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### I. Introduction — purpose, accounting context, and design
- Presents a tool suite for International Financial Reporting Standards 9 (IFRS 9)- and Current Expected Credit Loss (CECL)-compatible top-down stress testing.
- "Top-down" denotes an institutional perspective: forward-looking solvency analysis by an oversight organization (central bank, supervisor, IMF in FSAPs).
- Aim: present model elements instrumental for scenario-conditional expected credit loss (ECL) estimation.
- Design and use:
  - Limits model complexity and data needs; describes multiple modeling options based on different levels of data availability.
  - Models and conceptual underpinnings used in FSAPs since 2018: Canada, France, Korea, Latvia, and Singapore; part of technical assistance missions over the past two years.
- Challenges for top-down stress testing:
  - Interplay of regulatory and accounting rules increases complexity.
  - Often absent long and granular portfolio-level data in the public domain.
  - Complex to implement for supervisors without granular portfolio data.

### II. What is ECL — adoption, distinctions, pandemic context, incentives
- Adoption timelines and scope:
  - IFRS 9 published in 2014; effective January 1, 2018.
  - As of end-year 2018, 144 of 166 countries (87 percent) require IFRS standards (surveyed by IASB).
  - Five of the 20 G20 countries do not currently follow IFRS: China, India, Indonesia, Japan, and the United States.
  - IFRS 9 transposed into EU law in 2016.
  - FASB called for CECL adoption in June 2016; CECL adopted in the United States.
  - CECL effective implementation date for certain public firms: December 15, 2019; effective date for smaller firms delayed until January 2023. Banks were given the option to delay CECL implementation through the CARES Act.
- Conceptual distinctions:
  - IFRS 9 staging: assets enter Stage 1 upon origination; Stage 1 assets: 12-month provisioning horizon; Stages 2 and 3: lifetime provisioning horizon.
  - CECL: no staging required; all exposures are subject to lifetime provisioning.
- Pandemic context and policy responses:
  - Implementation of ECL coincided with COVID-19; concerns about negative effects on credit provision.
  - Relief/countercyclical measures: temporary postponements, transitional arrangements, guidance on moratoria, forbearance, defaults, sovereign guarantees.
  - IASB guidance: IFRS 9 models should not be used mechanistically; consider government support measures in determining lifetime losses.
  - SSM and ECB recommended centrally defined macroeconomic scenarios to address scenario uncertainty and avoid excessive provision increases.
- Implementation challenges and incentives:
  - Principle-based frameworks leave many implementation choices to banks (e.g., criteria for Stage 1→2 transitions).
  - Heterogeneous implementation complicates cross-bank comparisons.
  - ECL increases modeling complexity and model risk; IFRS 9 and CECL do not contain explicit back-testing requirements.
  - CECL implies less model risk from a top-down perspective regarding staging, but lifetime loss calculations remain complex.
- Evidence and industry expectations:
  - Literature and simulations indicate IFRS 9 and CECL imply a more pronounced provisions response to negative credit shocks relative to incurred loss regimes.
  - EBA (2016): “60% of the banks anticipate that IFRS 9 impairment requirements will have an impact on lending practices of banks in terms of the pricing of products.”
  - Behavioral incentives (optimistic bias in PDs/LGDs, herding, competition) may delay stage migrations and amplify procyclical outcomes.

### III. Economic implications, procyclicality, and policy tools
- Definitions and sources:
  - Procyclicality per Financial Stability Forum (2008): mutually reinforcing mechanism amplifying business fluctuations and possibly causing or exacerbating financial instability.
  - Sources of procyclical lending include borrower behavior, bank incentives, competition/herding, and regulation/policy (including accounting regimes).
- Policy tools to counteract procyclicality:
  - Dynamic capital buffers (e.g., countercyclical capital buffers) can be released to mitigate cliff effects at recession onset.
  - Stress testing to inform Basel Pillar 2 capital requirements and Pillar 2 guidance; set stress-test-based buffers (US FED “stressed capital buffers”, BoE).
    - For stress tests to inform such buffers, scenario design must be countercyclical (state-dependent).
  - Strengthened supervisory and audit oversight to challenge banks’ assumptions, scenarios, and provisions.
  - Development of top-down ECL model suites to support supervisory challenge and quantitative assessment.

### IV. Analytical tool suite for top-down ECL modeling — core components and modeling options
- High-level model categories:
  - Aggregate loss models: historical loan loss provision rates or write-off rates; regression linking loss rates to macro-financial conditions (useful under CECL).
  - Transition matrix (TM) models: capture staging transitions' dependence on macro-financial conditions (useful under IFRS 9).
  - Vintage models: track credit risk by origination cohort; data-demanding.
  - Loan-level data models: micro approach using loan tapes or credit registers; most granular and data-intensive.
- TM models: balance data richness and model complexity; suitable for IFRS 9 stress testing for top-down scenario-conditional forecasts.
- TM modeling choices:
  - Cell-level logit/probit regressions of individual TM cells on macro variables.
  - One-factor representation of the TM (Belkin et al. 1998 Z-score methodology) with regression of that factor on macro-financial variables.
  - Choice depends on historical TM data availability.
- Treatment of low-default portfolios:
  - Exempt sparse TM portfolios (e.g., central government loans) from TM modeling; alternatively relate point-in-time PD to macro variables and trigger Stage 2 on a multiple of PD change (example: three-fold increase).
- Model flow and modularity:
  - ECL Model Suite modular flow centers on TM concept; implemented options used in IMF FSAPs (Option 1 in Canada, France, Latvia, Singapore; Option 2 in 2019 Korea FSAP).

### V. Z-score (Box 1) and translating Z to scenario-conditional TMs (Box 2)
- Z-score methodology (Belkin et al., 1998):
  - Reduces time series of transition matrices to one number per point in time; assumes X = √(1−ρ) Y + √ρ Z with Y and Z independent unit normal and ρ capturing correlation between Z and X.
  - Fitted transition probabilities use Φ (standard normal CDF) and bin boundaries x_i from the long-term average TM.
  - Historical Z_t found by minimizing weighted sum of squared deviations between observed and fitted TM elements; double-loop search for ρ and Z_t subject to Var(Z_t)=1.
  - Interpretation: +1/−1 denotes one standard deviation from long-run average conditions.
  - Implementation note: Excel/VBA Excel module provided; more efficient Matlab/R implementations possible.
- Linking Z to macro-financial conditions:
  - Standard regression methods or approaches accounting for model uncertainty (e.g., Bayesian Model Averaging) to produce econometric bridge equations.
  - Scenario-conditional Ẑ_t paths translated back to TM paths using same functional form as historical fit; ρ and bin boundaries fixed.
- Augmenting TM for maturing (M) and write-off (WRO) flows:
  - Add scenario-conditional M_i and WRO_i as additional columns; normalize rows to sum to one again using TR*_{i,·} = TR_{i,·} / ∑ TR_{i,·} × (1 − M_i − WRO_i), ∀ i = 1,2,3 (one normalization considered).
  - Maturing percentages and write-offs can be pre-defined or linked to macro variables; write-offs often lag recessions and may follow supervisory rules.
- Implied S1/S2/S3 stock dynamics (flow-stock equations):
  - Preserve transition notation TR_{ij} and M/WRO terms in equations for S1_t, S2_t, S3_t (equations preserved as in source).
  - Alternative with explicit gross loan growth control: S_t = (1 + g_t) S_{t−1} and S1_t = max(0, S_t − S2_t − S3_t).
  - Relation to PL/NPL default-rate frameworks: PL_t and NPL_t stock-flow equations (equations preserved); default rate DR_t can be solved from these relations.

### VI. Alternative TM methods for weak-data environments (Section C)
- Option 1: “beta-linking”
  - When TM time series absent but default rate series exist; develop satellite model for default rates and use betas to link TR1-3 and TR2-3 to remaining probabilities.
  - Betas can be based on limited historical TM data, judgment, or borrowed from other jurisdictions; robustness analyses required.
- Option 2: “anchoring-in-PDs”
  - When TM data exist but do not cover a full cycle: compute a Z-factor on the shorter TM sample; develop satellite model for default rates that cover cycles; set Z path so implied PDs match satellite PD path.
  - Illustrated in the ECL Model Suite.
- Option 3: full Z-score-based methodology (preferred if sufficient TM time series exist).

### VII. LGD modeling for real-estate collateralized portfolios (Box 3)
- Rationale:
  - LGD requires macro-financial scenario dependence; structural models for real estate collateralized portfolios link collateral value to house price trajectories.
- Inputs for advanced model:
  - (1) current portfolio-level LTVs (ideally exposure-weighted);
  - (2) cure rates from a T0 transition matrix (S3→S2/1);
  - (3) LGD as of Year 0 for relevant portfolios.
- Simple LGD model:
  - LGD(t) = 1 − [1 − LGD(0)]^{φ(t)} (notation preserved); numerical example: LGD = 25 percent at reference date and house price drop = 20 percent → LGD rises to 40 percent per simple model.
  - Caveats: no cures, no overcollateralization, treats LGD as not forward-looking.
- Advanced LGD model:
  - LGD = (1 − Probability of cure) × LGL + Costs; LGL = max(1 − Expected Recovery Value / Loan, 0).
  - Sales ratio (SR) = Expected Recovery Value / Reported Current Collateral Value; SR modeled as a distribution (modified Normal specification preserved).
  - Application steps: find μ so model-implied LGD matches observed LGD or set μ and imply σ; compute scenario-conditional LTV(t) = LTV(0) × φ_houseprice(t).
- Recommendations:
  - Prefer the advanced LGD model for more realistic scenario-conditional LGD estimates across a range of initial LGD/LTV starting points.
- Uncollateralized portfolios:
  - Strategies: (1) econometric satellite LGD models if time series exist; (2) use regulatory downturn LGD estimates; (3) decompose aggregate loss projections into PDs and LGDs (Frye/Jacobs method, FED DFAST methodology).

### VIII. Lifetime ECL (LT-ECL) calculations and handling long residual maturities (Box 4)
- Need for lifetime calculations:
  - S2 and S3 exposures require lifetime horizon; CECL requires lifetime horizon for performing portfolio.
  - Lifetime horizon implies macro-financial scenarios must extend to residual maturity (e.g., mortgage portfolios average duration 15 years require up to 15-year TM forward paths).
- Options for long residual maturity treatment:
  - Employ assumptions on macro-financial factor behavior beyond initial scenario horizon (usually 3 to 5 years).
  - Conduct scenario simulations based on a macro-financial model suite explicitly farther into the future.
- Lifetime ECL structure:
  - Symbolic formula: ECL = sum_{s=1..M} [incremental PD * PiT LGD * exposure discounted by effective loan interest rate]; denominator includes effective loan interest rate for discounting.
  - Incremental PD: TR_t^{2-3,*} = TR_t^{2-3} * product_{u=1..t-1} (1 − TR_u^{2-3}) — i.e., PD in period s conditional on survival to s−1 approaching zero over time.
  - If M = 1, lifetime ECL reduces to 12-month ECL.
- Projection of S2 exposures:
  - Options include nonlinear repayment schedules or simplifying linear principal repayment paths; ECLs may be insensitive to choice.
  - For variable-rate portfolios, an expectation about loan interest rate is required.
- Recommendation:
  - Choose projection approach aware of potential limited sensitivity; consider prepayments and interest-rate expectations.

### IX. Provision stock and flow calculations (Box 5) — mapping ECL to accounting provisions
- Provision formulas preserved:
  - S1 (12-month ECL): PROV_{t,S1} = ECL_{t,S1} = TR_t^{S1|t} * LGD_{t+H|t} * S1_t.
  - S2 (lifetime ECL): PROV_{t,S2} = ECL_{t,S2} = sum_{s=1..M} [incremental PD_s * PiT LGD_s * S2_s discounted].
  - S3 (defaulted): PROV_{t,S3} = ECL_{t,S3} = LGD_{t+H|t} * S3_t.
  - Total provision stock: PROV_t = PROV_{t,S1} + PROV_{t,S2} + PROV_{t,S3}.
  - Provision flow: PROVFLOW_{t+1} = ΔPROV_{t+1} + WRO_t − LGD_t * S3_{t−1} (assumes LGD used to set pre-write-off provision equals realized LGD upon collateral sale).
- Observed patterns:
  - Under an adverse scenario, IFRS 9 and CECL-implied provision flows are more front-loaded than IAS 39.
  - IFRS 9 exhibits a “cliff effect” from 12-month horizon for S1 and lifetime horizon for S2; S2 provisions tend to increase significantly in year one of an adverse scenario.
  - Cumulative losses over a long adverse period are the same across accounting regimes absent second-round macro effects; timing differs.
- Top-down simplification:
  - Full lifetime ECL for combined S1+S2 portfolio is a useful benchmark; reduces data needs and model risk; Box 5 equation (1) becomes obsolete and equation (2) applies to combined S1+S2.
  - When using CECL in an IFRS 9 regime, model-implied Year 0 provision stocks will be larger than banks’ Year 0 provisions (banks provision S1 on 12-month horizon).

### X. Interplay between accounting provisions and regulatory capital (Section G and Box 6)
- Interactions and regulatory treatments:
  - Loan loss provisions + residual net equity capital = “gross equity”; provisions cover expected losses, residual capital covers unexpected losses.
  - IRB approach compatible with a 12-month ECL horizon using regulatory TTC PD and downturn LGD.
  - Regulatory treatment of accounting provisions:
    - IRB shortfall rule: if regulatory EL exceeds accounting provision stocks, the difference is subtracted from CET1.
    - If regulatory EL falls short, the difference may be added back to Tier 2 capital subject to a limit of 0.6 percent of credit risk RWA and regulatory prior approval.
    - For STA exposures, general provision stocks can be added back to Tier 2 subject to a limit of 1.25 percent of credit risk RWA.
  - BCBS March 2017 decision: not to change current regulatory treatment of accounting provisions until further notice.
- Linking PiT risk parameters to regulatory (TTC/downturn) parameters (Box 6):
  - Exposure-weighted PiT PD computed from TR1-3 and TR2-3 forward paths; link PiT PD forward path to regulatory TTC PD using smoothing and logit transforms:
    - Use logit/inverse logit to ensure TTC PD ∈ [0,1]; smoothing parameter α between 0 and 1 (example α = 0.75) avoids full pass-through (α = 1) and excessive fluctuations.
  - Regulatory LGD link: LGD_{reg,t} = max(LGD_{downturn at outset}, LGD_{PiT,t}).
  - Guidance: map PiT stress into regulatory parameters exercising judgment, mindful of scenario nature (cyclical vs structural) and model risk from ad hoc choices (time windows, α). Document linkages and sensitivity analyses.

### XI. Multiple scenarios, perfect foresight, and simulation-based approaches (Box 6 and Box 7)
- IFRS 9 requires multiple macroeconomic scenarios to be probability-weighted: paragraph 5.5.17 (IASB 2014) requires an “unbiased and probability-weighted amount determined by evaluating a range of possible outcomes.”
  - Industry practice: ad hoc and judgmental scenario construction and weights; most banks use three scenarios; small single-digit percentage use four.
- Perfect foresight:
  - Assumes one scenario materializes with 100 percent probability (e.g., adverse scenario); incompatible with IFRS 9 for accounting provisioning but permitted in top-down stress testing by BoE and ECB/EBA/SSM.
  - Reliance on one scenario risks hand-picking and scenario uncertainty.
- Strategies for long horizons:
  - Strategy 1: conditional forecasts of PiT risk parameters up to residual maturity requiring assumptions for all macro drivers.
  - Strategy 2: project baseline and adverse TM paths up to, e.g., five years, then assume steady baseline and reversion of adverse toward baseline over a reversion period (e.g., eight to 10 years), anchor end-point to long-term average TM or regulatory TTC parameters.
- Monte Carlo simulation recommendations (Box 7):
  - Use integrated macro-financial model suites; account for macro-financial feedback, residual/coefficient/model uncertainty.
  - Simulation example: trivariate VAR (1988–2018, 31 obs.) with real GDP lnYoY, nominal house prices lnYoY, and a private-sector PD (logit); LGD module connected to house prices; simulate 2,000 paths; scenario horizon 10 years; LGD module relevant horizon three years; starting LGD 50 percent; discount rate 1 percent.
  - Findings:
    - Accounting for coefficient uncertainty widens LT-ECL distribution, shifts mean and median upward, and increases skewness.
    - Hand-picked three-scenario point forecasts (upside 0.49 percent, baseline 0.62 percent, downside 0.86 percent) do not generally match simulated distributional moments; many weight combinations could match the simulated median (0.7 percent).
  - Conclusions:
    1. Weights on hand-picked scenarios remain ad hoc; tying weights to impulse-response shock probabilities is problematic.
    2. Stochastic simulations can obviate hand-picked scenarios and indeterminate weights once an integrated model suite is specified.
    3. LT-ECL distributions are likely markedly skewed; accounting for all uncertainty sources is warranted to avoid underestimating width and skewness.

### XII. Data templates and practical top-down implementation (Section V)
- Required bank-portfolio level data:
  - Banks’ Year 0 stock-balance sheet position (template exemplified in Figure 11).
  - Historical stocks of exposures in Stages 1/2/3, cross-stage flows, write-off flows (WRO), and new business flows (template in Figure 12).
  - Financial asset stocks and flows in monetary units; transition matrices with percentages computed by dividing time-t flows by end-of-previous period (t-1) stocks.
- Staging criteria and reporting options:
  - Option 1: banks use own staging criteria to report exposure stocks/flows.
  - Option 2: define common staging criteria and instruct banks to report according to those.
  - Practical compromise: banks report historical data per their criteria; stress tests assume simplified common staging criteria under stress.
- Use of historical regulatory exposure classifications:
  - Retrospective mapping: performing → Stage 1; substandard + doubtful → Stage 2; loss → Stage 3.
- Templates and model elements:
  - Full templates and model elements available from authors on request (note preserved from source).

### XIII. Conclusions — policy-relevant recommendations and empirical findings
- Aim recap:
  - Overview of ECL implications from macro-financial and economic perspectives: heterogeneity in provisioning models, limited comparability across banks, procyclicality, and lack of incentives for banks to measure risk appropriately.
  - Present integrated tool suite for top-down IFRS 9- and CECL-compatible solvency analyses (suitable for supervisors, central banks, and international organizations).
- Tool suite components:
  - Transition matrix modeling; lifetime PD modeling; two structural LGD variants for real-estate collateralized portfolios; link to risk-weighted assets and capital calculations.
- Empirical FSAP applications and findings:
  - Canada 2019 FSAP: under the adverse scenario, accounting impairment charges increase significantly under IFRS 9; in the adverse scenario, accounting impairment charges would exceed regulatory provisions for most banks.
  - France 2019 FSAP: scarce data can lead to a wide range of estimated losses; uncertainty driven by loan portfolio growth assumptions and differences in write-off policies.
  - 2019/20 Korea FSAP: long historical TM data allowed robust model approach using Z-factor methodology for the first time.
- Policy recommendations:
  - Oversight institutions should retain independent models for stress testing and ECL modeling due to banks' incentives to underestimate risk and the principles-based accounting framework.
  - Independent assessment of scenario design and stress testing is warranted.
  - Document methodology choices, linkages, and time-window selections; perform sensitivity analyses.
  - Consider full lifetime ECL benchmarks for top-down stress testing for robustness and reduced model risk.

### XIV. Key numeric and date-level facts (preserved verbatim)
- 2007-09 global financial crisis (GFC)
- G20 meeting in London in April 2009
- IFRS 9 published in 2014; effective January 1, 2018
- As of end-year 2018: 144 of 166 countries (87 percent) require IFRS standards (surveyed by IASB)
- Five of the 20 G20 countries do not currently follow IFRS: China, India, Indonesia, Japan, and the United States
- IFRS 9 transposed into EU law in 2016 (EC 2016)
- FASB called for CECL adoption in June 2016 (FASB 2016)
- CECL effective implementation date for certain public firms: December 15, 2019
- CECL effective date for smaller firms delayed until January 2023
- Stage 1 assets: 12-month provisioning horizon; Stages 2 and 3: lifetime provisioning horizon
- EBA (2016): “60% of the banks anticipate that IFRS 9 impairment requirements will have an impact on lending practices of banks in terms of the pricing of products.”

*Source: wpiea2020111-print-pdf (IMF working paper excerpt).*

### References .............................................................................................................

### wpiea2020111-print-pdf - References

### Figures
- 1. IFRS 9 Staging Principles ......................................................................................................8
- 2. Topics Related to the ...........................................................................................................10
- 3. Sources of procyclical lending .............................................................................................11
- 4. ECL Model Choices .............................................................................................................12
- 5. Transition Matrix (TM) Modeling Choices .........................................................................14
- 6. ECL Model Flow .................................................................................................................15
- 7. IFRS 9 Transition Matrices ..................................................................................................16
- 8. From Historical Transition Matrices to the Z-score ............................................................17
- 9. Uncertainty about Future Sales Price of Collateral Driving LGDs .....................................22
- 10. Treatment of Risk Parameters beyond an Initial Scenario Horizon under a Perfect Foresight Stress Test Mode ......................................................................................................34
- 11. Balance Sheet Stocks as of Year 0 .....................................................................................39
- 12. Financial Asset Stocks in Stages 1/2/3 and Historical Transition Flows  .........................40

### Boxes
- 1. The Z-Score Methodology ...................................................................................................17
- 2. From Scenario-Conditional Z-Scores to Transition Matrices and Implied S1-2-3 (Performing and Nonperforming) Exposure Stocks ................................................................19
- 3. A Simple and an Advanced LGD Model for Real Estate-Collateralized Portfolios ............23
- 4. Lifetime Expected Credit Loss (LT-ECL): Formula and Components ...............................26
- 5. Loan Loss Provision Stock and Flow Calculations .............................................................28
- 6. Risk Weighted Assets: Linking Regulatory Risk Parameters (IRB) to PiT Risk Parameters (Accounting) ............................................................................................................................32
- 7. Monte Carlo-based Lifetime Expected Loss Distributions Versus Self-Set Scenarios and Weights ....................................................................................................................................35

### I. INTRODUCTION
- Purpose:
  - Presents a tool suite for International Financial Reporting Standards 9 (IFRS 9)- and Current Expected Credit Loss (CECL)-compatible top-down stress testing.
  - "Top-down" denotes an institutional perspective: a forward-looking solvency analysis conducted by an oversight organization, such as a central bank, a supervisor, or an international organization such as the IMF while it is conducting stress tests as part of its risk assessment in Financial Sector Assessment Programs (FSAPs).
  - Aim: present a set of relevant top-down model elements instrumental for scenario-conditional expected credit loss (ECL) estimation.
- Accounting context and benefits:
  - IFRS 9 and CECL—and ECL more generally—aim at moving from a lagged incurred loss to a more time-contemporaneous recognition under the expected loss model.
  - Benefits cited: may prevent banks from providing excessive payouts to shareholders after the onset of material recessions when net income may still be positive due to delayed recognition of losses; may help improve investor and market confidence on banks’ balance sheet health during economic downturns.
- Challenges for top-down stress testing:
  - Enhanced complexity due to interplay of regulatory and (new) accounting rules.
  - Generally absent long and granular portfolio-level data in the public domain.
  - Major public stress testing programs (US Federal Reserve, Bank of Japan, European Banking Authority (EBA), European Central Bank (ECB), Bank of England (BoE), and so on) focus on credit losses estimated in line with the relevant accounting regimes.
  - Credit losses are subtracted from banks’ capital base, and risk weighted asset (RWA) dynamics are modeled according to regulatory rules.
  - Complexity is less of an issue for banks with granular exposure data; it is challenging for top-down stress testers without access to granular portfolio data.
  - The paper suggests model methods that top-down supervisors can use in data-weak environments.
- Design and use of the tool suite:
  - Designed to limit model complexity and hence data needs.
  - Describes multiple modeling options based on different levels of data availability.
  - These models and conceptual underpinnings have been used in various FSAPs since 2018: Canada, France, Korea, Latvia, and Singapore.
  - They also have been part of technical assistance missions over the past two years.
- Structure of the paper:
  - Section 2 summarizes what ECL is about, from an economics perspective.
  - Section 3 presents a tool suite comprising various analytical components for ECL modeling. The ECL Model Suite accompanies this paper.
  - Section 4 focuses on the concepts of multiple scenarios, perfect foresight, and related aspects.
- Footnote text preserved:
  - 2 The related technical notes documenting the stress test methodologies and results include the following: 2019 France FSAP (IMF 2019a), 2019 Singapore FSAP (IMF 2019b), 2019 Canada FSAP (IMF 2020a), 2019 Korea FSAP (IMF 2020b), 2019 Latvia FSAP (IMF 2020c).

*Source: wpiea2020111-print-pdf - References*

### Section 5 presents some exemplary database template structures for the collection of

### wpiea2020111-print-pdf - Section 5 presents some exemplary database template structures for the collection of

### II. WHAT IS ECL ABOUT?
- Background and motivation
  - ECL accounting was promoted shortly after the 2007-09 global financial crisis (GFC) in response to calls to overhaul then-existing accounting principles.
  - G20 decision in London in April 2009 aimed to strengthen the post-GFC financial system.
  - Criticism of the previous regime: too backward-looking and deferring recognition of loan losses, contributing to procyclical dynamics.

- Adoption timelines and scope
  - IFRS 9 published in 2014 and became effective on January 1, 2018.
  - As of end-year 2018, 144 of 166 countries (87 percent) that the IASB surveyed require IFRS standards (not all have adopted IFRS 9 specifically).
  - Among G20 countries, five of the 20 do not currently follow IFRS: China, India, Indonesia, Japan, and the United States.
  - IFRS 9 was transposed into EU law by the European Commission in 2016.
  - In June 2016, FASB called for adoption of the CECL approach (FASB 2016); CECL is adopted in the United States.
  - CECL effective implementation date for public firms meeting the SEC filer definition was December 15, 2019; effective date for smaller firms has been delayed until January 2023.
  - Banks were given the option to delay CECL implementation through the CARES Act.

- Conceptual distinctions between IFRS 9 and CECL
  - IFRS 9 consists of three categories: (1) classification and measurement of financial assets and liabilities; (2) expected loss-based impairment model principles; and (3) hedge accounting. The second is most significant for stress testing.
  - IFRS 9 staging: assets enter Stage 1 upon origination; based on change in default risk they may move to Stage 2 or 3. Stage 1 assets: 12-month provisioning horizon; Stages 2 and 3: lifetime provisioning horizon.
  - CECL: no staging required; all exposures are subject to lifetime provisioning.

- Pandemic context and policy responses
  - Implementation of ECL coincided with COVID-19 outbreak; concerns about negative effects on credit provision.
  - CECL requires immediate lifetime loss provisioning at origination, which can raise loan origination costs and potentially reduce new lending.
  - Relief and countercyclical measures included temporary postponements and transitional arrangements; guidance issued on moratoria, forbearance, defaults, and sovereign guarantees.
  - IASB guidance stressed that IFRS 9 models should not be used mechanistically and that government support measures should be considered in determining lifetime losses.
  - SSM and ECB recommended centrally defined macroeconomic scenarios to address scenario uncertainty and avoid excessive provision increases.

- Implementation challenges and incentives
  - Principle-based frameworks leave many implementation choices to banks (e.g., criteria for Stage 1→2 transitions, setting probabilities and severities of adverse scenarios).
  - Heterogeneous implementation across banks complicates cross-bank comparisons of accounting and regulatory metrics.
  - ECL regime increases modeling complexity and model risk; neither IFRS 9 nor CECL contain explicit back-testing requirements.
  - CECL implies less model risk from a top-down stress test perspective (except lifetime loss calculations), since no Stage 1/2 distinction exists.

- Evidence and industry expectations
  - Literature and simulations indicate IFRS 9 and CECL imply a more pronounced provisions response to negative credit shocks relative to incurred loss regimes (e.g., Abad and Suarez 2017; Chae et al. 2018).
  - EBA (2016) survey: “60% of the banks anticipate that IFRS 9 impairment requirements will have an impact on lending practices of banks in terms of the pricing of products.”
  - Behavioral incentives (optimistic bias in PDs/LGDs, herding, competition) may delay stage migrations and amplify procyclical outcomes.

### III. ECONOMIC IMPLICATIONS, PROCYCLICALITY, AND POLICY TOOLS
- Factors and definitions
  - Procyclicality defined by Financial Stability Forum (2008) as the “mutually reinforcing (‘positive feedback’) mechanism through which the financial system can amplify business fluctuations and possibly cause or exacerbate financial instability.”
  - The move to ECL relates to the fair-value versus book-value accounting debate; ECL aims for timelier loss recognition.

- Sources of procyclical lending (schematic)
  - Multiple sources: borrower behavior, bank incentives, competition/herding, and regulation/policy (including accounting regimes).

- Policy tools to counteract procyclicality
  - Dynamic capital buffers (for example, countercyclical capital buffers) can be released to mitigate cliff effects at recession onset.
  - Stress testing: inform Basel Pillar 2 capital requirements and Pillar 2 guidance (ECB/SSM); set stress test-based buffers (US FED “stressed capital buffers”, BoE).
    - For stress tests to inform such buffers, scenario design must be countercyclical (state-dependent).
  - Strengthened supervisory and audit oversight to challenge banks’ tools, assumptions, scenarios, and provisions.
  - Development of top-down ECL model suites to support supervisory challenge and quantitative assessment.

### IV. III. AN ANALYTICAL TOOL SUITE FOR TOP-DOWN ECL MODELING FOR STRESS TESTING PURPOSES
- High-level model categories for operationalizing ECL in top-down stress testing (Figure 4)
  - Aggregate loss models: historical loan loss provision rates or write-off rates; regression linking loss rates to macro-financial conditions (useful under CECL).
  - Transition matrix (TM) models: capture dependence of staging transitions on macro-financial conditions (useful under IFRS 9).
  - Vintage models: track credit risk characteristics by origination cohort; data-demanding.
  - Loan-level data models: micro approach using bank loan tapes or credit registers; most granular and data-intensive.

- TM models and suitability
  - TM-based approach balances data richness and model complexity; distinguishes PD and LGD dynamics; allows top-down scenario-conditional forecasts—suitable for IFRS 9 stress testing.
  - Aggregate loss models can be useful under CECL where lifetime PD/LGD estimation via historic loss models and vintages is operationally feasible.
  - Loan-level vintage models are data-intensive and may be developed as micro data accrues.

- TM modeling choices (Figure 5)
  - Options for relating historical TMs to macro-financial conditions:
    - Log-odds, fractional probit or logit modeling of individual TM cells (series of regressions of a TM’s individual cells on macro-financial variables).
    - One-factor representation of the TM with regression of that factor on macro-financial variables (Belkin et al. 1998 methodology).
    - Other methods (not detailed in supplied text) exist; choice depends on data availability.
  - Two particular options suitable for top-down scenario-conditional solvency analyses:
    - Cell-level logit/probit regressions.
    - One-factor TM representation with macro-financial linkage.

- Treatment of “singular” / low-default portfolios
  - Low-default portfolios (e.g., central government loans) produce sparse TMs and may be exempt from TM modeling.
  - Alternative: take point-in-time PD and relate it to macro variables; trigger Stage 2 migration on a multiple of PD change (example: three-fold increase).

- Model flow and modularity (Figure 6)
  - ECL Model Suite modular flow centers on TM concept; choice among TM modeling options depends on historical TM data availability.
  - IMF FSAP implementations:
    - Option 1 used in FSAPs for Canada, France, Latvia, and Singapore.
    - Option 2 used in the 2019 FSAP for Korea.

### V. A. HISTORICAL ONE-FACTOR REPRESENTATION OF TRANSITION MATRICES
- IFRS 9 TM specifications (Figure 7)
  - Two TM versions shown: simple and augmented (augmented makes explicit maturing flows from S1 and S2 and write-offs from S3).
  - Assumptions for stress testing:
    - S3 assets can be treated as nonperforming (principal and interest not repaid) → set maturing percentage to zero.
    - Assume S1 and S2 assets are not written off.
  - Maturing (M) and write-off (WRO) percentages can be set by assumptions or linked to macro variables via satellite models.
  - Write-off percentages often lag recessions and may be grounded in supervisory rules (e.g., mandatory write-off after one or two years).

- Z-score (single-index) compression of TM dynamics (Figure 8)
  - A Z-score summarizes a historical TM time series into one number per point in time.
  - Interpretation:
    - Z-score positive during expansions when downgrades are below long-term averages and cures are above averages.
    - Z-score negative during recessions when downgrades and defaults exceed historical averages.
  - Z-score methodology embedded in the tool suite accompanying the paper.

- Portfolio-level implementation guidance
  - IASB (2014) paragraph B5.5.5: impairment assessment may be individual or collective on groups with shared credit risk characteristics—portfolio-level TM modeling is the natural supervisory approach.
  - Typical portfolio splits for TM modeling: nonfinancial corporate loans and securities (optionally split by real estate collateralized), financial corporate, mortgage loans, consumer/retail loans, and sovereign loans and securities.

### VI. SUMMARY OF KEY NUMERIC and DATE-LEVEL FACTS (preserved verbatim)
- 2007-09 global financial crisis (GFC)
- G20 meeting in London in April 2009
- IFRS 9 published in 2014; effective January 1, 2018
- As of end-year 2018: 144 of 166 countries (87 percent) require IFRS standards (surveyed by IASB)
- Five of the 20 G20 countries do not currently follow IFRS: China, India, Indonesia, Japan, and the United States
- IFRS 9 transposed into EU law in 2016 (EC 2016)
- FASB called for CECL adoption in June 2016 (FASB 2016)
- CECL effective implementation date for certain public firms: December 15, 2019
- CECL effective date for smaller firms delayed until January 2023
- Stage 1 assets: 12-month provisioning horizon; Stages 2 and 3: lifetime provisioning horizon
- EBA (2016): “60% of the banks anticipate that IFRS 9 impairment requirements will have an impact on lending practices of banks in terms of the pricing of products.”

- Key methodologies and references embedded or cited
  - Belkin et al. (1998) one-factor TM methodology
  - Z-score methodology for TM compression (tool suite includes this)
  - BCBS (2015) guidance lists back-testing as a best practice to consider (para. 31)

*Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020111-print-pdf.pdf*

### Box 1. The Z-Score Methodology

### Box 1. The Z-Score Methodology

### A. Purpose and conceptual framework
- The Z-score methodology (Belkin et al., 1998) reduces the information in a time series of transition matrices to one number per point in time.
- Applicable to matrices of any size and irrespective of class criteria, and thus applicable to a time series of IFRS 9 TMs.
- Assumes a probability density X is a function of an idiosyncratic driver Y and a systematic economy-wide driver Z; Y and Z are independent unit normal random variables by assumption.
- The parameter 휌 captures the correlation between Z and X, with Z explaining a fraction 휌 of the variance of X.
- Key structural equation (notation preserved):
  - (1)  X = √(1−ρ) Y + √ρ Z

### B. Fitted transition probabilities and estimation
- Fitted transition probabilities, ∆(·), are expressed using the standard normal cumulative distribution function Φ and the bin boundaries x_i derived from the long-term average transition matrix:
  - (2)  ∆(x_i−1, x_i, Z, ρ) = Φ( [x_i − √(1−ρ)Y − √ρ Z] ) − Φ( [x_i−1 − √(1−ρ)Y − √ρ Z] )
  - (Φ is a standard normal cumulative distribution function; the terms x_i are the “bin boundaries”.)
- Historical deviation between an observed and fitted transition matrix is computed by minimizing a weighted sum of squared deviations across all matrix elements:
  - (3)  min_{Z_t} ∑∑ w_{G,g} [ P^{obs.}_{G,g,t} − ∆(x_{g−1}, x_g, Z_t, ρ) ]^2
  - (the two sums indicate summation over all elements in a transition matrix; 3x3=9 in an IFRS 9 transition matrix)
- Estimation approach:
  - For each point in time, conditional on ρ and bin boundaries from the long-term average TM, find Z_t that minimizes (3).
  - Because ρ is unknown, perform a “double-loop” search for both constant ρ and the time series Z_t subject to the constraint that the variance of Z_t equals one.
- Interpretation:
  - A +1/−1 value for Z denotes “1-standard deviation from normal (long-run average)” conditions.
- Implementation note:
  - An Excel/VBA-based implementation accompanies the paper, using an explicit grid search and simple VBA goal seek; more efficient implementations (Matlab, R) are possible.

*Italicized source attribution: IMF working paper, Box 1. The Z-Score Methodology (excerpt).*

---

### B. Linking the One-Factor Representation of Transition Matrices to Macro-Financial Conditions and Projecting Conditional on Scenarios

### Aims and methods
- Link the historical evolution of a Z-score to macro-financial variables to forecast Z conditional on macro-financial scenarios.
- Methods:
  - Standard regression model methods.
  - Methods that account for model uncertainty, e.g., Bayesian Model Averaging (BMA) (Gross and Población 2017).
- Output:
  - An econometric bridge equation relating the Z-score to time contemporaneous and lagged macro-financial variables.
- Use of scenario-conditional Z paths:
  - Translate scenario-conditional Z paths back to transition matrix (TM) paths to obtain exposure stocks, expected losses, provision stocks and flows.

*Italicized source attribution: IMF working paper, Box 1. The Z-Score Methodology (excerpt).*

---

### Box 2. From Scenario-Conditional Z-Scores to Transition Matrices and Implied S1-2-3 (Performing and Nonperforming) Exposure Stocks

### Translating Z back to TMs
- A TM forecast from a conditional Z forecast uses the same functional form as the historical fit (equation structure from Belkin et al. 1998):
  - (4)  ∆(x_{i−1}, x_i, Z_t, ρ) = Φ( ... ) − Φ( ... )  (same structural form as equation (2); bin boundaries and ρ are given)
- At this stage:
  - ρ and bin boundaries are fixed (previously estimated).
  - Only Z varies across scenarios, denoted Ẑ_t, implying transition probabilities across the TM along the scenario horizon.

### Augmenting and normalizing the TM for maturing and write-off flows
- Augment the 3x3 TM by adding scenario-conditional maturing percentages for S1 and S2 and write-off rate assumptions for S3 as a fourth and fifth column.
- Normalize each row to sum to one again. One normalization formula considered:
  - (5)  TR*_{i,·} = TR_{i,·} / ∑ TR_{i,·} × (1 − M_i − WRO_i),   ∀ i = 1,2,3
  - where only write-offs for initial S3 stocks would be positive.
- Normalization implications:
  - Pre-defined percentages for the maturing portion and write-offs will not change due to row normalization.
  - Alternative: normalize all elements in a row including M and WRO (WRO can capture asset sales to NPL/asset management firms).

### Deriving implied S1, S2, and S3 stocks (flow-stock equations)
- Using the augmented and normalized TM, implied stock evolution formulas:
  - (6)  
    - S1_t = S1_{t−1} + TR_{21,t−1} S2_{t−1} + TR_{31,t−1} S3_{t−1} − [TR_{12,t−1} S1_{t−1} + TR_{13,t−1} S1_{t−1} + M_{1,t−1} S1_{t−1}]
    - S2_t = S2_{t−1} + TR_{12,t−1} S1_{t−1} + TR_{32,t−1} S3_{t−1} − [TR_{21,t−1} S2_{t−1} + TR_{23,t−1} S2_{t−1} + M_{2,t−1} S2_{t−1}]
    - S3_t = S3_{t−1} + TR_{13,t−1} S1_{t−1} + TR_{23,t−1} S2_{t−1} − [TR_{31,t−1} S3_{t−1} + TR_{32,t−1} S3_{t−1} + WRO_{3,t−1} S3_{t−1}]
  - (notation preserves TR_{ij} as transition rates and M/WRO as maturing/write-off percentages)
- Stock dynamics caveat:
  - With no explicit control of new business flows (set to zero in S1 equation), total gross loan stock (S1+S2+S3) will fall if write-off percentages are positive (implied negative gross loan growth).

### Alternative with explicit gross loan growth control
- Alternative equations to control gross loan growth:
  - (7)  
    - S2_t = S2_{t−1} + TR_{12,t−1} S1_{t−1} + TR_{32,t−1} S3_{t−1} − [TR_{21,t−1} S2_{t−1} + TR_{23,t−1} S2_{t−1} + M_{2,t−1} S2_{t−1}]
    - S3_t = S3_{t−1} + TR_{13,t−1} S1_{t−1} + TR_{23,t−1} S2_{t−1} − [TR_{31,t−1} S3_{t−1} + TR_{32,t−1} S3_{t−1} + WRO_{3,t−1} S3_{t−1}]
    - S_t = S1_t + S2_t + S3_t = (1 + g_t) S_{t−1}
    - S1_t = max(0, S_t − S2_t − S3_t)
  - g_t is the period-on-period gross loan growth.
  - The max operator accounts for potentially unachievable desired gross loan growth (e.g., very negative g_t).

### Relation to PL/NPL and default rates
- When S1 and S2 are merged into performing loans (PL) and S3 is NPL, stock-flow dynamics under IAS 39/CECL emerge:
  - (8)  
    - PL_t = PL_{t−1} (1 − M_t − DR_t) + NB_t + Cure_t
    - NPL_t = NPL_{t−1} (1 − WRO_t) + DR_t (L_t−1 − NPL_{t−1}) − Cure_t
  - Terms:
    - M_t: maturing percentage of performing loan stock
    - DR_t: default rate
    - NB_t: new business flow
    - Cure_t: absolute flow of nonperforming back to performing stocks
- DR_t can be solved from (8) to imply historical default rates based on portfolio-level PL and NPL stocks, NPL write-off rates, and cure flows:
  - (9)  DR_t = [ ... ]  (equation preserved as in source for implied historical DR_t)

*Italicized source attribution: IMF working paper, Box 2. From Scenario-Conditional Z-Scores to Transition Matrices and Implied S1-2-3 (excerpt).*

---

### C. Alternative Transition Matrix Model Methods for Weak Data Environments

### Options when historical TM time series are short or absent
- Option 1: “beta-linking”
  - Use when historical TM time series are absent but historical default rate time series exist.
  - Develop a satellite model for default rates; link S2→S3 transition to the PD path; imply S1→S3 so that weighted average PD matches satellite PD path.
  - Use a set of “betas” to link TR1-3 and TR2-3 to remaining probabilities; betas can be based on limited historical TM data or set judgmentally or borrowed from jurisdictions with sufficient data.
  - Caveat: suboptimal; require robustness analyses of final provision flow and capital impact vs beta variations.
- Option 2: “anchoring-in-PDs”
  - Useful when TM historical data exist but do not cover a full business cycle.
  - Compute a Z-factor on the shorter TM sample for a given bank portfolio.
  - Develop a satellite model for default rates using historical default series that cover cycles.
  - Set a scenario path for Z so that implied PDs (exposure-weighted average of TR_{S1→S3} and TR_{S2→S3}) match the PD path from the satellite model.
  - The ECL Model Suite accompanying the paper illustrates this method.
- Option 3: full Z-score-based methodology as in subsections A and B (preferred when sufficient TM time series exist).

*Italicized source attribution: IMF working paper, Section C. Alternative Transition Matrix Model Methods (excerpt).*

---

### D. An LGD Model for Real Estate-Collateralized Portfolios

### Rationale and data requirements
- LGD component of ECLs requires macro-financial scenario dependence via either econometric time series models or structural models.
- Time series for LGDs are often scarce; structural models are considered for real estate-collateralized portfolios (commercial and residential).
- Principle: link the value of real estate collateral to house price scenario trajectories (commercial property prices for firm loan portfolios; residential prices for mortgage portfolios).
- Two structural variants presented: a simple model and a more advanced model.
- Required bank inputs for the advanced model:
  - (1) current portfolio-level LTVs, ideally exposure-weighted;
  - (2) cure rates from a T0 transition matrix in an IFRS 9 context (S3→S2/1);
  - (3) LGD as of Year 0, all for relevant portfolios.

### Simple LGD model (Box 3)
- Simple model linking LGD to house price trajectory:
  - (1)  LGD(t) = 1 − [1 − LGD(0)]^{φ(t)} = φ(·) = φ(·)
  - Numerical example: If LGD = 25 percent as of reference date and house price drop = 20 percent, LGD rises to 40 percent per the simple model.
- Caveats:
  - No explicit consideration of cures.
  - No account for overcollateralization.
  - Treats LGD as if not forward-looking.

### Advanced LGD model (Box 3)
- LGD definition (percentage form) incorporating probability of cure and “loss given loss” (LGL):
  - (2)  LGD = (1 − Probability of cure) × LGL + Costs
  - Costs: percentage reflecting administrative and legal expenses related to workout and collateral sale.
- LGL defined with a max operator:
  - (3)  LGL = max( (Loan − Expected Recovery Value) / Loan , 0 ) = max( 1 − Expected Recovery Value / Loan , 0 )
  - Re-expressed in terms of sales ratio (SR) by dividing numerator and denominator by reported current collateral value:
- Sales ratio (SR) definition:
  - (4)  SR = Expected Recovery Value / Reported Current Collateral Value
- Rationale for modeling SR as a distribution:
  - Reported collateral value may deviate from current or realized collateral values due to out-of-date valuations, worse condition of repossessed property, and fire-sale effects.
  - SR modeled with a modified Normal distribution specification (preserved from source):
    - (5)  SR = μ + Φ( (SR − ... ) / ... ) − Φ( ... ) + ...  (full distributional expression preserved as in source)
- Application steps for the advanced model:
  1. Find an effective sales ratio mean μ so the model-implied LGD matches the observed bank/portfolio LGD conditional on other parameters (Table 3.1 inputs).
     - Note: alternatively, set μ and imply standard deviation σ.
  2. Compute a house price scenario-conditional LTV:
     - (6)  LTV(t) = LTV(0) × φ_houseprice(t) = φ(·)
     - (notation preserved: LTV(t) formula links LTV(0) to scenario house price trajectory)

### Uncollateralized portfolios
- Three strategies:
  1. Use historical LGD time series and develop econometric satellite models (if available).
  2. Use regulatory downturn LGD estimates to inform an adverse LGD level for accounting provisions in a scenario.
  3. Decompose aggregate loss rate projections into PDs and LGDs using methods from Frye and Jacobs (2012) and Frye (2013) (method also involved in the FED’s DFAST methodology (FED 2017)).

*Italicized source attribution: IMF working paper, Box 3. A Simple and an Advanced LGD Model for Real Estate-Collateralized Portfolios (excerpt).*

### Box 3. A Simple and an Advanced LGD Model for Real Estate-Collateralized Portfolios

### Box 3. A Simple and an Advanced LGD Model for Real Estate-Collateralized Portfolios

### Comparison of Simple versus Advanced LGD models (concluding remarks)
- Scenario-conditional LGD can be implied from the scenario LTV in conjunction with equations (1)-(3).
- An Excel-based implementation of the two models accompanies this paper; the Excel solver can be used to find the sales ratio mean.
- Numerical example highlights that:
  - The “simpler” model (equation 1) results in larger scenario-conditional LGDs at low initial LGD levels, and smaller scenario-conditional LGDs at high initial LGD levels.
  - It is generally beneficial to consider the more advanced LGD model to obtain a more realistic scenario-conditional LGD estimate.

- Numerical-example assumptions used in the comparison (Figure 3.3):
  - house prices fall by 20 percent
  - cure rate in Year 0 is 20 percent, falling to 10 percent in the scenario
  - cost percentage of 5 percent
  - standard deviation of the sales ratio at 20 percentage points
  - cLTV denotes the current LTV

### Embedded numerical outputs shown in the module example
- Example image text (as presented in figure panel):
  - Y0ScenarioLGD44.0%
  - LGD30%‐
  - LTV55%‐
  - Cure rate10%5%
  - Sales haircut (SH)‐0.5702
  - LTV68.8%
  - V20%20%
  - Sales ratio (SR=1+SH)43.0%
  - LGL38.7%
  - Cost5%5%
  - Q0.27LGD41.7%
  - HP change‐‐20%
  - Effective sales ratio (eSR)   39.7%
  - LGL27.8%
  - LGD30.0%
  - dev^20.00044
  - Q*0.1
  - eSR*42.2%
  - Method 1 / Method 2
- The Excel module embeds an explanation of how the solver finds the sales ratio mean.

### Recommendation
- Prefer the advanced LGD model for more realistic scenario-conditional LGD estimates, particularly across a range of initial LGD/LTV starting points.

### Source
*Box 3 (concluded) and associated numerical example from the accompanying Excel module.*

### E. Lifetime Expected Credit Loss (LT-ECL) Calculations — key points
- Lifetime expected credit loss calculations are necessary because:
  - loan loss provisions for S2 and S3 exposures should have a lifetime horizon, and
  - performing portfolio under CECL requires a lifetime horizon.
- Lifetime horizon implies macro-financial scenarios need extending to residual maturity of the portfolio (example: mortgage portfolios with average duration 15 years would require up to 15-year TM forward paths).
- Two options to handle long residual maturity:
  - employ simple assumptions about how macro-financial factors and implied risk parameters move beyond an initial scenario horizon (usually 3 to 5 years);
  - conduct scenario simulations based on a macro-financial model suite explicitly farther into the future.
- A lifetime ECL formula forms the starting point for ECL calculations; the formula and component meanings are explained in Box 4.

### Box 4 — LT-ECL: Formula and Components (summary)
- Lifetime ECL structure:
  - Equation (1) (symbolic): ECL = sum over s=1..M of [incremental PD * PiT LGD * exposure discounted by effective loan interest rate], with M denoting the average residual maturity of a portfolio. Lifetime ECL is measured in monetary units.
  - The denominator includes an effective loan interest rate for discounting ECL along the loan lifetime.
- Incremental PD formula:
  - Equation (2) (symbolic): TR_t^{2-3,*} = TR_t^{2-3} * product over prior periods of (1 − TR_u^{2-3}) — incremental PD equals the PD in period s conditional on survival to s−1 and approaches zero over time.
  - TR_t^{2-3} is the unconditional transition probability for S2 stocks from the transition matrix forecast path.
- Notes and illustrative behavior:
  - If M = 1, lifetime ECL reduces to a 12-month ECL and incremental PD equals unconditional PD.
  - PiT PD in examples can be set constant or scenario-varying.
- Projection of S2 exposure term:
  - Options: nonlinear repayment schedule resembling fixed/variable rate loans, or simplifying linear principal repayment path; ECL estimates may not be overly sensitive to this choice.
  - For variable rate portfolios, an expectation about the loan interest rate must be considered.
  - Mixed portfolios could combine repayment schedules; modeling prepayments explicitly is an option (beyond scope).

### Footnote context (preserving phrasing)
- One may assume loan default probability after some time (say, five years) is sufficiently low so lifetime ECL calculations can be confined to that shorter horizon; loan prepayments reduce effective expected duration and can permit shorter scenario horizons.

### Figure reference
- Figure 4.1 depicts cumulative survival probability, cumulative PD, and PiT versus incremental PDs; PiT PD in the example (right chart, green) is set to a constant but may vary in scenarios (perfect foresight discussed later).

### Recommendation
- Choose projection approach (linear vs nonlinear repayment) with awareness that ECL sensitivity to this choice may be limited; consider prepayments and interest-rate expectations for variable-rate portfolios.

### Source
*Box 4 (LT-ECL formula and components) and accompanying explanatory text.*

### F. Loan Loss Provision Stock and Flow Calculations — summary
- ECL estimates for exposures across risk categories must be translated into accounting provision stocks.
- Loan loss provisions apply to exposures in all three stages (S1, S2, S3) and change as underlying risk parameters (PDs PiT and implied lifetime, LGDs) change.
- Contrast with IAS 39:
  - Under IAS 39, performing exposures were not provisioned for (except IBNR); nonperforming exposures provisioned based only on LGD once in NPL stock.
- Provision calculations can be refined by distinguishing risk parameters (e.g., LGDs) across cross-stage migrations; more granular models increase data needs and potential data-quality issues.

### Box 5 — Provision stock and flow formulas (key formulae preserved)
- For S1 exposures under IFRS 9 (12-month ECL):
  - (1) PROV_t,S1 = ECL_t,S1 = TR_t^{S1|t} * LGD_t+H|t * S1_t
  - TR_t^{S1|t} denotes expected default rate for S1 exposures conditional on end-of-period-t information for the following year.
  - LGD_t+H|t denotes forward-looking LGD beyond one-year horizon if expected time until collateral sale > 1 year.
- For S2 exposures (lifetime ECL — Box 4 applies):
  - (2) PROV_t,S2 = ECL_t,S2 = sum_{s=1..M} [incremental PD_s * PiT LGD_s * S2_s discounted]
- For S3 exposures (defaulted exposures):
  - (3) PROV_t,S3 = ECL_t,S3 = LGD_t+H|t * S3_t
- Total provision stock:
  - (4) PROV_t = PROV_t,S1 + PROV_t,S2 + PROV_t,S3
- Provision flow (change in stock adjusted for write-offs):
  - (5) PROVFLOW_t+1 = ΔPROV_t+1 + WRO_t − LGD_t * S3_t−1
  - Adjustment assumes LGD estimate used to set pre-write-off provision equals realized LGD upon collateral sale for written-off exposures.
- Under IAS 39:
  - provision stock formula (4) would exclude S1 and S2 terms; provision flow expression (5) unchanged.

### Numerical example and observed patterns
- Embedded numerical example in the tool suite (provision stock and flow module) demonstrates:
  - Under an adverse scenario, IFRS 9 and CECL-implied provision flows are more front-loaded than IAS 39.
  - IFRS 9 exhibits a “cliff effect” from 12-month horizon for S1 and lifetime horizon for S2, with S2 provisions tending to increase significantly in year one of an adverse scenario.
  - Cumulative losses over a longer adverse period are the same under all accounting regimes absent second-round macro effects; differences are timing of recognition.
- Full lifetime ECL for combined S1+S2 portfolio is a useful top-down stress-testing benchmark:
  - Rationale: compare S1/S2 differentiated provisioning vs full lifetime provisioning; require less data; reduce model risk since transition matrix reduces to 2x2 and only PiT PD (12-month) modeling may be needed.
  - LGD model strategy can use modules described in Section IV.C and Box 3.
  - Lifetime PD calculations simplify when applying equation (1) in Box 4 to total performing exposure stock and equation (2) to overall PD instead of TR_2-3 alone.
  - Provisioning calculations simplify: Box 5 equation (1) becomes obsolete; Box 5 equation (2) applies to combined S1+S2.
  - When using CECL in an IFRS 9 regime, beware model-implied Year 0 provision stocks will be larger than banks’ Year 0 provisions (banks provision S1 on 12-month horizon). CECL stress-test provision flows should reference model-implied Year 0 provision stocks.

### Recommendation
- For top-down stress testing under IFRS 9 regimes, a full lifetime ECL approach akin to CECL can be advantageous for benchmarking and robustness, but adjust comparisons to banks’ Year 0 provision stocks when necessary.

### Source
*Section F and Box 5: Loan Loss Provision Stock and Flow Calculations, and numerical example observations.*

### G. Interplay Between Accounting and Capital Regulation — main points
- Interaction arises because both regulatory capital and accounting provisions shield future credit losses:
  - Loan loss provisions + residual net equity capital = “gross equity.”
  - Provisions cover expected losses; residual capital covers unexpected losses.
- Since Basel II, IRB approach is compatible with a 12-month ECL horizon based on regulatory risk parameters (TTC PD and downturn LGD).
- Regulatory treatment of accounting rules considers provisioning shortfall or excess:
  - For IRB portfolios, “IRB shortfall” rule: if regulatory EL exceeds accounting provision stocks, the difference is subtracted from CET1.
  - If regulatory EL falls short of accounting provision stock, the difference may be added back to Tier 2 capital subject to a limit of 0.6 percent of credit risk RWA and regulatory prior approval.
  - For STA exposures, general provision stocks can be added back to Tier 2 subject to a limit of 1.25 percent of credit risk RWA.
- BCBS position:
  - Following industry consultation (October 2016) BCBS concluded in March 2017 to not change current regulatory treatment of accounting provisions until further notice.
- Discussion items and open questions:
  - Whether the regulatory treatment should change given redesign of accounting provisions (IFRS 9 / CECL) is unresolved.
  - The role of general provisions under STA is questioned given accounting treats provisions as specific; some suggest IFRS 9 provisions be interpreted as specific provisions.
  - BCBS has left mapping of IFRS 9 provisions to general/specific provisions to individual jurisdictions.
- Linking regulatory and PiT risk parameters:
  - For IRB portfolios, it is possible to establish a link between regulatory risk parameter scenario paths and accounting PiT risk parameters.
  - A rise in PiT risk parameters under an adverse scenario prevailing for a reasonably long period (for example three to five years) could warrant upward adjustment to regulatory risk parameters for consistency and conservatism.
  - Degree of linkage should consider scenario narrative:
    - Cyclical scenarios (short-lived) may call for less adjustment to regulatory parameters.
    - Structural shock scenarios (longer-lived, state-independent) may warrant making regulatory parameters a function of PiT parameters.
  - Steering regulatory parameters as a function of PiT parameters is often ad hoc and introduces model risk (e.g., choice of 5- or 10-year windows for historical PiT averages).
- Box 6 presents a simple methodology for linking regulatory and PiT risk parameters and framing it in an IFRS 9-specific environment (Box 6 content not included here).

### Recommendation
- Exercise judgment in mapping PiT stress into regulatory parameters, mindful of scenario nature (cyclical vs structural) and model risk from ad hoc choices; where used, document linkage methodology and time-window choices explicitly.

### Source
*Section G: Interplay Between Accounting and Capital Regulation.*

*Content extracted from the PDF module: Box 3 (conclusion), Sections E–G, Box 4, and Box 5.*

### Box 6. Risk Weighted Assets: Linking Regulatory Risk Parameters (IRB) to PiT Risk

### Box 6. Risk Weighted Assets: Linking Regulatory Risk Parameters (IRB) to PiT Risk

### Linking exposure-weighted PiT PDs to regulatory TTC PDs
- Compute an exposure weighted average PiT PD based on the transition rates TR1-3 and TR2-3 along the scenario horizon:
  - (1)   PD
୲ାଵ|୲
୔୧୘
ൌ
ୗଵ
౪
ൈ୘ୖଵଷ
౪శభ|౪
ାୗଶ
౪
ൈ୘ୖଶଷ
౪శభ|౪
ୗଵ
౪
ାୗଶ
౪
- Link the resulting PiT PD forward path to the regulatory, TTC PD path using smoothing and logit transforms:
  - (2)  PD
୲ାଵ|୲
୘୘େ
ൌlogit
ିଵ
൫logit൫PD
୲|୲ିଵ
୘୘େ
൯൅αൈ∆logitሺPD
୲ାଵ|୲
୔୧୘
ሻ൯
- Purpose and properties of the transformation:
  - The logit and inverse logit functions are involved to guarantee that the TTC PD never leaves the [0-1] interval.
  - The term α is a smoothing parameter that should be set to a value between 0 and 1, for example, to 0.75.
  - α’s purpose is to retain the TTC concept for the PD and to avoid excessive fluctuations (and potential procyclicality) that a full “pass-through” from PiT PD to TTC PD changes would cause.
  - A “full pass-through” would amount to setting α to 1.
  - The α parameter can be informed by banks’ time window used for computing moving averages of PiT parameters to obtain the TTC measure; otherwise α requires a judgmental setting and sensitivity analyses.
- Mathematical notes:
  - The logit function has the form: logit(x)=ln(x/(1-x)).
  - The inverse logit (Sigmoid) has the form: logit-1(y)=exp(y)/(1+exp(y)).
  - Alternative transforms: standard normal and inverse standard normal distribution function, or absolute-change with max-min cap/floor at 1 and 0. All three options generally result in similar quantitative outcomes.

### Linking PiT LGD to regulatory downturn LGD
- Consider the following link for the regulatory LGD (downturn LGD, DT):
  - (3)  LGD
୲ାଵ|୲
ୈ୘
ൌmax൫LGD
୲ୀ଴ 
ୈ୘
,LGD
୲ାଵ|୲ 
୔୧୘
൯
- Interpretation:
  - Regulatory LGD is the maximum of the downturn LGD observed for a bank portfolio at the outset and the PiT LGD along the scenario horizon.
  - The PiT LGD may or may not exceed the downturn LGD either at the outset or along the scenario horizon.
- Application:
  - The resulting regulatory PD path from equation (2) and the downturn LGD path from equation (3) can be used to feed the Basel risk weight formulas.

### IFRS 9 multiple scenarios requirement and scenario construction
- IFRS 9 requires multiple macroeconomic scenarios for ECL estimates to be weighted by scenario probabilities; paragraph 5.5.17 in IASB (2014) requires an “unbiased and probability-weighted amount that is determined by evaluating a range of possible outcomes.”
- Implication: at least two scenarios are to be considered; open questions remain on how to construct scenarios and set weights.
- Industry practice: banks appear to adopt an ad hoc and judgmental approach in constructing scenarios and setting weights; most banks consider three scenarios as standard, a small single-digit percentage use four scenarios. Scenario calibration may be in-house or purchased from external providers; weights set judgmentally.
- Perfect foresight:
  - “Perfect foresight” assumes one scenario materializes with 100 percent probability (e.g., an adverse scenario).
  - This is incompatible with IFRS 9 for accounting provisioning; permitted in top-down stress testing (BoE and ECB/EBA/SSM have employed it).
  - Reliance on one scenario risks hand-picking a scenario that does not address macro-financial risks (scenario uncertainty).
- Strategies for lifetime horizons longer than conventional 2–5 year stress test horizons:
  - Strategy 1: develop conditional forecasts of PiT risk parameters up to average residual maturity (e.g., TM paths), requiring assumptions for all relevant macro drivers.
  - Strategy 2: use simplifying assumptions—project baseline and adverse TM paths up to, for example, five years, then assume steady baseline and reversion of adverse back toward baseline over a self-defined reversion period (e.g., eight to 10 years). End-point may be set to long-term average transition matrix (including two default rates), anchoring in regulatory TTC parameters.
- Nonlinearities and IFRS 9:
  - Multiple scenarios are intended to help capture nonlinearities in relationships between macro-financial variables and bank risk metrics.
  - High-level IFRS 9 guidance is not concrete; ad hoc scenario choices and weights are unlikely to capture specific nonlinearities properly.

### Monte Carlo simulations to address scenario uncertainty
- Monte Carlo-type simulations with integrated macro-financial model suites can help account for scenario uncertainty and nonlinearities.
- A simulation-based approach should:
  - Account for macro-financial feedback (two-way relationship at most between real activity and credit growth metrics).
  - Consider residual uncertainty, coefficient uncertainty, and model uncertainty.
  - Recognize scenario uncertainty as a function of the three fundamental uncertainty sources plus the scenario shock narrative chosen.

### Box 7: Exemplary Monte Carlo simulation setup and findings
- Model components and setup:
  - Trivariate VAR with annual frequency (1988–2018, 31 obs.), containing real GDP (natural log differences YoY, lnYoY), nominal house prices (lnYoY), and a PD for the private sector (logit levels).
  - Simpler version of the two structural LGD models (Box 3, equation 1) connected to house price growth.
  - Linear repayment scheme for the S2 exposure.
  - Lifetime loss calculation scheme (Box 4, equations 1 and 2) connected to the system.
- Simulation specifics:
  - Two simulation schemes: (i) accounting for residual uncertainty; (ii) accounting for residual and coefficient uncertainty.
  - Simulate 2,000 paths under both schemes for all variables, including LGD, incremental and lifetime PDs, and the lifetime ECL ratio.
  - Scenario horizon: 10 years (average residual maturity assumed 10 years).
  - LGD module relevant horizon: first three years (average time to sale of collateral assumed three years).
  - Starting point LGD: 50 percent.
  - Interest rate for discounting: 1 percent (treated as exogenous).
  - Simulation methods: parametric bootstrap (multivariate Normal) for residual uncertainty; pseudo-data resampling for coefficient uncertainty plus residual bootstrap.
- Illustrative empirical observations:
  - Figure 7.2 (not reproduced here) shows the LT-ECL distribution at the outset; accounting for coefficient uncertainty in addition to residual uncertainty widens the distribution, shifts mean and median upward, and increases skewness.
  - Baseline point forecast path and two impulse response-based alternative paths (upside and downside) produced by shocking GDP growth at the 10th and 90th percentile of the GDP growth VAR residuals.
- Comparison of hand-picked scenarios vs simulation:
  - Hand-picked LT-ECL point forecasts: upside 0.49 percent, baseline 0.62 percent, downside 0.86 percent.
  - The baseline point forecast (0.62 percent) does not equal the mean or median of the simulated LT-ECL distribution; it falls short of all mean and median estimates from both simulation types.
  - The mean LT-ECL under distribution B is close to the downside scenario-implied point estimate (both at about 0.86 percent).
  - There exist infinitely many weight combinations on the three hand-picked scenarios that would match the simulated median LT-ECL (0.7 percent).
- Conclusions from Box 7:
  1. The weight choice for three (or more) hand-picked scenarios will always remain entirely ad hoc. Tying weights to scenario probabilities (for example, impulse response shock probabilities) almost surely does not yield a weighted-average LT-ECL close to a “true” LT-ECL; informing weights based on such probabilities is problematic.
  2. The LT-ECL can be obtained by stochastic simulations based on an integrated model suite containing relevant macro drivers and structural and/or econometric satellite models. Once a simulation scheme is considered, there is no longer a need to consider hand-picked scenarios and indeterminate weights. In practice, an integrated model suite would be more refined than the simplistic illustrative one used here.
  3. LT-ECL distributions are likely markedly skewed; accounting for all sources of uncertainty in a simulation apparatus is warranted to avoid underestimating the width and skewness of the distribution. Numerous nonlinearities in an underlying model suite drive such non-normal, skewed LT-ECL distributions.

*Source: Box 6 and related text in the provided IMF content unit.*

### 4. As long as practitioners do not employ stochastic simulation-based methodologies, but handpicked

### 4. As long as practitioners do not employ stochastic simulation-based methodologies, but handpicked scenarios and self-set weights, the accounting regime based on the latter scheme is bound to imply a notable risk of “ad hoc-ness.”

### V. EXEMPLARY IFRS 9 DATA TEMPLATES
- Data required at the bank-portfolio level to operationalize the credit risk model-suite:
  - Banks’ Year 0 stock-balance sheet position (template exemplified in Figure 11).
  - Historical stocks of exposures in the three stages, cross-stage flows, write-off flows (WRO), and new business flows (template exemplified in Figure 12).
  - Financial asset stocks and flows recorded in monetary units (for example, USD, EUR); transition matrices (TMs) with percentages computed by dividing time-t flows by end-of-previous period (t-1) stocks.
- Staging criteria and data-collection options:
  - Option 1: Instruct banks to employ their own staging criteria and generate exposure stocks and flows accordingly.
  - Option 2: Define a common set of staging criteria and instruct banks to report according to those.
  - Practical compromise: Let banks report based on their own staging criteria for historical data, while assuming a simplified common staging criteria set under stress tests.
    - Rationale: Different staging criteria likely correlate strongly in practice (references to PDs, changes in ratings, changes in CDS correlate and suggest similar staging dynamics).
- Use of historical regulatory exposure classifications:
  - For retrospective staged exposure data before January 2018, regulatory exposure classification systems (performing, substandard, doubtful, loss) can be mapped to IFRS 9 stages (example: performing → Stage 1; substandard + doubtful → Stage 2; loss → Stage 3).
  - Over time, reliance on historical regulatory exposure stock and flow data may vanish as direct IFRS 9 accounting-based data accrues.
- Templates and model elements:
  - Full templates are available from the authors on request, as are the model elements presented in earlier sections.34
- Figures referenced:
  - Figure 11: Balance Sheet Stocks as of Year 0 (structure for portfolio segmentation: nonfinancial corporate, financial corporate, household mortgages, consumer credit and other retail loans, sovereign, other; distinctions such as domestic/foreign, on/off-BS, stages, accounting categories like Amortized cost, FVOCI, FVPL; labels include FI1, FI2, STA, STAIRB).
  - Figure 12: Financial Asset Stocks in Stages 1/2/3 and Historical Transition Flows (structure replicable for different portfolio segments; MAT = flows of maturing business; WRO = write-off flows).

### VI. CONCLUSIONS
- Aims of the paper:
  - Present an overview of what ECL implies from a macro-financial system and economics perspective (heterogeneity in provisioning models, assumptions and limited comparability across banks, procyclicality of accounting regimes, and lack of incentives for banks to measure risk appropriately in competitive market economies).
  - Present an integrated tool suite as a starting point for analytical, top-down IFRS 9- and CECL-compatible solvency analyses (suitable for top-down macro and macroprudential stress-test institutions, supervisors, central banks, and international organizations).
- Components of the tool suite:
  - Transition matrix modeling.
  - Lifetime PD modeling.
  - Two variants of a structural LGD model for real estate collateralized portfolios.
  - Link to risk-weighted assets and capital calculations.
- Empirical applications and findings from IMF FSAPs:
  - IMF FSAPs in 2019 and 2020 applied several model options presented in this paper.
  - Canada 2019 FSAP:
    - In the adverse scenario, compared to the baseline, credit impairments increase significantly under IFRS 9.
    - Accounting impairment charges in the adverse scenario would exceed regulatory provisions for most banks.
    - Implication: importance of considering the accounting layer in stress testing.
  - France 2019 FSAP:
    - Data availability is scarce and may lead to a wide range of estimated losses.
    - Uncertainty driven by assumptions about loan portfolio growth and differences in loan write-off policies across a sample of banks.
  - 2019/20 Korea FSAP (IMF 2020b):
    - Long historical transition matrix data were available at the individual bank-portfolio level, derived from stocks and flows under the regulatory risk classification mapped into IFRS 9 accounting stages.
    - This allowed employment of a robust model approach involving elements of the Z-factor methodology for the first time.
- Policy-relevant recommendations and observations:
  - Oversight institutions should retain their own, independent models for stress-test modeling in general and for ECL modeling specifically.
    - Rationale: inherent incentives for financial institutions to underestimate risk, which banks may exploit due to the principles-based nature of the accounting framework.
  - Independent assessment of scenario design and stress testing is warranted.
  - Differences between institutional and bank-internal stress testing approaches can be significant due to:
    - Complexity of model suites.
    - Differences in aggregation level and perimeter.
    - Discrepancies in prevailing assumptions underpinning either type of stress tests.
  - A significant body of literature confirms distorted incentives on the side of banks (references provided in the paper).

*Source: wpiea2020111-print-pdf (IMF working paper excerpt).*

### 93. Amsterdam, Netherlands: Elsevier Academic Press.

### wpiea2020111-print-pdf - 93. Amsterdam, Netherlands: Elsevier Academic Press.

### Major themes represented in the referenced literature
- Accounting standards and impairment regimes: IFRS 9, CECL, delayed expected loss recognition, regulatory and supervisory guidance on impairment accounting and provisioning (IASB, 2014; FASB, 2016; BoE, 2017; BoE, 2019; EBA, 2016; EBA, 2017; ESRB, 2017; SSM, 2020).
- Procyclicality of banking, capital requirements, and macro-financial interactions: capital adequacy, procyclical leverage, cyclical implications of Basel rules, and financial stability implications (Blum and Hellwig, 1995; Danielsson, Shin, and Zigrand, 2012; Brunnermeier and Sannikov, 2014; Estrella, 2004; Kashyap and Stein, 2004; FSB, 2009; FSF, 2008).
- Stress testing, supervisory practice, and model uncertainty: EU-wide stress tests, supervisory stress-testing guidance, and implications of model uncertainty for bank stress testing (EBA, 2018a; EBA, 2018b; BoE, 2018; BoE, 2019; Gross and Población, 2019; IMF technical notes 2019–2020).
- Credit migration and credit risk modelling: transition/migration matrices, rating transitions, multi-factor migration models, forecasting migration with business cycle effects (Jafry and Schuermann, 2004; Lando and Skodeberg, 2002; Maehlmann, 2006; Malik and Thomas, 2012; Truck, 2008; Truck and Rachev, 2009; Wei, 2003).
- Bank risk-taking, competition, and internal models: theories of bank risk-taking, incentives and quality of internal risk models, manipulation of risk-weights (Boyd and Nicolo, 2005; Repullo, 2004; Martinez-Miera and Repullo, 2010; Plosser and Santos, 2014; Mariathasan and Merrouche, 2014).
- Empirical and supervisory assessments of IFRS 9 implementation and effects: impact assessments, industry surveys, and supervisory communications addressing IFRS 9 and provision/regulatory treatment (EBA, 2016; EBA, 2017; Deloitte, 2018; EY, 2016; EY, 2018a; EY, 2018b; Novotny-Farkas, 2015; PWC, 2017; PWC, 2018).

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020111-print-pdf.pdf_