Wang & Zheng (2015), §4.2.3 printed pp70–74 / PDF85–89, especially pending-order exposure pp72–73.
ACCOUNTING INTERPRETATION
Valuation inputs and measurement uncertainty
A model result and a documented fair-value measurement answer different questions. For each important input, record its source, observation date, market accessibility and whether it is observed, adjusted or estimated. A quoted number is not automatically an active-market price for the identical instrument. Where a significant input is unobservable, retain the rationale and show how reasonable alternatives affect the result. Compare valuation techniques using consistent currency, horizon and cash-flow conventions. The scenario sliders in these Labs illustrate sensitivities; they do not independently establish an accounting hierarchy classification or an auditable reporting value.
Decision, data and controls
Decision: use the input, challenge it or disclose the gap. Evidence: observable quotes, adjustments, significance assessment and sensitivity range. Control: do not count the same uncertainty in both cash flows and discount rates.
Scope, limitations and source
The book is dated study material. Lab sensitivities do not independently certify a fair-value hierarchy or an auditable reporting value.
Cathrynne Service, Gripping GAAP, 23rd ed. (2024), ch.25 §3.9.3–3.9.4, printed pp.1197–1200 / PDF1206–1209. Book amendment coverage ends 10 December 2023.
Decision risk: read scenarios without false certainty
Overconfidence can increase turnover and understate uncertainty. The disposition effect can encourage selling gains quickly while retaining losses. Hindsight can then make the outcome appear inevitable. Review decisions and their evidence, rather than realised P&L alone.
Application to the workflow
Proposed application: record the thesis, falsifying evidence, adverse scenarios, position size and next review. Assess winners and losers with the same criteria and independently challenge material decisions. Synthesis: distinguish process quality, accepted risk and outcome; a gain alone does not establish a sound decision.
Assumptions and limits
Assumptions: timestamp the decision log before execution, trace costs and define limits before the scenario. Increasing exposure after a fall can follow a documented strategy and does not prove bias. Scenarios are conditional tests: a 3D surface assigns no probabilities to displayed regions and does not predict their occurrence.
MBS MODEL REVIEW
Prepayment assumptions before interpretation
Record current balance, remaining term, loan age, gross/net coupon and the CPR or PSA convention. A benchmark ramp specifies a cash-flow scenario; it does not estimate refinancing incentives, turnover, burnout or borrower constraints. Keep observed repayments separate from entered assumptions.
MBS MODEL REVIEW
Which sensitivity has actually been calculated?
Fixed-flow duration and convexity move discounting while preserving the schedule. Scenario cash-flow duration regenerates one schedule per entered CPR. A stochastic option-adjusted analysis would require a calibrated rate model, path-dependent prepayment and averaging path values. Changing a label or drawing a surface does not provide those missing components.
MBS MODEL REVIEW
Controls and a decision record
Reconcile principal returned with opening balance, check IO plus PO under the same discount curve, and review the maturity and payment-date convention. Compare all three scenario prices before using a duration number. Retain input versions, shock size and exceptions; a numerical identity is a control, not evidence of calibration or of a hedge’s realised performance.
Sources and scope
Fabozzi (ed.), The Handbook of Mortgage-Backed Securities, 7th ed. (2016): ch.3 pp.93–99 / PDF120–126; Joshi, Davis & McCoy, ch.24 pp.510–515 / PDF537–542; Fabozzi, ch.31 pp.694–698 / PDF721–725. Original AHS control synthesis; historical source, no current agency rules asserted.
Open MBS cash-flow scenarios →Operational risk: losses, controls and continuity
Explore a question, inspect its evidence requirements, then choose a method. The cards are Working papers describing research designs; they do not run estimators. The separate demonstrator below performs only the displayed calculation using synthetic inputs.
O01Combine internal losses and experts
Working paper · AHS application
Required data
Dated losses and independently elicited scenarios
Method and intended use
Combine evidence with explicit expert weights and dependence assumptions.
Limits and checks
Repeated opinions are not independent evidence.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Peters & Hübner, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 1, printed pp. 3–5, 18–19 / PDF pp. 33–35, 48–49.
Reference: supplied book, chapter and printed/PDF pages above.
O02Audit reporting thresholds
Working paper · AHS application
Required data
Event counts, thresholds and exposure periods
Method and intended use
Distinguish no event from an unreported small loss before frequency calibration.
Limits and checks
Truncation can bias frequency and severity together.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Peters & Hübner, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 1, printed pp. 3–5, 18–19 / PDF pp. 33–35, 48–49.
Reference: supplied book, chapter and printed/PDF pages above.
O03Compare business-line loss rates
Working paper · AHS application
Required data
Counts and comparable activity exposure
Method and intended use
Normalize event frequency by exposure before comparing units.
Limits and checks
Differences in reporting cultures can dominate observed rates.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Peters & Hübner, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 1, printed pp. 3–5, 18–19 / PDF pp. 33–35, 48–49.
Reference: supplied book, chapter and printed/PDF pages above.
O04Calibrate rare-loss scenarios
Working paper · AHS application
Required data
Expert loss quantiles and scenario horizon
Method and intended use
Translate elicited severity ranges into a transparent scenario distribution.
Limits and checks
Expert confidence is not empirical tail validation.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Peters & Hübner, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 1, printed pp. 3–5, 18–19 / PDF pp. 33–35, 48–49.
Reference: supplied book, chapter and printed/PDF pages above.
O05Model annual aggregate loss
Working paper · AHS application
Required data
Annual intensity and nonnegative severities
Method and intended use
Combine random frequency and severity to construct annual loss scenarios.
Limits and checks
IID losses and stable intensity are restrictive assumptions.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Rachedi & Fantazzini, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 10, printed pp. 197–198 / PDF pp. 227–228. Historical AMA context; internal research application only.
Reference: supplied book, chapter and printed/PDF pages above.
O06Fit extreme-loss tails
Working paper · AHS application
Required data
Loss exceedances above candidate thresholds
Method and intended use
Use extreme-value tail models and compare threshold sensitivity.
Limits and checks
Few exceedances can produce highly unstable quantiles.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Rachedi & Fantazzini, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 10, printed pp. 197–198 / PDF pp. 227–228. Historical AMA context; internal research application only.
Reference: supplied book, chapter and printed/PDF pages above.
O07Compare copula dependence
Working paper · AHS application
Required data
Loss cells and marginal distributions
Method and intended use
Compare joint losses under alternative copulas with the same marginals.
Limits and checks
Linear correlation does not determine tail dependence.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Rachedi & Fantazzini, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 10, printed pp. 197–198 / PDF pp. 227–228. Historical AMA context; internal research application only.
Reference: supplied book, chapter and printed/PDF pages above.
O08Stress common-shock events
Working paper · AHS application
Required data
Shared incident scenarios and affected units
Method and intended use
Use a common Poisson shock component to link event counts.
Limits and checks
Shared severity and recovery assumptions still need specification.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Rachedi & Fantazzini, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 10, printed pp. 197–198 / PDF pp. 227–228. Historical AMA context; internal research application only.
Reference: supplied book, chapter and printed/PDF pages above.
O09Estimate rare quantiles efficiently
Working paper · AHS application
Required data
Loss model and a proposal distribution
Method and intended use
Use importance sampling with likelihood weights and numerical-error checks.
Limits and checks
Poor proposal choice can create unstable weights.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Bee & Espa, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 8, printed pp. 155–157 / PDF pp. 185–187. Historical AMA context; research method only.
Reference: supplied book, chapter and printed/PDF pages above.
O10Challenge diversification claims
Working paper · AHS application
Required data
Stand-alone losses and joint scenarios
Method and intended use
Compare aggregate tail loss across dependence assumptions.
Limits and checks
Adding VaRs is not a universal upper bound.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Rachedi & Fantazzini, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 10, printed pp. 197–198 / PDF pp. 227–228. Historical AMA context; internal research application only.
Reference: supplied book, chapter and printed/PDF pages above.
O11Assess payment-system outage
Working paper · AHS application
Required data
Payment flows, downtime and queued obligations
Method and intended use
Map delayed settlement to liquidity needs and service recovery priorities.
Limits and checks
A capital buffer cannot restore an unavailable service.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Russo & Stecconi, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 19, printed pp. 397–400 / PDF pp. 427–430.
Reference: supplied book, chapter and printed/PDF pages above.
O12Stress a shared service provider
Working paper · AHS application
Required data
Service dependencies and recovery times
Method and intended use
Trace one provider outage across dependent payment processes.
Limits and checks
This is an AHS adaptation, not a vendor failure prediction.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Russo & Stecconi, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 19, printed pp. 397–400 / PDF pp. 427–430.
Reference: supplied book, chapter and printed/PDF pages above.
O13Test recovery sequencing
Working paper · AHS application
Required data
Critical processes and restart dependencies
Method and intended use
Compare restoration sequences against the critical service path.
Limits and checks
Nominal restart time does not prove end-to-end recovery.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Russo & Stecconi, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 19, printed pp. 397–400 / PDF pp. 427–430.
Reference: supplied book, chapter and printed/PDF pages above.
O14Study a cyber disruption scenario
Working paper · AHS application
Required data
Hypothetical outage, data integrity and payment queues
Method and intended use
Apply service-continuity analysis to a cyber-triggered disruption.
Limits and checks
The book framework is adapted; attack probabilities are not supplied.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Russo & Stecconi, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 19, printed pp. 397–400 / PDF pp. 427–430.
Reference: supplied book, chapter and printed/PDF pages above.
O15Challenge stale prices
Working paper · AHS application
Required data
Quote timestamps and valuation overrides
Method and intended use
Identify stale inputs and require independent price challenge.
Limits and checks
An old price is a warning signal, not proof of misvaluation.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Jones, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 23, printed pp. 465–466 / PDF pp. 495–496.
Reference: supplied book, chapter and printed/PDF pages above.
O16Audit model-based fund NAV
Working paper · AHS application
Required data
Holdings, model inputs and independent valuations
Method and intended use
Separate market movements from operational valuation errors.
Limits and checks
Independent estimates may share the same data weakness.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Jones, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 23, printed pp. 465–466 / PDF pp. 495–496.
Reference: supplied book, chapter and printed/PDF pages above.
O17Review valuation conflicts
Working paper · AHS application
Required data
Pricing authority, overrides and compensation arrangements
Method and intended use
Map who supplies inputs, approves marks and benefits from valuation changes.
Limits and checks
A conflict map does not establish misconduct.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Jones, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 23, printed pp. 465–466 / PDF pp. 495–496.
Reference: supplied book, chapter and printed/PDF pages above.
O18Reconcile external loss evidence
Working paper · AHS application
Required data
External incidents, internal scope and reporting rules
Method and intended use
Document comparability before pooling internal and external losses.
Limits and checks
Size, business mix and reporting differences prevent naive pooling.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Peters & Hübner, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 1, printed pp. 3–5, 18–19 / PDF pp. 33–35, 48–49.
Reference: supplied book, chapter and printed/PDF pages above.
O19Design a loss-data quality review
Working paper · AHS application
Required data
Event dates, recoveries, currency and linked incidents
Method and intended use
Reconcile duplicates and distinguish gross loss from recoveries.
Limits and checks
Cleaning rules change measured loss distributions.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Peters & Hübner, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 1, printed pp. 3–5, 18–19 / PDF pp. 33–35, 48–49.
Reference: supplied book, chapter and printed/PDF pages above.
O20Separate internal risk from regulatory capital
Working paper · AHS application
Required data
Jurisdiction, effective rules and internal loss model
Method and intended use
Keep research loss measures separate from Basel OPE25 capital calculations.
Limits and checks
Basel is an international standard; local implementation must be verified.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
BCBS, Basel Framework, OPE25, Standardised approach, international standard effective 1 January 2023, version published 5 July 2024; checked 15 October 2026. Local implementation is outside this module.
Primary source ↗Annual loss: frequency and severity
Interactive demonstrator · AHS · 15 October 2026
Independent Poisson incident count and IID lognormal severities, with user-supplied severity mean and coefficient of variation. Controls proportionally reduce frequency and severity; their effectiveness is assumed. No tail quantile or regulatory capital is computed.
Equation, units and interpretation
\mathbb E[L]=\lambda m,\quad \mathrm{SD}(L)=m\sqrt{\lambda(1+c^2)},\quad \lambda_c=\lambda(1-r_f),\quad m_c=m(1-r_s)
λ: incidents/year; m: mean severity in euros; c: dimensionless severity coefficient of variation; L: annual aggregate loss in euros; r_f and r_s: assumed reduction fractions. λ_c and m_c are the controlled intensity and mean.
Rachedi & Fantazzini, in Gregoriou (ed.), Operational Risk toward Basel III (2009), ch. 10, printed pp. 197–198 / PDF pp. 227–228. Historical AMA context; internal research application only.
The equation and implementation are simplified AHS applications of the cited framework.
Systemic risk: channels and institutions
Explore a question, inspect its evidence requirements, then choose a method. The cards are Working papers describing research designs; they do not run estimators. The separate demonstrator below performs only the displayed calculation using synthetic inputs.
S01Trace a default cascade
Working paper · AHS application
Required data
Bilateral claims, capital and recovery assumptions
Method and intended use
Apply each default loss once and trace secondary failures.
Limits and checks
A cascade illustration is not an equilibrium clearing model.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Anand, Trebilcock & Rosenstock, in Anand (ed.), Systemic Risk, Institutional Design, and the Regulation of Financial Markets (2016), ch. 1, printed pp. 1–6, 37 / PDF pp. 24–29, 60.
Reference: supplied book, chapter and printed/PDF pages above.
S02Distinguish common shocks from contagion
Working paper · AHS application
Required data
Common holdings and bilateral links
Method and intended use
Compare direct asset losses with additional network losses.
Limits and checks
Shared exposures alone do not identify interbank transmission.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
ECB, Economic shocks and contagion in the euro area banking sector: a new micro-structural approach, Financial Stability Review (May 2019), sections 2–6 and Box A.
Primary source ↗S03Stress overlapping portfolios
Working paper · AHS application
Required data
Security-level holdings and price-impact assumptions
Method and intended use
Trace forced sales into losses on commonly held assets.
Limits and checks
Price impact and liquidation ordering are scenario assumptions.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
ECB, Economic shocks and contagion in the euro area banking sector: a new micro-structural approach, Financial Stability Review (May 2019), sections 2–6 and Box A.
Primary source ↗S04Stress interbank funding withdrawal
Working paper · AHS application
Required data
Funding maturities and available liquidity
Method and intended use
Compare liquidity shortfalls with direct credit losses.
Limits and checks
Liquidity distress and insolvency are different states.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
ECB, Economic shocks and contagion in the euro area banking sector: a new micro-structural approach, Financial Stability Review (May 2019), sections 2–6 and Box A.
Primary source ↗S05Study maturity-transformation fragility
Working paper · AHS application
Required data
Short-term funding and long-term assets
Method and intended use
Map rollover needs under funding refusal scenarios.
Limits and checks
The scenario does not estimate the probability of a run.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Schwarcz, in Anand (ed.), Systemic Risk, Institutional Design, and the Regulation of Financial Markets (2016), ch. 2, printed pp. 41–44 / PDF pp. 64–67.
Reference: supplied book, chapter and printed/PDF pages above.
S06Map cross-border supervisory gaps
Working paper · AHS application
Required data
Legal entities, activities and authority mandates
Method and intended use
Identify handoff gaps in a hypothetical cross-border crisis.
Limits and checks
This is institutional analysis, not a statement of current legal powers.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Anand, Trebilcock & Rosenstock, in Anand (ed.), Systemic Risk, Institutional Design, and the Regulation of Financial Markets (2016), ch. 1, printed pp. 1–6, 37 / PDF pp. 24–29, 60.
Reference: supplied book, chapter and printed/PDF pages above.
S07Review incentives that amplify fragility
Working paper · AHS application
Required data
Risk metrics, compensation and investment horizons
Method and intended use
Compare short-term incentives with long-horizon loss exposure.
Limits and checks
An incentive mechanism does not prove behavior by a particular institution.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Schwarcz, in Anand (ed.), Systemic Risk, Institutional Design, and the Regulation of Financial Markets (2016), ch. 2, printed pp. 41–44 / PDF pp. 64–67.
Reference: supplied book, chapter and printed/PDF pages above.
S08Discuss emergency liquidity design
Working paper · AHS application
Required data
Collateral, liquidity gaps and solvency assessments
Method and intended use
Compare hypothetical liquidity support and no-support scenarios.
Limits and checks
The 2016 discussion does not establish current eligibility or legal authority.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Lastra, in Anand (ed.), Systemic Risk, Institutional Design, and the Regulation of Financial Markets (2016), ch. 7, printed pp. 177–178 / PDF pp. 200–201. Historical institutional analysis, not current eligibility criteria.
Reference: supplied book, chapter and printed/PDF pages above.
S09Study a bank-sovereign feedback
Working paper · AHS application
Required data
Sovereign holdings and bank capital exposures
Method and intended use
Map a sovereign repricing shock into bank losses and potential public support.
Limits and checks
Feedback strength requires an explicit fiscal and pricing model.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Anand, Trebilcock & Rosenstock, in Anand (ed.), Systemic Risk, Institutional Design, and the Regulation of Financial Markets (2016), ch. 1, printed pp. 1–6, 37 / PDF pp. 24–29, 60.
Reference: supplied book, chapter and printed/PDF pages above.
S10Include nonbank transmission
Working paper · AHS application
Required data
Banks, funds and short-term funding links
Method and intended use
Map transmission outside the commercial banking perimeter.
Limits and checks
Missing nonbank exposures can understate vulnerabilities.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Anand, Trebilcock & Rosenstock, in Anand (ed.), Systemic Risk, Institutional Design, and the Regulation of Financial Markets (2016), ch. 1, printed pp. 1–6, 37 / PDF pp. 24–29, 60.
Reference: supplied book, chapter and printed/PDF pages above.
S11Compare single and combined channels
Working paper · AHS application
Required data
Same initial shock and consistent balance sheets
Method and intended use
Run credit, liquidity and fire-sale channels separately and jointly.
Limits and checks
Combined effects need not equal the sum of isolated effects.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
ECB, Economic shocks and contagion in the euro area banking sector: a new micro-structural approach, Financial Stability Review (May 2019), sections 2–6 and Box A.
Primary source ↗S12Compare resilience interventions
Working paper · AHS application
Required data
Baseline network and explicit intervention costs
Method and intended use
Compare buffers and liquidity provision under a fixed stress scenario.
Limits and checks
Scenario improvement is not a causal estimate of policy effectiveness.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Schwarcz, in Anand (ed.), Systemic Risk, Institutional Design, and the Regulation of Financial Markets (2016), ch. 2, printed pp. 41–44 / PDF pp. 64–67.
Reference: supplied book, chapter and printed/PDF pages above.
Four-bank default cascade
Interactive demonstrator · AHS · 15 October 2026
AHS deterministic illustration: B lends to A, C to B, D to C and A to D, with the same claim size. A takes the initial external loss. Equity at or below zero triggers default; each creditor loss is applied once. Recoveries are fixed. No liquidity, netting, fire sales, feedback pricing or clearing equilibrium is modeled.
Equation, units and interpretation
\ell_i=s_i+\sum_{j\in D}(1-R)A_{ij},\quad E_i=K_i-\ell_i,\quad i\in D\ \mathrm{if}\ E_i\leq0
A_ij: creditor i’s claim on debtor j; K_i: initial equity; s_i: external loss (only A is shocked); ℓ_i: cumulative loss; E_i: remaining equity, all in € million; R: recovery fraction; D: cumulative default set. Newly defaulted debtors generate one loss per creditor in the next round.
Anand, Trebilcock & Rosenstock, in Anand (ed.), Systemic Risk, Institutional Design, and the Regulation of Financial Markets (2016), ch. 1, printed pp. 1–6, 37 / PDF pp. 24–29, 60.
The equation and implementation are simplified AHS applications of the cited framework.
Systematic risk: common-factor exposure
Explore a question, inspect its evidence requirements, then choose a method. The cards are Working papers describing research designs; they do not run estimators. The separate demonstrator below performs only the displayed calculation using synthetic inputs.
F01Decompose market and residual variance
Working paper · AHS application
Required data
Beta, market variance and residual variance
Method and intended use
Use a single-factor return model with zero factor-residual covariance.
Limits and checks
Systematic exposure is not systemic contagion.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
William F. Sharpe, Capital Asset Prices with and without Negative Holdings, Nobel Lecture (1990), beta as covariance with the market divided by market variance.
Primary source ↗F02Stress a portfolio market beta
Working paper · AHS application
Required data
Portfolio weights, betas and a market return shock
Method and intended use
Aggregate beta and approximate the common-factor return contribution.
Limits and checks
Nonlinear instruments require additional risk terms.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
William F. Sharpe, Capital Asset Prices with and without Negative Holdings, Nobel Lecture (1990), beta as covariance with the market divided by market variance.
Primary source ↗F03Model multiple common factors
Working paper · AHS application
Required data
Returns and identified observed or latent factors
Method and intended use
Estimate factor exposures and reconstruct conditional covariance.
Limits and checks
Latent factor rotations and residual dependence require controls.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Jacquier & Polson, in The Oxford Handbook of Bayesian Econometrics (2011), ch. 9 §4.2, printed pp. 467–468 / PDF pp. 480–481.
Reference: supplied book, chapter and printed/PDF pages above.
F04Challenge apparent diversification
Working paper · AHS application
Required data
Portfolio weights, factor loadings and covariance
Method and intended use
Separate name diversification from shared factor concentration.
Limits and checks
Many holdings can still carry one dominant common exposure.
Source framework; the decision workflow above is an AHS adaptation, not a reproduced case or an empirical finding.
Jacquier & Polson, in The Oxford Handbook of Bayesian Econometrics (2011), ch. 9 §4.2, printed pp. 467–468 / PDF pp. 480–481.
Reference: supplied book, chapter and printed/PDF pages above.
Common factor versus residual risk
Interactive demonstrator · AHS · 15 October 2026
AHS single-factor illustration with zero covariance between the factor and the residual. Volatilities are annualized percentages; beta is dimensionless. A supplied factor shock gives only its linear return contribution, excluding alpha and the residual shock.
Equation, units and interpretation
\sigma_p^2=\beta^2\sigma_m^2+\sigma_\epsilon^2,\quad q=\frac{\beta^2\sigma_m^2}{\sigma_p^2},\quad \Delta r_p^{factor}=\beta\Delta r_m
β: market beta; σ_m: market volatility; σ_ε: residual volatility; σ_p: total volatility, all volatilities in %/√year; q: factor variance share; Δr_m: factor return shock (%); Δr_p: return contribution (%). q is undefined when total variance is zero.
William F. Sharpe, Capital Asset Prices with and without Negative Holdings, Nobel Lecture (1990), beta as covariance with the market divided by market variance.
The equation and implementation are simplified AHS applications of the cited framework.