## Appendix I – The Use of Copula in Financial Risk Analysis

## Source details

**Canonical URL:** [Appendix I – The Use of Copula in Financial Risk Analysis](https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024104-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2024/english/wpiea2024104-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2024/english/wpiea2024104-print-pdf.pdf.json)

---

### Copula methodology and shock generation
- Copula models joint distributions with marginal distributions uniform on [0, 1], enabling high-dimensional marginals corresponding to specific shock parameters.
- Two-step generation:
  - Generate pairs (Z1, Z2) from a bivariate normal distribution with pre-defined statistical dependence (Rank Correlation Coefficients); each has a normal marginal distribution.
  - Apply transformations (G1, G2) via inverse CDFs to change marginals to target distributions.
- Beta distributions selected as final marginals for Gaussian Copula to allow set boundaries and severity of shocks.
- Dependence structure estimation options:
  - Parametric (maximum likelihood).
  - Semiparametric (parametric copula, nonparametric marginals).
  - Non-parametric (kernel density estimation).
- Alternative copulas (e.g., Student’s T) noted as possible to increase joint extreme event probability.

### Shock calibration and selection (framework specifications)
- Parameters are exogenous but can be estimated or identified based on historical evidence or literature.
- Peaks of the shocks aligned with traditional bank cash-flow analysis over a three-month horizon.
- Additional stress parameters calibrated based on historical volatility or expert judgement when historical time series are not readily available (examples: share redemption rate of investment funds; phase-out rate of short-term corporate funding).
- Severity of shocks may differ by stress testing horizon: some liquidity shocks unfold in days, others over longer periods.
- Framework covers a range of shocks rather than a single point estimate.
- Calibration ranges (as presented):
  - Bond selling rate: [0,40]
  - Sovereign bond yield shock: [0,4] with average shock at 200 bps
  - Corporate bond yield shock: [0,8] with average shock at 400 bps
  - Credit line triggering rate: [0,40]
  - Corporate deposit run-off rate: [0,50]
  - Household deposit run-off rate: [0,20]
  - Share redemption: [0,40]
  - Short term debt phase-out rate: [0,40]

### Monte Carlo simulation and correlated shocks
- Monte Carlo simulation:
  - One-thousand simulations (in earlier description) produce distributions of net liquidity position per agent; elsewhere described as Ten thousand Monte Carlo simulations run using shocks from calibration.
  - Simulations generate distributions of net liquidity positions to identify maximum liquidity shortfalls and tipping points (e.g., net liquidity position equals 0).
- Copula used to assign correlated shocks; marginal distributions often specified as pre-defined beta distributions with symmetric bell-curve shape and upper/lower bounds.
- Correlation factor adjustable; sensitivity analysis across correlation parameters recommended when long time series are not available.
- Higher correlation intensifies downside risks (example: correlation factor 0.9 produces a flatter distribution of commercial banks’ net liquidity position with a fatter left tail than correlation factor 0.2).

### Market valuation shocks and transmission channels
- Market valuation shocks:
  - Shocks to market value of sovereign securities follow a modified duration approach; sovereign and corporate shocks simulated via parallel shifts of yield curves along maturity buckets.
  - Corporate securities assumed higher upper bound shift due to higher risk premium; bank bond yield shocks assumed higher than sovereign and lower than corporate securities under each simulation.
- Market revaluation variables and formula elements:
  - P = bond valuation
  - D = duration (selected at midpoint within each maturity bucket)
  - B = bond yield
  - M = outstanding amount
  - r = risk-free rate
  - s = bond spreads assumed in shock calibration
- Market revaluations affect balance sheets via:
  - Reduced market value of unencumbered collateral.
  - Margin calls on encumbered collateral underlying secured funding and derivative margin positions.
- Both channels reduce liquidity buffers of single agents and increase tail risks of systemwide liquidity stress.

### Market clearing mechanism and behavioral pecking order
- Market clearing pecking order (behavioral response under stress):
  1. Use cash and cash equivalents first.
  2. Phase out (or not rollover) outstanding reverse repo transactions or short-term bond investments.
  3. Pledge unencumbered collateral via repo transactions to obtain liquidity; commercial banks and the central bank are main counterparties.
- Behavioral preferences (e.g., preference for cash over less liquid assets) affect market clearing outcomes.
- Phase-out of reverse repo contracts treated as liquidity-neutral (outflow and inflow offset; encumbered assets convert back to unencumbered assets at discounted market price).
- Assumptions on absorption of sovereign securities sold by foreign investors under Narrative 1:
  - Absorbed pro-rata by all market agents based on existing holdings, conditional on sufficient liquidity after initial shocks.
  - Development banks and investment funds purchase only if they still have cash; remaining purchases go to commercial banks.
  - Commercial banks can purchase and immediately pledge to the central bank to obtain cash.

### Fire-sales and shock amplification
- Fire-sale scenario implemented as an additional behavioral response to capture market amplification from asset sales by weak agents (investment funds treated as last line of defense).
- Price impact modeled via a non-linear relationship based on Kyle (1985) and Fukker, Kaijser, Mingarelli, and Sydow (2021):
  - Price change depends on total amount sold S, Kyle’s lambda λ (price impact parameter), and an impact boundary parameter B (set as the most negative return observed in the history of a security to prevent prices falling below 100 percent).
  - Quantification achieved via an iterative process to equilibrium price, constrained by securities available for sale and diminishing marginal price impact.
- Fire-sales produce additional market haircuts for sovereign and corporate securities holdings across agents, shrinking balance sheets and liquid assets.
- Key finding: post fire-sale distributions show higher market discount across tradable securities and higher tail liquidity risks; post fire-sale distributions have longer and fatter left tails across all market agents.
- Threshold for triggering fire-sales: when the NBFI sector exhausts all cash and equivalents and is forced to sell other liquid assets, assuming no direct access to repo markets or central bank facilities.

### Case study application — Mexico: calibration inputs and stylized features
- Coverage and data:
  - Agents collectively represent about 64 percent of total financial sector assets.
  - Data compiled by Banxico as of December 2021: aggregate balance-sheet composition by agent type; bilateral who-to-whom exposures; collateral data (encumbered and unencumbered, central bank eligible and non-eligible, by issuer and remaining maturities); margin positions; haircut information for repo transactions.
- Stylized agent features:
  - Encumbrance of sovereign securities: 58 percent for commercial banks and 84 (percent) for development banks.
  - Bulk of sovereign securities duration between one to five years.
  - Off-balance sheet credit and liquidity lines at around 3 trillion pesos (both revocable and irrevocable).
- Four stressed narratives for Mexico:
  - Narrative 1: Tighter global financial condition inducing investors’ selling of sovereign and corporate bonds; triggering margin calls.
    - Foreign holdings of domestic sovereign securities and corporate shares are currently at around 20 and 33 percent, respectively.
  - Narrative 2: Tighter global funding conditions triggering credit and liquidity lines of corporates (credit/liquidity lines around 3 trillion pesos).
  - Narrative 3: Capital outflows via wholesale deposit run-off (firms move deposits on-shore to off-shore).
  - Narrative 4: Share redemption shocks triggering investment funds’ liquidity strains; partial deposit inflows back to commercial banks possible.

### Results for Mexico — systemwide insights and agent roles
- Overall finding: financial system remains resilient against the four narratives with commercial banks backstopping liquidity needs of all agents (Figure 13).
- Commercial banks:
  - Act as shock absorbers by providing liquidity via repo transactions.
  - Show only marginal liquidity shortfalls (a thin negative tail) mainly driven by triggering of contingent credit lines and wholesale deposits’ outflows.
  - Largest transmission of shocks from corporates and investment funds.
  - At minimum cut-off point under Narrative 4, liquidity outflows from corporates contribute most to net liquidity decline.
- Investment funds:
  - Ranked second in contribution to liquidity outflows but bring roughly equal inflows to commercial banks.
  - Transactions with commercial banks are often repo financing or direct sale of debt securities, generally liquidity neutral (exchange of cash for liquid collateral).
- Development banks:
  - More vulnerable when liquidity constraints are binding; have the most illiquid asset profile with 46 percent of assets lending to private sector and remaining holdings sovereign securities with high encumbrance.
  - Corporates contribute 45 percent of development bank outflows; investment funds contribute 40 percent of development bank outflows.
  - Short-term financing to development banks from corporates and investment funds: 35 percent and 27 percent of total short-term financing, respectively (as of end-2021).
- Systemwide contributors:
  - Commercial banks and investment funds persistently contribute most to systemwide liquidity changes due to larger balance sheet size and higher exposure to market liquidity outflows.
- Correlation effect:
  - Higher correlation intensifies downside risks; correlation factor 0.9 produces a flatter distribution for commercial banks with a fatter left tail compared with correlation factor 0.2.

### Policy experiments and behavioral sensitivity
- Investment funds’ access to repo market:
  - Assuming higher discount rates for investment funds implemented by imposing on the initial market revaluation shock a multiplier of 1.5 for their holdings of sovereign securities shifts their net liquidity distribution to the left.
  - Lifting restrictions (complete lift of limited access) could bolster investment funds’ liquidity position and enhance system resiliency.
- Commercial bank constraints and spillovers:
  - If commercial banks face binding liquidity constraints (e.g., mandatory LCR or behavioral minimum buffers), larger liquidity shortfalls could materialize for other agents, notably development banks.
  - Sensitivity experiment: freezing repo activities of commercial banks when they reach a pre-defined LCR limit pushed part of development banks’ distribution into negative territory.
  - Alternative experiment: commercial banks pulling back on short-term funding pushes development banks’ net liquidity distribution left but less severely than freezing repos.
  - Relaxing the LCR requirement at time of liquidity stress could better promote banks’ role as backstop; assumption used: commercial banks breach LCR limit if liquid assets decline by 50 percent.
- Policy uses:
  - Calibrate macroprudential and crisis management policies; identify institutions and markets most susceptible to liquidity strains; preemptively assess adjustments to limits or buffers, expansion of eligible collateral under ELA, or market access for certain agents.

### Model structure and selected equations (overview; Appendix II and Commercial bank block)
- Four main blocks compute post-shock outflows, inflows, liquidity buffer changes, and market clearing pecking order:
  1. Market revaluation of tradable securities subject to yield shock (formulas for s_sov_b_b_bnk,i, s_sov_b_db,i, s_sov_b_ivf,i).
  2. Investment fund block (outflow O_ivf,i, liquid assets LA_ivf,i, net liquidity position B_ivf,i, pecking order rules).
  3. Development bank block (allocation formulas for ivf_db_repo_sov_i, ivf_db_repo_corp_i, outflow O_db,i, LA_db,i, B_db,i, pecking order rules).
  4. Commercial bank block (detailed formulas and pecking order provided; selected elements excerpted below).
- Selected commercial bank formulas and definitions:
  - Allocation of repos and collateral release (examples):
    - ivf_bnk_repo_sov_i = ivf_bnk_repo_i ∙ (sov_bnk ∙ e_sov_bnk) / (sov_bnk ∙ e_sov_bnk + corp_bnk ∙ e_corp_bnk) ∙ 1/(1−hh_sov_b_i)
    - ivf_bnk_repo_corp_i = ivf_bnk_repo_i ∙ (corp_bnk ∙ e_corp_bnk) / (sov_bnk ∙ e_sov_bnk + corp_bnk ∙ e_corp_bnk) ∙ 1/(1−hh_corp_b_i)
  - Liquidity outflow:
    - O_bnk,i = cl_corp ∙ clr_i + s_sov_bbnk,i + ( s_sov_bivf,i − a_s_sov_bivf,i) + ( s_sov_bdb,i − a_s_sov_bdb,i)
      + max(0, sov_bbnk ∙ e_sov_bbnk − ivf_bnk_repo_sov_i − db_bnk_repo_sov_i − corp_bnk_repo_sov_i) ∙ hc_sov_b_i
      + max(0, corp_bbnk ∙ e_corp_bbnk − ivf_bnk_repo_corp_i − db_bnk_repo_corp_i − corp_bnk_repo_corp_i) ∙ hc_corp_b_i
      + m_sov_bbnk ∙ hc_sov_b_i + m_corp_bbnk ∙ hc_corp_b_i
      + ivf_bnk_repo_i + ivf_bnk_nonrepo_i + db_bnk_repo_i + db_bnk_nonrepo_i
      + bnk_dep_corp ∙ dep_ror_corp_i + bnk_dep_hh ∙ dep_ror_hh_i
      + bnk__repo_corp ∙ repo_ror_corp_i + bnk_b_corp ∙ b_ror_corp_i
      + s_hh ∙ r_i ∙ dep_ror_hh_i + s_corp ∙ r_i ∙ dep_ror_corp_i
  - Liquid assets:
    - LA_bnk,i = cash_bnk + cash_eq_bnk + other_rev_repo_db
      + bnk_b_bnk ∙ (1−hc_bnk_b_i)
      + corp_bbnk ∙ (1 − e_corp_bbnk) ∙ (1−hc_corp_b_i)
      + sov_bbnk ∙ (1 − e_sov_bbnk) ∙ (1−hc_sov_b_i)
      + (ivf_bnk_repo_sov_i + corp_bnk_repo_sov_i + db_bnk_repo_sov_i) ∙ (1−hc_sov_b_i)
      + (ivf_bnk_repo_corp_i + corp_bnk_repo_corp_i + db_bnk_repo_corp_i) ∙ (1−hc_corp_b_i)
      + s_sov_bbnk,i + ( s_sov_bivf,i − a_s_sov_bivf,i) + ( s_sov_bdb,i − a_s_sov_bdb,i)
      + (s_hh + s_corp) ∙ r_i
      + db_bnk_nonrepo_i + ivf_bnk_nonrepo_i
  - Net liquidity position:
    - B_bnk,i = LA_bnk,i − O_bnk,i
- Variable definitions provided for bnk, db, ivf, i, s_sov_b, hc_sov_b, sov_b, O, LA, B, m_sov_b, m_corp_b, hc_corp_b, s, r, cash, cash_eq, bnk_rev_repo, db_rev_repo, other_rev_repo, db_b, bnk_b, hc_bnk_b, corp_b, a_s_sov_b, ivf_db_repo, ivf_db_nonrepo, ivf_bnk_repo, ivf_bnk_nonrepo, ivf_db_repo_sov, e_sov_b, e_corp_b, hh_sov_b, ivf_db_repo_corp, hh_corp_b, corp_db_repo_sov, corp_db_repo_corp, repo_ror_corp, db_repo, db_dep, dep_ror_corp, dep_ror_hh, b_ror_corp, db_bnk_repo, db_bnk_nonrepo, ivf_bnk_repo_sov, ivf_bnk_repo_corp, db_bnk_repo_sov, db_bnk_repo_corp, corp_bnk_repo_sov, bnk_repo, corp_bnk_repo_corp, bnk_dep, cl, clr.

### Limitations and areas for further work
- Framework does not separately investigate liquidity risks associated with currency denominations.
- Framework does not quantify additional margin required due to large fluctuations in underlying assets (e.g., stock prices or benchmark interest rates); this may underestimate actual liquidity stress.
- Dependency structure of correlated liquidity shocks currently calibrated by expert judgment; can be better estimated via parametric or nonparametric methods with sufficiently long historical data.
- Structural models could capture all impact channels of fire-sales but are costly; current reduced-form approach offers tractability and dynamic evolution to steady-state.

*Source: wpiea2024104-print-pdf — IMF Working Paper: "A Framework for Systemwide Liquidity Analysis" (Appendix I and Appendix II excerpts).*

### Appendix I – The Use of Copula in Financial Risk Analysis ..............................................................

### wpiea2024104-print-pdf - Appendix I – The Use of Copula in Financial Risk Analysis

### Appendix inventory
- Appendix I — The Use of Copula in Financial Risk Analysis: page 37
- Appendix II — Equations of the Model: page 39

### Content scope (as titled in the source)
- Appendix I: Title indicates treatment of copula methods applied to financial risk analysis.
- Appendix II: Title indicates presentation of model equations.

*Source: wpiea2024104-print-pdf - Appendix I – The Use of Copula in Financial Risk Analysis (pages 37, 39).*

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

### wpiea2024104-print-pdf - References

### Figures Inventory
- Figure 1. Systemwide Liquidity Analysis — A Comparison with Existing Methodologies (p.12)
- Figure 2. Workflow of System-Wide Liquidity Analysis (p.13)
- Figure 3. Mexico: Trade and Financial Openness (p.15)
- Figure 4. Mexico: Cross-sectoral Interlinkage (p.16)
- Figure 5. Mexico: Deposit, Bond, and Stock Holdings (p.17)
- Figure 6. Mexico: Sectoral Balance Sheet (p.18)
- Figure 7. Mexico: Duration of Debt Securities (p.19)
- Figure 8. Mexico: Data Input for Debt Securities and Margin Position (p.20)
- Figure 9. Mexico: Narrative Design of System-Wide liquidity Analysis (p.22)
- Figure 10. Mexico: Shock Calibration of System-Wide liquidity Analysis (p.24)
- Figure 11. Mexico: Market Valuation Shock on Debt (p.26)
- Figure 12. Mexico: Pecking Order of Market Clearing (p.27)
- Figure 13. Mexico: Results of the System-Wide Liquidity Analysis (p.28)
- Figure 14. Mexico: A Comparison of Correlation Factor (p.30)
- Figure 15. Mexico: Contribution to System-Wide Liquidity Stress (p.30)
- Figure 16. Mexico: Policy Experiment of the System-Wide Liquidity Analysis (p.32)
- Figure 17. Mexico: Pecking Order of Market Clearing (p.34)
- Figure 18. Impact of Fire-sales on Market Revaluation on Security Holdings and Agents’ Net (p.35)

### Glossary (selected acronyms)
- BOE Bank of England
- CB Central Bank
- DB Development Bank
- ELA Emergency Lending Assistance
- FDI Foreign Direct Investment
- FC Financial Corporation
- FSAP Financial Sector Assessment Program
- GOV General Government
- HH Household
- IF Investment Fund
- LCR Liquidity Coverage Ratio
- NFC Nonfinancial Corporation
- NFBI Non-bank Financial Institution
- PD Probability of Default
- PF Pension Fund
- ROW Rest of World
- SWL Systemwide Liquidity
- VAR Vector-Auto Regression

### Executive Summary — Key findings and framework features
- Purpose:
  - Develop a novel Systemwide Liquidity (SWL) framework to identify potential liquidity stress beyond commercial banks, using Mexico as a case study.
- Framework capabilities:
  - Go beyond banks and assess transmission and amplification of liquidity stress within the financial system.
  - Apply analysis at aggregate agent level (banks, investment funds, pension funds, insurance companies, etc.) or at the level of individual entities.
  - Use data on asset encumbrance and collateralized exposures (repo, etc.) to capture agents’ liquidity buffers, quantify margin calls, and trace collateral flows under stress.
  - Adapt to any jurisdiction regardless of depth and complexity of its financial system with tailored shock narratives.
  - Apply distribution of shocks with pre-defined correlation, instead of single point estimates, to tackle scenario uncertainty and identify tipping points leading to liquidity shortfalls.
  - Measure the relative contribution of each agent to system-wide liquidity stress.
  - Incorporate behavioral elements, such as order of asset liquidation or fire-sales, and their implication on other agents or system-wide liquidity.
  - Allow policy simulation to assess capacity and willingness of agents to intermediate when facing regulatory constraints.
- Main results for Mexico:
  - Commercial banks act as shock absorbers by providing liquidity through repo transactions and show only marginal liquidity shortfalls even under the most severe narratives.
  - Development banks are more vulnerable when liquidity constraints are binding; binding LCR or minimum liquidity buffers for investment funds can lead to larger system shortfalls for certain agents.
  - Expanding investment funds’ access to the repo market could reinforce systemwide resiliency and liquidity conditions.
  - Fire-sales by certain agents (e.g., investment funds) trigger broad-based mark-to-market asset devaluations, worsening liquidity positions systemwide; post fire-sale distributions show longer and fatter left tails for all market agents.

### Policy implications and uses
- Calibration of macroprudential and crisis management policies:
  - Identify critical areas of concern via comprehensive assessment of liquidity buffers and direct/indirect balance sheet exposures.
  - Inform micro- and macroprudential liquidity measures (e.g., limiting certain asset and funding exposure or building more liquidity buffers).
  - During crisis, identify institutions and markets most susceptible to liquidity strains and quantify liquidity needs.
  - Preemptively assess adjustments to limits or buffers, expansion of eligible collateral under ELA framework, or market access for certain agents.

### Introduction — Context and motivation
- Systemwide liquidity analysis motivated by:
  - Growing linkages between financial institutions and recent episodes (e.g., global dash-for-cash in 2020, SVB and Credit Suisse episodes).
  - Need to monitor and strengthen systemwide liquidity resilience amid increasing uncertainties and severity of liquidity shocks.
- Challenges addressed:
  - Data limitations and lack of standardized approach for systemwide analysis.
  - Requirement for granular data (balance sheets, bilateral claims, asset encumbrances, margin positions).
  - Country-specific tailored scenarios are often hard to harmonize—framework aims to be generic and adaptable.

### Literature Review — Relation to existing work
- Builds on and complements prior studies and tools:
  - Oura (2022) — Excel-based tool for FX liquidity stresses.
  - Sydow et al. (2021), Fukker et al. (2022), Farmer et al. (2020) — joint stress testing of banks and funds, fire sales, collateral/margin channel.
  - Bank of England SWES exercise — exploring risks to and from NBFIs.
  - Lô and Carpantier (2023); Gourdel and Sydow (2023); Fricke and Wilke (2020) — fund liquidity and contagion dynamics.
  - Drechsler et al. (2023); Jiang et al. (2023) — interest rates, bank run risks, uninsured deposits.
  - ESRB (2020) — corporate bond downgrade liquidity impact.
  - Studies on capital flows and drivers for emerging markets: Alba et al. (2021); Tellez-Leon and Ibarra (2019); Bush and Canon (2021); Vega (2021, 2019); Bush (2019).
  - Interconnectedness methodologies: Espinosa-Vega and Sole (2010), Covi et al. (2019), Xu (2012), Beirne and Bricco (2014), Cortes et al. (2018), Hamilton et al. (2015).
  - Market-based systemic indicators: CoVaR (Adrian and Brunnermeier, 2008), SRISK (Acharya, Engle, Richardson, 2012), systemic contingent claims (Jobst and Gray, 2013).
- Value added:
  - Integrates liquidity and interconnectedness approaches, traces money and collateral flows, addresses correlated liquidity shocks, captures behavioral responses and second-round effects, enables sensitivity and counterfactual policy experiments.

### Key Features of the Framework — Methodological overview
- Three-step process:
  1. Narrative design: formulate country-specific liquidity stress narratives.
  2. Shock generation: generate shocks aligned with narratives using correlated distributions via copula and marginal distributions (Appendix I).
  3. Monte Carlo simulation: simulate shocks to compute distributions of net liquidity position for each agent.
- Notable methodological elements:
  - Use of copula-based correlated shock generation; marginal distributions often represented by a pre-defined beta distribution with symmetric bell-curve shape.
  - Market clearing mechanisms guiding flow of liquidity, including collateral exchange and reversal of repo transactions.
  - Behavioral preferences (e.g., preference for cash over less liquid assets) affect market clearing outcomes.
  - Ability to simulate policy changes (e.g., allowing greater access of investment funds to repo market) and regulatory constraints (e.g., LCR).

### Case Study: Mexico — Background and motivations
- Openness and exposures:
  - Trade openness: exports and imports around 90 percent of GDP (2022, Figure 3).
  - Stock of FDIs at around 700 billion US dollar as of 2022.
  - United States accounts for nearly 80 percent of Mexico’s exports and 50 percent of FDIs.
  - Mexican peso is the third most actively traded currency in the Americas and most actively traded in Latin America.
- System composition and interlinkages (Figure 4):
  - Major agents: central bank, government, commercial banks, development banks, investment funds, nonfinancial corporations, households, foreign investors.
  - Agents fund/receive via direct lending, repos, debt securities issuance, deposits.
  - Offshore market important in trading Mexican peso and providing liquidity via domestic sovereign bonds and corporate stocks.
- Historical co-movement:
  - March 2020 illustrates strong co-movements among sovereign securities sell-off, commercial bank deposit outflows, and liquidation by foreign investors of Mexican corporate stocks (Figure 5).

### Mexico: Stylized agent balance sheets and vulnerabilities
- Business model features:
  - Commercial and development banks engage in maturity transformation; commercial banks rely mostly on retail and wholesale deposits; development banks obtain wholesale funding from investment funds and NFCs via short-term repo and bond issuance.
  - Investment funds finance via share issuance and invest mostly in sovereign securities while providing reverse repos and holding cash and equities—more liquid than banks.
  - Brokerage firms are small and excluded from the analysis (Figure 6).
- Encumbrance and collateral:
  - Encumbrance of sovereign securities: 58 percent for commercial banks and 84 (percent) for development banks.
- Duration profile:
  - Bulk of sovereign securities duration between one to five years (Figure 7).
- Contingent exposures:
  - Off-balance sheet credit and liquidity lines at around 3 trillion pesos (both revocable and irrevocable) — potential source of liquidity risk if triggered.

### Scope, data inputs, and granularity
- Coverage:
  - Agents collectively represent about 64 percent of total financial sector assets.
- Data compiled by Banxico as of December 2021:
  - Aggregate balance-sheet composition by agent type.
  - Bilateral who-to-whom exposures: loans, debt securities, reverse repo (assets); deposits, issuance of debt securities and shares, repo financing (liabilities).
  - Collateral data: encumbered and unencumbered, split into central bank eligible and non-eligible, by issuer type and remaining maturities.
  - Margin positions covered with debt securities (derivatives) to capture second-round margin call effects.
  - Haircut information for repo transactions by maturity and split into central bank operations and secondary market.

### Narrative design for Mexico — Four narratives stressed
- Narrative 1: Tighter global financial condition inducing investors’ selling of sovereign and corporate bonds; triggering margin calls for existing funding and derivatives positions.
  - Foreign holdings of domestic sovereign securities and corporate shares are currently at around 20 and 33 percent, respectively.
- Narrative 2: Tighter global funding conditions triggering credit and liquidity lines of corporates (credit/liquidity lines around 3 trillion pesos).
- Narrative 3: Capital outflows via wholesale deposit run-off (firms move deposits on-shore to off-shore).
- Narrative 4: Share redemption shocks triggering investment funds’ liquidity strains; partial deposit inflows back to commercial banks possible as withdrawn cash is redeposited.

### Shock generation and simulation specifics
- Calibration:
  - Shocks calibrated for triggering points identified in narratives: deposit outflow rates, sovereign bond yield shocks, triggering of credit/liquidity lines, investment fund share redemptions.
- Statistical approach:
  - Use of copula to assign correlated shocks; marginal distributions often specified as pre-defined beta distributions with symmetric bell-curve shape and upper/lower bounds (Appendix I).
  - Correlation factor adjustable to reflect country-specific co-movement; in absence of long time series, sensitivity analysis across correlation parameters recommended.
- Monte Carlo:
  - One-thousand simulations produce one-thousand net liquidity positions per agent, generating post-shock distributions to identify maximum liquidity shortfalls and tipping points (e.g., net liquidity position equals 0).

### Behavioral and market mechanisms modeled
- Market clearing and pecking order:
  - Agents may prioritize cash, sovereign securities, or short-term reverse repos to meet obligations; changes in preference alter net liquidity outcomes.
  - Market clearing captures exchange/reversal of collateral when repo funding is not rolled over.
- Second-round effects:
  - Fire-sales induce mark-to-market devaluations across commonly held tradable securities, amplifying system stress.
- Policy simulation:
  - Framework can test effects of regulatory binding constraints (e.g., LCR) on agents’ willingness to intermediate and simulate policies such as broader repo access or expanding eligible collateral under ELA.

*Source: wpiea2024104-print-pdf - References (IMF Working Paper: A Framework for Systemwide Liquidity Analysis).*

### 0.9 to simulate high co-movement under stress (see Figure 10 bottom panel).  Figure 10 top panel provides

### A Framework for Systemwide Liquidity Analysis — Mexico: Shock Calibration and Results

### Shock calibration and selection
- Parameters are exogenous in the framework but can be estimated separately or identified based on historical evidence or literature.
- Peaks of the shocks were closely aligned with traditional bank cash-flow analysis over a three-month horizon.
- Additional stress parameters calibrated based on historical volatility or expert judgement when historical time series are not readily available (examples: share redemption rate of investment funds; phase-out rate of short-term corporate funding).
- Severity of shocks may differ by stress testing horizon: some liquidity shocks unfold in days (e.g., confidence shock induced bank runs), others over longer periods (e.g., exit from medium- or long-term contractual positions).
- The framework covers a range of shocks rather than a single point on the shock distribution, making it less prone to scenario uncertainties than other liquidity stress tests.

- Calibration ranges (as presented):
  - Bond selling rate: [0,40]
  - Sovereign bond yield shock: [0,4] with average shock at 200 bps
  - Corporate bond yield shock: [0,8] with average shock at 400 bps
  - Credit line triggering rate: [0,40]
  - Corporate deposit run-off rate: [0,50]
  - Household deposit run-off rate: [0,20]
  - Share redemption: [0,40]
  - Short term debt phase-out rate: [0,40]

### Market valuation shocks and transmission channels
- Shocks to market value of sovereign securities follow a modified duration approach.
- Sovereign and corporate shocks simulated via parallel shifts of both yield curves along maturity buckets; corporate securities assumed to have a higher upper bound shift due to higher risk premium.
- Bank bond yield shocks assumed higher than sovereign and lower than corporate securities under each simulation.
- Granular inputs used: holdings by agents, encumbrance status, eligibility for central bank operations, maturity buckets.
- Market valuation impacts derived using modified duration formula where variables include:
  - P = bond valuation
  - D = duration (selected at midpoint within each maturity bucket)
  - B = bond yield
  - M = outstanding amount
  - r = risk-free rate
  - s = bond spreads assumed in shock calibration
- Market revaluations affect balance sheets via two main channels:
  - Reduced market value of unencumbered collateral.
  - Margin calls on encumbered collateral underlying secured funding and derivative margin positions.
- Both channels can reduce liquidity buffers of single agents and increase tail risks of systemwide liquidity stress.

### Monte Carlo simulation and market clearing mechanism
- Ten thousand Monte Carlo simulations run using shocks from calibration to generate distributions of net liquidity positions for each agent.
- Results reflect direct funding and market stress impacts and second-round revaluation effects (e.g., calls on encumbered collateral).
- Behavioral and policy analysis can be applied to subsets of simulations (e.g., banks reluctant to intermediate as liquidity ratios approach regulatory minimum).
- Market clearing pecking order (behavioral response under stress):
  1. Use cash and cash equivalents first.
  2. Phase out (or not rollover) outstanding reverse repo transactions or short-term bond investments.
  3. Pledge unencumbered collateral via repo transactions to obtain liquidity; commercial banks and the central bank are main counterparties.
- Assumptions regarding sovereign securities sold by foreign investors under narrative 1:
  - Absorbed pro-rata by all market agents based on existing holdings, conditional on sufficient liquidity after initial shocks.
  - Development banks and investment funds purchase only if they still have cash on balance sheets; remaining purchases go to commercial banks.
  - Commercial banks can purchase and immediately pledge to the central bank to obtain cash.
- Phase-out of reverse repo contracts considered neutral from liquidity perspective (outflow and inflow offset; encumbered assets convert back to unencumbered assets at discounted market price).
- Released amount of encumbered collateral upon repo termination allocated into unencumbered collateral pro-rata based on starting encumbered corporate and sovereign securities composition.

### Results for Mexico (systemwide analysis)
- Overall finding: financial system remains resilient against the four narratives with commercial banks backstopping liquidity needs of all agents (Figure 13).
- Under most severe combined-narrative shocks and assuming no binding regulatory constraints, commercial banks show only marginal liquidity shortfalls (a thin negative tail) mainly driven by:
  - Triggering of contingent credit lines.
  - Wholesale deposits’ outflows.
- Commercial banks act as shock absorbers by providing liquidity via repo transactions.
- Development banks and investment funds can withstand significant outflows, but risks arise depending on agents’ risk-off behavior and potential binding liquidity constraints.
- If commercial banks face binding liquidity constraints (e.g., mandatory LCR or behavioral minimum buffers) or minimum liquidity buffers for investment funds are imposed, larger liquidity shortfalls could materialize, including for development banks.

- Agent-specific insights:
  - Commercial banks: largest transmission of shocks from corporates and investment funds.
    - At the minimum cut-off point on the distribution of commercial banks’ net liquidity position post-shock under narrative 4, liquidity outflows from corporates contribute the most to net liquidity decline (high exposure to wholesale deposits and contingent credit/liquidity lines).
    - This is marginally offset by small reduction in margin calls and increase in unencumbered assets due to phase-out of short-term repo financing provided by corporates.
  - Investment funds: ranked second in contribution to liquidity outflows but bring roughly equal inflows to commercial banks.
    - Transactions with commercial banks are often repo financing or direct sale of debt securities, which are generally liquidity neutral (exchange of cash for liquid collateral).
  - Development banks: place into or obtain little deposits and credit lines from commercial banks; do not significantly drain liquidity via capital flight.
    - Have the most illiquid asset profile: 46 percent of assets are lending to private sector; remaining holdings are sovereign securities with a high share already encumbered for short-term funding.
  - Government: indirectly influences systemwide liquidity via price impacts and transactions of sovereign securities.
    - Decline in sovereign securities value reduces liquid asset holdings of commercial banks.
    - Purchases of sovereign securities by commercial banks considered liquidity neutral, but net impact on commercial banks’ liquidity is negative when combining channels.

- Contribution to development bank outflows:
  - Corporates contribute 45 percent of development bank outflows.
  - Investment funds contribute 40 percent of development bank outflows.
  - Short-term financing to development banks from corporates and investment funds: 35 percent and 27 percent of total short-term financing, respectively (as of end-2021).

- Systemwide contribution across simulations:
  - Commercial banks and investment funds persistently contribute most to systemwide liquidity changes due to larger balance sheet size and higher exposure to market liquidity outflows (deposits’ withdrawals, drawing on credit/liquidity lines, share redemptions).

- Correlation of liquidity shocks:
  - Higher correlation intensifies downside risks.
  - Comparison: correlation factor 0.9 produces a flatter distribution of commercial banks’ net liquidity position with a fatter left tail than correlation factor 0.2, indicating stronger co-movement amplifies liquidity stress.

### Policy experiments and behavioral sensitivity
- Policy experiment on investment funds’ access to repo market:
  - Assuming higher discount rates for investment funds (Mexico only has limited access to the repo market) shifts distribution of their net liquidity position to the left.
  - Conversely, lifting restrictions (complete lift of limited access) could bolster investment funds’ liquidity position and enhance system resiliency.
  - Implementation note: higher discount rates implemented by imposing on the initial market revaluation shock a multiplier of 1.5 for their holdings of sovereign securities.
- Commercial banks’ behavioral response and knock-on to development banks:
  - If commercial banks change liquidity preference in a downside scenario or face binding liquidity constraints, development banks could face stress and may resort to central bank liquidity support.
  - Sensitivity experiment: freezing repo activities of commercial banks when they reach a pre-defined LCR limit pushed part of development banks’ distribution into negative territory, suggesting liquidity strains induced by commercial bank behavior.
  - Alternative experiment: commercial banks pull back on short-term funding (deposit withdrawal or unwillingness to refinance short-term debt), which pushes development banks’ net liquidity distribution left but less severely than freezing repos (development banks have limited short-term funding from commercial banks compared to repo funding).
  - Development banks could seek direct central bank liquidity support as they can participate in repo market and transact directly with central bank.

*Source: IMF staff.*

### 1.75 for bank securities and 2 for corporate securities. To address risks of over-simplicity, section IX developed a ful

### wpiea2024104-print-pdf - 1.75 for bank securities and 2 for corporate securities. To address risks of over-simplicity, section IX developed a ful

### Shock amplification and fire-sale scenario
- Fire-sale scenario implemented as an additional behavioral response under the market clearing mechanism to capture market amplification from asset sales by weak agents (investment funds treated as last line of defense).
- Artificial data (generated by adding a random component on top of initial balance sheet data while ensuring accounting identity) used for confidentiality reasons.
- Fire-sales produce additional market haircuts for sovereign and corporate securities holdings across agents, shrinking balance sheets and liquid assets.
- Price impact of sales modeled via a non-linear relationship based on Kyle (1985) and Fukker, Kaijser, Mingarelli, and Sydow (2021): price change depends on total amount sold S, Kyle’s lambda λ (price impact parameter), and an impact boundary parameter B (set as the most negative return observed in the history of a security to prevent prices falling below 100 percent).
- Quantification achieved via an iterative process to equilibrium price post-shock, constrained by securities available for sale and diminishing marginal price impact.

### Key findings from fire-sale experiments
- Post fire-sale distributions show higher market discount across tradable securities and higher tail liquidity risks; post fire-sale distributions have longer and fatter left tails across all market agents.
- The additional behavioral layer reveals further deterioration of liquidity positions system-wide.
- The threshold for triggering fire-sales: when the NBFI sector (e.g., investment funds) has exhausted all cash and equivalents (cash, reverse repo) and is forced to sell other liquid assets (e.g., sovereign securities), assuming the NBFI sector does not have direct access to repo markets or central bank facilities.
- The analysis is not intended to provide precise loss estimates but to link fire-sales with agents’ balance sheets, interconnections, and a market clearing mechanism in a tractable manner.

### Systemwide Liquidity (SWL) framework results and implications
- Framework uses copula to impose joint liquidity shocks and to trace liquidity flows among agents; complements standard liquidity and interconnectedness analyses.
- Application to Mexico:
  - Confirms commercial banks’ role as liquidity backstop; commercial banks act as final shock absorber by providing liquidity through repo transactions.
  - Commercial banks’ liquidity shortfalls are marginal even under the most severe narratives.
  - Development banks are more vulnerable due to funding concentration; vulnerability increases when binding liquidity constraints (e.g., mandatory LCRs) are considered.
- Relaxing the LCR requirement at time of liquidity stress could better promote banks’ role as backstop with respect to other agents under stress.
- Given data mapping limitations, assumption used: commercial banks breach LCR limit if liquid assets decline by 50 percent.
- Expanding access of investment funds to the repo market could strengthen systemwide resiliency.
- In absence of adequate policy supports, fire-sale as last line of defense could represent a significant negative externality to systemwide liquidity via higher market discount and shrinkage of liquid assets and margin positions.

### Limitations and areas for further work
- Framework does not separately investigate liquidity risks associated with currency denominations.
- Framework does not quantify additional margin required due to large fluctuations in underlying assets (e.g., stock prices or benchmark interest rates); this may underestimate actual liquidity stress.
- Dependency structure of correlated liquidity shocks currently calibrated by expert judgment; can be better estimated via parametric or nonparametric methods with sufficiently long historical data.
- Structural models could capture all impact channels of fire-sales but are costly; current reduced-form approach offers tractability and dynamic evolution to steady-state.

### Copula use and methodological notes (Appendix I)
- Copula models joint distributions with marginal distributions uniform on [0, 1]; allows high-dimensional marginal distributions corresponding to specific shock parameters.
- Two-step generation:
  1. Generate pairs (Z1, Z2) from a bivariate normal distribution with pre-defined statistical dependence (Rank Correlation Coefficients); each has a normal marginal distribution.
  2. Apply transformations (G1, G2) via inverse CDFs to change marginals to target distributions.
- Beta distributions selected as final marginals for Gaussian Copula to allow set boundaries and severity of shocks.
- Dependence structure estimation options: parametric (maximum likelihood), semiparametric (parametric copula, nonparametric marginals), and non-parametric (kernel density estimation).
- Alternative copula choices (e.g., Student’s T) are possible to increase joint extreme event probability.

### Model structure and equations (Appendix II) — overview of blocks
- Four main blocks of formulas compute post-shock outflows, inflows, liquidity buffer changes, and market clearing pecking order:
  1. Market revaluation of tradable securities subject to yield shock (market absorption of securities sold by foreign investors with formulas for s_sov_b_bnk,i, s_sov_b_db,i, s_sov_b_ivf,i).
  2. Investment fund block:
     - Outflow O_ivf,i = m_sov_b_ivf∙hc_sov_b_i + m_corp_b_ivf∙hc_corp_b_i + (s_hh + s_corp)∙r_i
     - Liquid assets LA_ivf,i formula summing cash, cash_eq, repo receivables, and holdings net of haircuts.
     - Net liquidity position B_ivf,i = LA_ivf,i − O_ivf,i
     - Detailed pecking order rules for asset sales and repo/non-repo utilisations depending on B_ivf,i and available cash buckets.
  3. Development bank block:
     - Short-term repo funding phase-out allocations (ivf_db_repo_sov_i, ivf_db_repo_corp_i, corp_db_repo_sov_i, corp_db_repo_corp_i) specified with exact allocation formulas using sov_b_db, corp_b_db, e_sov_b_db, e_corp_b_db and haircut adjustments (1/(1−hh_sov_b_i) etc.).
     - Outflow O_db,i = max (0, sov_b_db∙e_sov_b_db − ivf_db_repo_sov_i − corp_db_repo_sov_i)∙hc_sov_b_i + max (0, corp_b_db∙e_corp_b_db − ivf_db_repo_corp_i − corp_db_repo_corp_i)∙hc_corp_b_i + ivf_db_repo_i + ivf_db_nonrepo_i + db_dep_corp∙dep_ror_corp_i + db_dep_hh∙dep_ror_hh_i + db__repo_corp∙repo_ror_corp_i + db_b_corp∙b_ror_corp_i
     - Liquid assets LA_db,i formula including cash, cash_eq, repo receivables, holdings net of haircut and allocated repo inflows adjusted for haircuts.
     - Net liquidity position B_db,i = LA_db,i − O_db,i
     - Detailed pecking order rules for market clearing analogous to investment fund block, with conditional allocations for a_s_sov_b_db,i, db_bnk_repo_i, db_bnk_nonrepo_i.
  4. Commercial bank block (formulas and pecking order provided in the Appendix but not excerpted in full in this content unit).

*IMF WORKING PAPERS A Framework for Systemwide Liquidity Analysis — INTERNATIONAL MONETARY FUND*

### 3. Commercial bank block

### 3. Commercial bank block

### Allocation of repos and collateral release
- ivf_bnk_repo_sov_i = ivf_bnk_repo_i ∙ (sov_bnk ∙ e_sov_bnk) / (sov_bnk ∙ e_sov_bnk + corp_bnk ∙ e_corp_bnk) ∙ 1/(1−hh_sov_b_i)
- ivf_bnk_repo_corp_i = ivf_bnk_repo_i ∙ (corp_bnk ∙ e_corp_bnk) / (sov_bnk ∙ e_sov_bnk + corp_bnk ∙ e_corp_bnk) ∙ 1/(1−hh_corp_b_i)
- db_bnk_repo_sov_i = db_bnk_repo_i ∙ (sov_bnk ∙ e_sov_bnk) / (sov_bnk ∙ e_sov_bnk + corp_bnk ∙ e_corp_bnk) ∙ 1/(1−hh_sov_b_i)
- db_bnk_repo_corp_i = db_bnk_repo_i ∙ (corp_bnk ∙ e_corp_bnk) / (sov_bnk ∙ e_sov_bnk + corp_bnk ∙ e_corp_bnk) ∙ 1/(1−hh_corp_b_i)
- corp_bnk_repo_sov_i = bnk_repo_corp ∙ repo_ror_corp_i ∙ (sov_bnk ∙ e_sov_bnk) / (sov_bnk ∙ e_sov_bnk + corp_bnk ∙ e_corp_bnk) ∙ 1/(1−hh_sov_b_i)
- corp_bnk_repo_corp_i = bnk_repo_corp ∙ repo_ror_corp_i ∙ (corp_bnk ∙ e_corp_bnk) / (sov_bnk ∙ e_sov_bnk + corp_bnk ∙ e_corp_bnk) ∙ 1/(1−hh_corp_b_i)

### Liquidity outflow (O_bnk,i)
- O_bnk,i = cl_corp ∙ clr_i + s_sov_bbnk,i + ( s_sov_bivf,i − a_s_sov_bivf,i) + ( s_sov_bdb,i − a_s_sov_bdb,i)
- + max(0, sov_bbnk ∙ e_sov_bbnk − ivf_bnk_repo_sov_i − db_bnk_repo_sov_i − corp_bnk_repo_sov_i) ∙ hc_sov_b_i
- + max(0, corp_bbnk ∙ e_corp_bbnk − ivf_bnk_repo_corp_i − db_bnk_repo_corp_i − corp_bnk_repo_corp_i) ∙ hc_corp_b_i
- + m_sov_bbnk ∙ hc_sov_b_i + m_corp_bbnk ∙ hc_corp_b_i
- + ivf_bnk_repo_i + ivf_bnk_nonrepo_i + db_bnk_repo_i + db_bnk_nonrepo_i
- + bnk_dep_corp ∙ dep_ror_corp_i + bnk_dep_hh ∙ dep_ror_hh_i
- + bnk__repo_corp ∙ repo_ror_corp_i + bnk_b_corp ∙ b_ror_corp_i
- + s_hh ∙ r_i ∙ dep_ror_hh_i + s_corp ∙ r_i ∙ dep_ror_corp_i

### Liquid assets (LA_bnk,i)
- LA_bnk,i = cash_bnk + cash_eq_bnk + other_rev_repo_db
- + bnk_b_bnk ∙ (1−hc_bnk_b_i)
- + corp_bbnk ∙ (1 − e_corp_bbnk) ∙ (1−hc_corp_b_i)
- + sov_bbnk ∙ (1 − e_sov_bbnk) ∙ (1−hc_sov_b_i)
- + (ivf_bnk_repo_sov_i + corp_bnk_repo_sov_i + db_bnk_repo_sov_i) ∙ (1−hc_sov_b_i)
- + (ivf_bnk_repo_corp_i + corp_bnk_repo_corp_i + db_bnk_repo_corp_i) ∙ (1−hc_corp_b_i)
- + s_sov_bbnk,i + ( s_sov_bivf,i − a_s_sov_bivf,i) + ( s_sov_bdb,i − a_s_sov_bdb,i)
- + (s_hh + s_corp) ∙ r_i
- + db_bnk_nonrepo_i + ivf_bnk_nonrepo_i

### Net liquidity position
- B_bnk,i = LA_bnk,i − O_bnk,i

### Variable definitions (as in source)
- bnk: Commercial bank
- db: Development bank
- ivf: Investment fund
- i: Simulation number
- s_sov_b: Sovereign securities sold by foreign investors
- hc_sov_b: Valuation shock to sovereign securities due to yield shock
- sov_b: Holdings of sovereign securities
- O: Liquidity outflow
- LA: Liquid Assets + Liquidity inflow
- B: Net liquidity position
- m_sov_b: Margin position on sovereign securities
- m_corp_b: Margin position on corporate securities
- hc_corp_b: Valuation shock to corporate securities due to yield shock
- s: Investment fund shares
- r: Redemption rate on investment fund shares
- cash: Cash
- cash_eq: Cash equivalents
- bnk_rev_repo: Reverse repo claims on commercial banks
- db_rev_repo: Reverse repo claims on development banks
- other_rev_repo: Reverse repo claims on commercial others
- db_b: Holdings of development bank securities
- bnk_b: Holdings of commercial bank securities (commercial papers, etc.)
- hc_bnk_b: Valuation shock to commercial bank securities (commercial papers, etc.) due to yield shock
- corp_b: Holdings of corporate securities
- a_s_sov_b: Purchase/Absorption of sovereign securities sold by foreign investors
- ivf_db_repo: Investment fund withdrawal of reverse repo funding to development banks
- ivf_db_nonrepo: Investment fund withdrawal of funding other than reverse repo to development banks
- ivf_bnk_repo: Investment fund withdrawal of reverse repo funding to commercial banks
- ivf_bnk_nonrepo: Investment fund withdrawal of funding other than reverse repo to commercial banks
- ivf_db_repo_sov: The release of sovereign securities collateral associated with investment fund withdrawal of reverse repo funding to development banks
- e_sov_b: Share of encumbered sovereign securities in total sovereign securities
- e_corp_b: Share of encumbered corporate securities in total corporate securities
- hh_sov_b: Haircut on encumbered sovereign securities when pledged for reverse repo transactions
- ivf_db_repo_corp: The release of corporate securities collateral associated with investment fund withdrawal of reverse repo funding to development banks
- hh_corp_b: Haircut on encumbered corporate securities when pledged for reverse repo transactions
- corp_db_repo_sov: The release of sovereign securities collateral associated with corporate withdrawal of reverse repo funding to development banks
- corp_db_repo_corp: The release of corporate securities collateral associated with corporate withdrawal of reverse repo funding to development banks
- repo_ror_corp: The rate of corporate withdrawal of reverse repo funding
- db_repo: Repo liability of development banks
- db_dep: Deposit liability of development banks
- dep_ror_corp: Corporate deposit run-off rate
- dep_ror_hh: Household deposit run-off rate
- b_ror_corp: The rate of corporate withdrawal of bond funding
- db_bnk_repo: Development bank withdrawal of reverse repo funding to commercial banks
- db_bnk_nonrepo: Development bank withdrawal of funding other than reverse repo to commercial banks
- ivf_bnk_repo_sov: The release of sovereign securities collateral associated with investment fund withdrawal of reverse repo funding to commercial banks
- ivf_bnk_repo_corp: The release of corporate securities collateral associated with investment fund withdrawal of reverse repo funding to commercial banks
- db_bnk_repo_sov: The release of sovereign securities collateral associated with development bank withdrawal of reverse repo funding to commercial banks
- db_bnk_repo_corp: The release of corporate securities collateral associated with development bank withdrawal of reverse repo funding to commercial banks
- corp_bnk_repo_sov: The release of sovereign securities collateral associated with corporate withdrawal of reverse repo funding to commercial banks
- bnk_repo: Repo liability of commercial banks
- corp_bnk_repo_corp: The release of corporate securities collateral associated with corporate withdrawal of reverse repo funding to commercial banks
- bnk_dep: Deposit liability of commercial banks
- cl: Bank credit lines to corporate
- clr: Triggering rate of corporate credit lines

*Source: IMF Working Papers — "A Framework for Systemwide Liquidity Analysis", Section 3: Commercial bank block.*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024104-print-pdf.pdf_