## wpiea2019250-print-pdf

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### Background and aim
- Solvency-liquidity feedback loops can amplify capital losses: funding withdrawals → asset liquidation → market liquidity deterioration → mark-to-market losses → further funding withdrawals (Adrian and Shin 2010; BCBS 2015).
- Post-GFC shifts: funding liquidity increasingly provided by central banks (broadened collateral frameworks); secured funding (repos/reverse repos) dominates wholesale funding; central bank asset purchases increased market liquidity of sovereign and corporate bonds.
- Core aim: develop a practical tool to calculate dynamic haircuts for assets in a stylized banking system that captures solvency‑liquidity feedback loops and regime-dependent market liquidity premia using Markov regime-switching models and historical daily trading data.
- Key modeling features:
  - Links haircuts with amounts of securities sold (individual and system-wide).
  - Links haircuts with liquidity stress tests (to compute system-wide sales) and solvency stress tests (to compute capital effects via mark-to-market losses).
  - Can include market volatility indexes (e.g., VIX) as predictors of regime switching.

### Contingent liquidity risks (Box 1) — nature, drivers, and behavioral responses
- Drivers and instruments:
  - Contingent liquidity arises from repos (SFT), derivatives, and rehypothecation; initial/variation margins can trigger fire sales.
  - Collateral posted/received typically comprised of cash or sovereign bonds; sometimes equities.
- Netting and encumbrance:
  - Netting (especially via CCPs) can reduce gross collateral needs; if a bank posts more collateral than it receives, asset encumbrance (AE) increases and dries out CBC.
  - Repricing of repos/reverse repos across maturities provides a rough approximation of additional liquidity needs absent granular data.
- Behavioral options and limits:
  - Use secured funding (repos, collateral swaps), including central bank facilities, up to encumbrable assets minus haircuts; asset fire sales are last resort.
  - Repos are subject to margin calls and can amplify liquidity risk if counterparties refuse to extend funding (examples: Lehman, triparty repo reluctance).
- Reasons for asset liquidation (from source):
  - Profitability risk (e.g., low-yielding assets funded with short-term wholesale funding).
  - Regulatory constraints (changes in risk-weighted assets or HQLA requirements).
  - Funding liquidity risk itself.
- Pecking-order and systemic vs idiosyncratic events:
  - In systemic crises banks may hoard liquidity and may be forced to sell liquid assets first; in idiosyncratic shocks a bank may sell less liquid assets but risk signalling trouble.
  - Systemic events produce larger haircuts because aggregate amounts sold are larger and demand-side capacity may be constrained.

### Framework: regime-switching market liquidity and haircut estimation
- Regime concept:
  - Two regimes: non-stress (high liquidity) and stress (low liquidity). Market liquidity can switch between them; switches can be common across asset classes or asset-class specific.
- Security- and aggregate-level measures:
  - Amihud (2002) measure: ratio of absolute daily returns to daily trading volume.
  - Price-impact measure: slope coefficient of regression of price change on signed order flow (suitable because fire-sales are seller-initiated).
  - Aggregate market liquidity for an asset class is the average of security-level price-impact measures.
- Regime-switching estimation steps (aggregate market liquidity):
  1. Identify marketable asset classes and compute daily security-level price impact measures.
  2. Average to obtain aggregate price impact measure per asset class.
  3. For each asset class j, estimate a two-regime Markov model: PPPP_t_j = beta_0_j,s + epsilon_t_j,s (with regime-dependent beta_0_j,s and variance sigma_s^2).
- Price impact and haircut calculation:
  - Total amount sold by all banks in asset class j: VVVV_aaaaaa_j ≡ sum_i VVVV_ii_j (i = 1..P).
  - Price impact in regime s: beta_0_j,s ∙ VVVV_aaaaaa_j (subject to a scenario‑conditional floor to avoid unrealistic prices).
  - Assumes linear relationship between price impact and total amount sold (simplifying if trade sizes are not “too” large).
- Volatility extension:
  - Country VIX decomposed into common US VIX component and residual: V_t_c = alpha_0 + alpha_1 ∙ VIX_t_US + epsilon_t_c.
  - Regime model with volatility: PPPP_t_j = beta_0_j,s + beta_1_j,s ∙ VIX_t_US + beta_2_j,s ∙ epsilon_t_c + epsilon_t_j,s.
  - Model allows different beta coefficients across regimes; regime-switching probabilities are not conditioned on VIX to avoid computational instability.

### Model specifications and estimation tools
- Five main specifications:
  1. Asset class-specific regimes and regime-switching variances without a volatility index (baseline).
  2. Asset class-specific regimes and non-regime-switching variances without a volatility index.
  3. Common regimes and regime-switching variances without a volatility index.
  4. Asset class-specific regimes and regime-switching variances with a volatility index.
  5. Asset class-specific regimes and non-regime-switching variances with a volatility index.
- Software:
  - Matlab programs (MS_Regress package basis) to estimate Markov regime-switching models.
  - Excel-based tool to compute haircuts and CAR impacts from aggregate amounts sold.
- Country volatility indexes referenced: CAC 40 (France), VDAX‑New (Germany), PSI 20 (Italy), AEX (Netherlands), IBEX 35 (Spain), FTSE 100 (United Kingdom), CBOE VIX (United States).

### Example application — euro area banks (data and grouping)
- Sample: 29 largest euro area banks using 2016 EBA transparency exercise data (sovereign exposures by country and remaining maturity; regulatory capital and RWA).
- Transaction data for European sovereign bonds: MTS Markets dataset (May 2005–April 2015).
- Asset classes: sovereign bonds grouped by issuer country (France, Germany, Italy, Netherlands, Spain, United States, others) and residual maturity buckets: zero to three years, four to six years, seven to 11 years, 11+ years.
- Concentration:
  - Sovereign bond holdings (in percent of total sovereign bond holdings): Italy 15%, Spain 15%, Germany 11%, France 13%, Netherlands 5%, US 8%, Other 33%.
  - Sovereign bond holdings (AFS + HFT, in percent): Italy 16%, Spain 16%, Germany 12%, France 12%, Netherlands 5%, US 9%, Other 30%.
- Banks grouped by business model: G‑SIBs, internationally active, domestic focus.

### Simulation assumptions (5 percent fire-sale experiment) and haircut properties
- Key simulation assumptions:
  - Time horizon of liquidation: one day; all banks sell the same share of their sovereign bond holdings in one day.
  - Sale amount: all banks sell 5 percent of their sovereign bond holdings of the largest five sovereign exposures in their CBC.
  - No pecking order assumed.
  - Implementation shortfall assumed to be 50 percent.
  - For volatility-including specifications:
    - US VIX assumed to increase to 23.9 percent.
    - Country volatility indexes for the five countries assumed to increase by two standard deviations from values at end‑Q1 2018.
- Haircut estimation:
  - Haircuts computed based on total amount sold using Markov regime-switching models (models (1) and (6)) estimated in Matlab; Excel tool used for aggregation and CAR impacts.
  - Haircuts reflect both price impact estimates and holdings (volume effect): large absolute holdings can produce larger haircuts on “safe” bonds when sales are proportional (5 percent).
- Empirical regularities:
  - Italian and Spanish sovereign bond haircuts typically higher than Dutch, French, German—especially in stress regimes.
  - Specification 3 (common regimes) shows flight‑to‑quality: Italian and Spanish haircuts higher in stress regime; Dutch, French, German haircuts generally lower in stress regime.
  - Specifications with non-regime-switching variances (2 and 5) produce much higher haircuts than regime-switching-variance specifications (1 and 4) because of high stress‑regime volatilities.
  - Specifications 1 and 4 (regime-switching variances) generally provide better goodness of fit.

### Impact on banks’ capital (CET1 / CAR) — results for 5 percent sale
- Loss formulation (from text):
  - L_VS_s_i = sum_{j=1}^{J} [ 1/2 * β_{j,s} * VAA_j * VHV_{i,j} + (β_{j,s} * VAA_j) * SSV_cS_{i,j} ]
    - J = total number of asset classes; β_{j,s} = price impact of asset class j in regime s.
- CET1 CAR after shock:
  - CET1_CAR_i_shocked;M = CET1_CAR_i_initial − L_losses_i_M / RWA_i
- Median CET1 CAR (before asset liquidation) by bank type:
  - G‑SIB: 12.72
  - Internationally active: 14.29
  - Domestic focus: 14.29
- Median CET1 CAR after asset liquidation (selected specifications):
  - specification 1, stressed: 12.29 (G‑SIB), 13.99 (Internationally active), 13.57 (Domestic focus)
  - specification 1, non-stressed: 12.69, 14.26, 14.24
  - specification 2, stressed: 10.93, 13.23, 11.50
  - specification 2, non-stressed: 12.57, 14.20, 14.06
  - specification 3, stressed: 12.60, 14.18, 14.02
  - specification 3, non-stressed: 12.59, 14.22, 14.11
  - specification 4, stressed: 12.22, 13.97, 13.58
  - specification 4, non-stressed: 12.70, 14.28, 14.29
  - specification 5, stressed: 11.35, 13.31, 12.20
  - specification 5, non-stressed: 12.49, 14.15, 13.96
- Key quantitative findings:
  - Largest stressed vs non‑stressed difference observed in specification 2: a 152‑bp difference in CET1 impact (weighted average of banks), with a 95‑percent confidence interval between 141 bps and 162 bps.
  - Higher market volatility leads to higher haircuts and larger losses.
  - Domestic‑focused banks suffer larger stressed/non‑stressed differences due to concentrated domestic sovereign holdings and less diversification.
  - G‑SIBs and international banks show smaller impacts due to diversified liquid asset portfolios.

### Conclusions, policy implications, and potential extensions
- Conclusions:
  - Fire sales in stress periods produce statistically significantly higher price impacts than in non‑stress periods; haircuts are highly nonlinear and much larger in stress regimes.
  - Stress‑regime haircuts are more appropriate for systemic events; non‑stress haircuts for idiosyncratic events.
  - Including regime‑switching haircuts in stress tests can materially reduce banks’ capital ratios compared with using constant haircuts.
- Policy implications:
  - Stress testers should account for market liquidity regime switching when estimating haircuts for stress tests.
  - Compare CET1 impacts from fire‑sale modules with CET1 from solvency stress tests without fire‑sale loops, and link CET1 impacts to macro variables to estimate second‑round effects on the real economy.
  - Supervisors can use granular supervisory data to derive bank‑specific, loss‑minimizing sale strategies.
- Potential extensions:
  - Model pecking order and sequencing of asset sales; incorporate time horizon of sales and price evolution over multiple days.
  - Extend to non‑bank financial institutions (MMFs, insurers, pension funds) and allow for stabilizing demand from such institutions.
  - Incorporate second‑round contagion among financial institutions (network effects) and use reduced‑form results to calibrate general‑equilibrium models.

### Operational tools, appendices, and empirical notes
- Components available:
  - Matlab program for Markov regime‑switching estimation (based on MS_Regress).
  - Excel tool with tabs for Results_Stressed, Charts, Stress parameters (user inputs), Haircuts_regressions, Exposures, Scenario1_VIX/Scenario2_VIX, CAR_data, Total_amount_sold, CAR calculations.
- Key Excel inputs and defaults:
  - Liquidity stress input: percentage of assets sold by bank, by security type and maturity.
  - Implementation shortfall default: 50 percent (user-adjustable 0–100).
  - Option to revalue all bonds (AFS, HFT, HTM, FVPL, FVOCI, FVAC) or a subset.
  - Scenarios can link haircuts to global VIX (US) and country VIX residuals.
- Funding costs and solvency‑liquidity interactions (empirical magnitudes cited):
  - Schmitz and others (2017): a 1 percent decrease in regulatory capital ratios leads to a decrease in funding costs of 1.05 percent; an increase of funding costs by 1 percent reduces CAR by 0.3 percent on average.
  - Aymanns and others (2016): a 1 percentage point decline in CAR leads to a 0.02 percentage‑point increase in average funding costs, and a 0.04 percentage‑point increase for wholesale funding costs.
- Markov regime‑switching used to obtain stressed funding costs (Appendix II example for Japan):
  - ∆FFC_t_USD = β0_k + β1 ∙ ∆LIBOR_t + β2_k ∙ LCS_t + ε_t_k (k = liquidity regime; LCS_t = bid‑ask spread of 3‑month USD/JPY swap).

*Source — wpiea2019250-print-pdf (References, Box 1, Sections 1 and 5, Appendices I–III).*

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

### References

### Tables
- 1. Classification of Liquidity Events .......................................................................................18
- 2. Results of 5 Percent of Asset Fire Sales ..............................................................................30

### Figures
- 1. Fire Sales, Asset Types, and Liquidity Constraints ...............................................................9
- 2. Transmission of Shocks and Solvency-Liquidity Feedback Loop ......................................11
- 3. Transmission of Shocks in Stress and Non-Stress Regimes ................................................12
- 4. Sales Amounts, Haircuts, and the Liquidation Horizon ......................................................15
- 5. Aggregation of Liquidity Needs for Haircut Calculation ....................................................16
- 6. Amihud Measure of Market Liquidity .................................................................................18
- 7. Price Impact Measures of Market Liquidity ........................................................................18
- 8. Volatility Indexes for Selected Countries ............................................................................22
- 9. Sovereign Bond Holdings ....................................................................................................25
- 10. Accounting Classification of Sovereign Bond Holdings ....................................................25
- 11. Haircuts on Selected European Sovereign Bonds ..............................................................28
- 12. Heatmap of Results under Different Models .....................................................................31

### Box
- (Box entry not enumerated in supplied content)

*Source: wpiea2019250-print-pdf - References, wpiea2019250-print-pdf.pdf*

### 1. Contingent Liquidity ................................................................................................

### 1. Contingent Liquidity

### Background: interaction of solvency and liquidity risks
- Solvent financial institutions may be forced to liquidate assets, face losses, and become insolvent; feedback loops between solvency and liquidity risks can amplify capital losses and lead to liquidity problems (Adrian and Shin 2010; BCBS 2015).
- Funding withdrawals can lead to further liquidity shortages and asset liquidation, undermining market liquidity and increasing mark-to-market losses.
- During the Global Financial Crisis (GFC), asset fire sales produced contagion: funding withdrawals forced asset sales at prices below fundamentals; government interventions such as the Troubled Asset Relief Program (TARP) and broadened collateral frameworks for central bank refinancing operations stopped the vicious circle.
- Central bank interventions since the GFC have:
  - shifted funding liquidity sources from market to central banks via broadened collateral frameworks (including full allotment auctions and acceptance of high-quality credit claims as eligible collateral),
  - increased market liquidity of sovereign and corporate bonds through massive asset purchase programs,
  - led secured funding (repos and reverse repos) to dominate wholesale funding markets.
- These trends shifted structural liquidity risks away from funding to market liquidity, raising questions:
  - To what extent would market liquidity of securities be affected if central banks changed their accommodative policy course?
  - To what extent would migration to secured funding increase contingent liquidity risks?
- Aim of the paper: develop a practical tool to calculate dynamic haircuts for assets in a stylized banking system that captures solvency-liquidity feedback loops including changes in market liquidity premia.
  - Uses an empirical approach (Markov regime-switching models for market liquidity) linking haircuts with volumes of securities to be sold (individual and system-wide).
  - Does not require extensive parameter calibrations; uses historical daily trading data to estimate haircuts by type and maturity of security.
  - Links haircuts with liquidity stress tests to estimate system-wide amounts of securities sold and with solvency stress tests to estimate capital effects via mark-to-market losses.
  - Can be tailored to any security with historic daily trading data.
  - Further extension links haircuts with market volatility indexes (such as VIX) as predictors of illiquidity episodes.
- Moral hazard concern: public support expectations may encourage longer-than-optimal maturity transformation, riskier asset investment, and lower/less diversified liquidity buffers.
- Emerging markets: central banks may be unable to buy large amounts of sovereign or corporate bonds due to limited FX reserves or inflation concerns, making market liquidity considerations crucial in stress testing.

### Literature review: market and funding liquidity, regime behavior, and fire sales
- Liquidity risk modeling is central to banks’ Internal Liquidity Adequacy Assessment Process and supervisory assessments; liquidity stress tests assess whether internal resources (liquidity buffers) are sufficient to withstand adverse funding shocks.
- Two broad, reinforcing types of liquidity risks:
  - Funding liquidity risk: the risk a bank cannot cover current/future cash outflows in case of runoff in funding liabilities, contingent obligations, or cash inflow disruptions. Includes contingent liquidity risks such as undrawn loan commitments, repurchase obligations, margin calls, and withdrawal from wholesale short-term financing arrangements.
  - Market liquidity risk: the risk a bank cannot buy or sell a sizeable volume of securities at low cost with limited price impact (IMF 2015). Market liquidity has dimensions of time, cost, and quantity; resilience (sudden dry-up) is a significant component.
- Market liquidity tends to exhibit regime-switching behavior: a high-liquidity regime and a low-liquidity regime where liquidity can evaporate rapidly (Acharya and others 2013; IMF 2015; Flood and others 2015).
- Liquidity spirals:
  - Margin spiral: margin calls and higher haircuts force position reductions, triggering price drops and lower market liquidity (Brunnermeier and Pedersen 2009).
  - Loss spiral: market illiquidity leads to losses, tightening funding constraints and forcing further sales (Brunnermeier and Pedersen 2009).
  - Market illiquidity often associates with higher funding costs, pressuring solvency (example: FX swap costs increased when FX swap market liquidity dried up in late 2007).
- Fire-sale theory and evidence:
  - Pulvino (1998) finds capital-constrained sellers receive lower prices.
  - Schleifer and Vishny (2010) overview fire-sales theory and policy interventions.
  - Fire sales depend on information asymmetry, funding and capital constraints of buyers and sellers; marketable assets may remain liquid if sufficient buyers without constraints exist.
  - Figure conceptualization: fire sale likelihood depends on whether buyers and/or sellers face liquidity/capital constraints and whether assets are marketable or non-marketable.
- Existing models and gaps:
  - Some stress-testing models consider rollover risk, funding costs, or losses on marketable securities feeding into solvency stress tests (Anand and others 2014; Bank of Korea; ECB; Oesterreichische Nationalbank).
  - Many frameworks assume constant haircut ratios and do not endogenously link haircuts with amounts sold or with market liquidity regime.
  - Modeling stressed market liquidity premium (MLP) provides a practical integration of solvency and liquidity risks; MLP measures interaction between market liquidity conditions and the impact of asset sales on prices.
  - Markov regime-switching models have been used to characterize regime behavior of market liquidity (Acharya and others 2013; IMF 2015; Flood and others 2015).
  - Complex models (e.g., Baranova and others 2017b; Aikman and others 2009) require multiple parameter calibrations that can be difficult given data limitations.

### The framework: overview and transmission loop
- Core element: methodology to estimate impact of asset liquidation on asset prices (haircut ratios) in stress scenarios.
  - Question addressed: how much below current market prices would assets be valued during systemic liquidity events?
  - In Markov regime-switching models, market liquidity can switch from high-liquidity to low-liquidity regime during systemic events, increasing market liquidity premia and reducing asset prices.
- Framework summarized as a solvency-liquidity feedback loop (three-step transmission):
  - Funding liquidity shocks (for example, unforeseen wholesale or retail funding withdrawals) lead to a shortage of liquid assets in a group of banks.
  - Asset liquidation by one or multiple banks causes market liquidity problems and price impacts.
  - Market liquidity problems produce mark-to-market losses on fair value securities, worsening solvency and potentially causing further funding withdrawals.
- Regime dependence:
  - In systemic stress regime (multiple institutions affected), haircuts are driven by stressed (low-liquidity) regime.
  - In non-stress regime (one or few institutions affected), price impacts are driven by non-stress regime haircuts.
  - Market volatility indexes are used as an indicator for regime switching.
- Definition of a fire sale in the framework:
  - A forced sale due to liquidity problems.
  - Transaction price substantially below fundamental (intrinsic) value, creating an arbitrage opportunity for the buyer.
  - Fire sales depend on both demand and supply; buyers receive both risk premium and higher illiquidity premium.
- Modeling steps described in the framework:
  - Estimate haircuts as a function of the amount to be sold and market liquidity regime.
  - Link haircuts with liquidity stress tests to compute system-wide security sales.
  - Link resulting price impacts to solvency tests to determine capital effects from mark-to-market losses.

### Funding liquidity: shocks, liquidity needs, and aggregation of asset liquidation
- Funding liquidity risk has many forms and has evolved over time: from deposit outflows to undrawn loan commitments, repurchase obligations, margin calls due to CCP adoption, and wholesale short-term loans.
- Liquidity stress tests typically assess whether counterbalancing capacity (CBC)—bank assets available for liquidation to offset negative funding gaps—and expected cash inflows are adequate to cover expected cash outflows over a defined stress horizon; the gap between these is a funding gap and informs potential asset liquidation volumes and possible ELA needs.
- Simple cash flow-based liquidity stress tests often assume constant haircut ratios for liquidation of CBC; the proposed framework endogenizes haircuts via market liquidity regimes and amount sold.

*Source: wpiea2019250-print-pdf*

### Box 1. Contingent Liquidity

### Box 1. Contingent Liquidity

### Nature and drivers of contingent liquidity risks
- Contingent liquidity risks arise from contractual financial instruments contingent on market events: (1) repos (securities financing transactions [SFT]); (2) derivatives; and (3) rehypothecation.
- These instruments require exchange of initial and variation margins, which can cause fire sales if a counterparty is short of high-quality collateral (cash and/or government bonds).
- Haircuts to derivatives and securities lending transactions may be determined endogenously and lead to negative feedback loops (Geanakoplos (2010)).
- The importance of contingent liquidity risks grew with migration of OTC SFTs and derivatives into centralized clearinghouses and with bilateral contract margining requirements.
- Collateral posted and received is typically highly liquid assets (cash or sovereign bonds), though sometimes less liquid assets (such as equities) are posted.

### Netting, CCPs, and the role of asset encumbrance
- The net effect of posted versus received collateral is critical: a bank with balanced trading positions would both post and receive collateral, allowing netting of liquidity needs—especially when contracts are cleared via CCPs (see Figure 2).
- If a bank must post more collateral than it receives, its asset encumbrance (AE) ratio increases, which:
  - Dries out core banking credit (CBC).
  - May lead to idiosyncratic shocks such as inability to rollover unsecured wholesale funding.
- Repricing all repos and reverse repos across maturity horizons can provide a rough approximation of additional liquidity needs in absence of very granular data.

### Stress testing contingent liquidity and funding shocks
- Estimating impact from funding liquidity shocks under stress requires data on:
  - Asset structure.
  - Contractual and behavioral cash flows of a bank and the banking system.
  - These data are typically obtained from supervisory returns.
- Sequence of funding liquidity analysis:
  1. Identification of reasons for asset liquidation.
  2. Liquidity gap (based on maturity gap analysis using contractual and behavioral cash flows) for each bank.
  3. Liquidity risk management and optimization strategy of each bank in the system.
- Under negative funding liquidity shocks, a bank unable to roll over short-term (or maturing) funding may be forced to liquidate assets to cover shortfalls. The analysis focuses on this reason (8).
- Liquidity gaps are calculated using contractual and stressed cash flows over respective time buckets. Under extreme stress, behavioral cash flows would approach contractual ones (important for wholesale funding).
- A liquidity gap in each time horizon is closed using available liquidity buffers or assets included in the CBC.
- Banks’ optimization strategies vary; to minimize asset revaluation risk, a bank may spread sales over longer time horizons depending on contractual and behavioral liquidity gaps (for example, when withdrawals may happen) (9). This minimizes market-price impact (see Casey and others (2017), Figure 4).

### Reasons for asset liquidation (from the source)
- Three potential reasons for asset liquidation (8):
  - Profitability risk: liquidation of “unprofitable” assets (for example, low-yielding assets funded via short-term wholesale funding), leading to shift in asset composition and potential systemic effects if many banks follow the same strategy.
  - Regulatory constraints: forced reductions in risk-weighted assets or increases in holdings of high-quality liquid assets due to capital or liquidity regulations, changing balance sheet composition.
  - Funding liquidity risk itself.

### Behavioral options to avoid fire sales and limits of secured funding
- Behavioral options in liquidity shocks:
  - Use secured funding transactions (repos, collateral swaps), including transactions with central banks (drawing on lending facilities), to pledge securities for cash.
  - Such transactions can be used up to the full amount of assets available for encumbrance minus haircuts10; thus asset fire sales are generally a last resort.
- Limitations and amplification risks:
  - Repos are subject to margin calls and can elevate liquidity risks during stress.
  - Funding liquidity can vanish suddenly if a financial institution faces reputational or legal issues, prompting counterparties to refuse to enter or extend repos (example: Lehman Brothers; triparty repo counterparties reluctant to extend repos despite collateral) (see Copeland and others 2014).

*Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019250-print-pdf.pdf*

### Box 1 illustrates how contingent liquidity risks arise and are linked with AE.

### Box 1: How contingent liquidity risks arise and are linked with AE

### Contingent liquidity risk mechanism and asset liquidation
- Stress tester should consider banks’ ability to obtain liquidity using repos with central banks as a substitute for market-based repo or outright asset sales; the model in the paper considers only outright sales (asset liquidation).
- The pecking order of liquidation matters in theory, but in reality banks may have limited options because of fire-sale externalities:
  - In a prolonged systemic crisis with many banks facing liquidity shortages, banks may hoard liquidity and attempt to liquidate less liquid assets first, but may end up only able to sell liquid assets due to larger haircuts on less liquid assets and lack of demand.
  - In an idiosyncratic shock to a single bank, the bank may be able to liquidate less liquid assets, but doing so may signal liquidity problems and stimulate further outflows; hence the bank may be unwilling to liquidate illiquid assets first.
  - Banks have incomplete information about other banks’ securities and funding shortages; strategic considerations can lead banks either to sell liquid securities first (risking price changes) or to sell less liquid securities first to minimize market price impact before being affected by others’ fire sales.
- Identification of systemic vs idiosyncratic events matters for the size of haircuts:
  - In systemic liquidity events (multiple banks facing shortages), haircuts would be larger because they depend on how much aggregate assets may be liquidated by type and currency, given higher outflows require institutions to balance with inflows from asset liquidation.
  - The stress tester could check whether changes in dealer intermediation have affected private sector capacity to absorb liquidation (for example, by examining balance sheets of pension and insurance companies), though data limitations often make such demand-side analysis difficult.

### Market liquidity and regime-switching behavior
- The model considers only marketable assets/securities for haircut estimation because non-marketable assets typically lack a market to trade and are difficult to measure for market liquidity.
- Aggregate market liquidity of an asset class is defined as a measure of market liquidity averaged across all securities in the asset class and is assumed to have regime-switching behavior (for example, a high-liquidity regime and a low-liquidity regime).
- The regime switch can be triggered by asset fire sales by some banks covering negative funding gaps, leading to valuation losses through implementation shortfall and repricing of marked-to-market assets; this affects both selling banks and other banks holding these assets.
- Assumption used in the paper: market liquidity would switch to a stress (low-liquidity) regime under asset fire sales in systemic events, implying a higher price impact, but would remain in the nonstress (high-liquidity) regime under asset fire sales in idiosyncratic events. This is a simplifying assumption (see Table 1).

### Classification of liquidity events (Table 1)
- Stress regime — Systemic: Occurs when multiple financial institutions face liquidity shortfalls and when market liquidity shock is due to investors’ loss aversion and/or increase in volatility.
- Non-stress regime — Systemic: Occurs when multiple financial institutions face liquidity shortfalls, but market fundamentals are sound (i.e., no change in volatility and/or levels of risk tolerance).
- Stress regime — Idiosyncratic: Occurs when one or a few small banks or other financial institutions face liquidity shortfalls and when market liquidity shock is due to investors’ loss aversion and/or increase in volatility.
- Non-stress regime — Idiosyncratic: Occurs when one or a few small banks or other financial institutions face liquidity shortfalls but market liquidity conditions are not affected.

### Security-level and aggregate market liquidity measures
- Two widely used security-level price-impact measures:
  - Amihud (2002) measure: defined as the ratio between the absolute value of daily returns and daily trading volume of a frequently traded security.
  - Price impact measure: defined as the slope coefficient of a regression of price change on signed order flow (buyer-initiated trades minus seller-initiated trades); this assigns “signs” to trades and is suitable for modeling haircuts because most fire sales are seller-initiated.
- Aggregate market liquidity measures tend to be correlated across asset classes and countries; some asset classes may share the same stress/nonstress regimes and exhibit flight-to-quality effects.
- The paper estimates “common” regimes in addition to individual asset-class regimes when certain asset classes share the same stress or nonstress regimes.

### Estimation steps for regime-switching model (aggregate market liquidity)
- Step 1: Identify marketable asset classes and securities that banks hold as CBC and calculate the price impact measure at the security level using transaction data (the price impact measure is calculated daily in this paper).
- Step 2: Average the security-level price impact measures for all securities in the same asset class to obtain an aggregate price impact measure for each asset class.
- Step 3: For each asset class j, estimate the baseline Markov regime-switching model:
  - PPPP_t_j = beta_0_j,s + epsilon_t_j,s
  - Two regimes assumed: non-stress (high-liquidity) and stress (low-liquidity); beta_0_j,s varies across regimes and epsilon_t_j,s has mean zero and variance sigma_s^2; the variance is also assumed to vary across regimes (the paper also considers the case where the variance is the same across regimes).

### Calculating price impact and haircuts given fire-sale amounts
- The total amount of securities in asset class j liquidated by all banks, VVVV_aaaaaa_j, is VVVV_aaaaaa_j ≡ sum_i VVVV_ii_j for i = 1 to P, where P is the total number of banks in the system.
- The price impact for asset class j in regime s is computed as beta_0_j,s ∙ VVVV_aaaaaa_j, subject to a scenario-conditional floor between the price impact of fire sales and the total amount of fire sales.
  - For idiosyncratic events (nonstress regime): price impact = beta_0_j,nonstress ∙ VVVV_aaaaaa_j,nonstress
  - For systemic events (stress regime): price impact = beta_0_j,stress ∗ VVVV_aaaaaa_j,stress
- Notes and simplifying assumptions:
  - The model assumes a linear relationship between price impact measure and total amount of fire sales with a conditional floor; this prevents unrealistic or negative post-trade prices.
  - The actual price impact could be nonlinear; linearity is a simplifying assumption used when trade sizes are not “too” large.
  - The total amount of fire sales is obtained from the liquidity stress test; a pecking order and time horizon of sales must be assumed to determine how much securities in each asset class will be sold.
  - Aggregation from security-level to asset-class level simplifies the calculation; security-level analysis is possible with more granular CBC data.

### Incorporating market uncertainty and volatility indexes
- The model is extended to include a measure of market uncertainty, such as the Chicago Board Options Exchange (CBOE) VIX index for the United States.
- Country-specific volatility indexes are decomposed into a common term explained by the US VIX and a residual term orthogonal to the US VIX via the regression:
  - V_t_c = alpha_0 + alpha_1 ∙ VIX_t_US + epsilon_t_c
  - This allows designing scenarios by changing the residual epsilon_t_c^� given a scenario for the US VIX.
- The Markov regime-switching model with volatility terms for asset class j is:
  - PPPP_t_j = beta_0_j,s + beta_1_j,s ∙ VIX_t_US + beta_2_j,s ∙ epsilon_t^� + epsilon_t_j,s
  - The effects of the US VIX and the residual term vary across nonstress and stress regimes.
- Practical considerations:
  - Lagged VIX and residuals could mitigate endogeneity; results in the case study do not change when lagged variables are used, likely due to high autocorrelation of VIX.
  - The model does not let regime-switching probabilities depend on VIX variables to avoid computational burden and estimation instability.

### Model specification choices and implications
- Model estimates depend on:
  - Whether regimes are different or common across asset classes;
  - Whether the variance of the error term is regime-switching or not;
  - Whether the model includes a volatility index or not.
- Based on different combinations, the paper computes haircuts of fire sales using five specifications, each with two regimes (non-stress and stress).

*Source: wpiea2019250-print-pdf - Box 1 illustrates how contingent liquidity risks arise and are linked with AE.*

### 1. Asset class-specific regimes and regime-switching variances without a volatility

### 1. Asset class-specific regimes and regime-switching variances without a volatility index (as in equation 1);

### Model specifications and estimation tools
- Five main specifications considered in the analysis:
  1. Asset class-specific regimes and regime-switching variances without a volatility index (as in equation 1);
  2. Asset class-specific regimes and non-regime-switching variances without a volatility index (as in equation 1);
  3. Common regimes and regime-switching variances without a volatility index (as in equation 1);
  4. Asset class-specific regimes and regime-switching variances with a volatility index (as in equation 6);
  5. Asset class-specific regimes and non-regime-switching variances with a volatility index (as in equation 6).
- Specification 1 is the baseline to estimate asset class-specific regimes; other asset class-specific specifications are used mainly for robustness checks.
- Equation (6) with common regimes is not considered a separate specification in this paper due to the significantly increased computational burden after including the volatility variables in the Markov regime-switching model.
- Software tools:
  - A Matlab program is used to estimate the Markov regime-switching models presented.
  - An Excel-based tool is used to estimate haircuts based on the total amount of assets sold by all banks in the system.
- Volatility indices referenced (by country):
  - 1/CAC 40 volatility index for France
  - VDAX-New index for Germany
  - call-implied volatility index PSI 20 for Italy
  - AEX volatility index for Netherlands
  - IBEX 35 volatility index for Spain
  - FTSE 100 volatility index for United Kingdom
  - CBOE market volatility index for United States

### Solvency: asset valuation, fire-sale losses, and feedback loops
- Conceptual feedback loop:
  - Liquidity shocks → liquidation of assets → accounting losses → lower capital → higher funding costs → further deterioration of funding liquidity.
  - Changes in capital adequacy and leverage ratios typically lead to further changes in funding costs (a lower capital adequacy ratio (CAR) leads to higher funding costs and vice versa) and more severe funding liquidity problems.
  - The loop is iterated until the change in the CAR becomes very small.
- Two types of losses from fire sales:
  - Implementation shortfall: difference between the market price at time of sale and the volume-weighted average price (VWAP) during liquidation. Empirical examples use 1/2, corresponding to a VWAP midway between pre- and post-fire-sales prices (following Cont and Schaanning (2017)).
  - Marked-to-market losses.
- Bank i’s losses in regime s (nonstress or stress) are written as equation (7):
  - L_VS_s_i = sum_{j=1}^{J} [ 1/2 * β_{j,s} * VAA_j * VHV_{i,j} + (β_{j,s} * VAA_j) * SSV_cS_{i,j} ]
  - Where J denotes the total number of asset classes, β_{j,s} is the price impact of asset class j in regime s, and SSV_cS_{i,j} is bank i’s total holdings of securities that belong to asset class j.
  - In model (1), β_{j,s} is a regime-switching constant; in model (6), β_{j,s} is a regime-switching function of VIX variables.
- Applicability and extensions:
  - Framework applied to banks but can be extended to estimate price impacts and haircuts from asset sales of multiple participants, including asset managers (mutual funds) and insurance and pension fund companies.
  - Can be incorporated into FSAPs as it is based on standard stress-testing tools, data, and software.

### Example application: euro area banks — data
- Sample and data sources:
  - Potential fire-sale losses estimated for the 29 largest euro area banks using data from the 2016 European Banking Agency (EBA) transparency exercise.
  - Data contained banks’ sovereign exposures by country and remaining maturity; also used regulatory capital and risk-weighted assets (RWA).
  - Transaction-level prices and trading volumes for European sovereign bonds obtained from the MTS Markets dataset used in IMF (2015), covering May 2005 to April 2015.
- Grouping and classification:
  - Banks grouped by business model into three categories: G-SIBs (as in Financial Stability Board’s list), internationally active banks, and banks with purely domestic focus.
  - Bond-level price impact measure calculated daily and aggregated into 20 asset classes by residual maturity and issuer country: sovereign bonds issued by France, Germany, Italy, Netherlands, and Spain, with residual maturity buckets of one to three years, four to six years, seven to 11 years, and 11+ years.
  - For the exercise, remaining maturities grouped into four buckets: zero to three years, four to six years, seven to 11 years, and 11+ years.
- Concentration and accounting classification:
  - Most banks’ sample sovereign bond exposures concentrated into six countries: France, Germany, Italy, Netherlands, Spain, and United States (67 percent).
  - Majority of exposures designated as traded assets and subject to marked-to-market repricing.
  - Data used are from 2016, reflecting AFS and HFT classification; note on IFRS9 (effective January 2018) eliminating AFS and HFT classification but majority of debt securities still fall under market price valuation (Fair Value).
- Caveats:
  - Sales of sovereign bonds could affect prices of other securities, but paper focuses on sovereign bonds due to lack of public data on holdings of other securities.
  - More granular analysis (e.g., by ISIN or CUSIP) would require identifiers in banks’ balance-sheet data.

### Example application: euro area banks — simulations
- Simulation specifications (denoted for country/maturity-specific regime):
  1. Country/maturity-specific regimes and regime-switching variances without a volatility index (as in equation 1);
  2. Country/maturity-specific regimes and non-regime-switching variances without a volatility index (as in equation 1);
  3. Common regimes across all countries in the same maturity bucket and regime-switching variances without a volatility index (as in equation 1);
  4. Country/maturity-specific regimes and regime-switching variances with a volatility index (as in equation 6);
  5. (Implicitly) country/maturity-specific regimes and non-regime-switching variances with a volatility index (as listed earlier in the model specifications).
- Sovereign bond holdings (selected percentages from exposure figures):
  - Sovereign Bond Holdings by Large Euro Area Banks (In percent of total sovereign bond holdings): Italy 15%, Spain 15%, Germany 11%, France 13%, Netherlands 5%, US 8%, Other 33%.
  - Sovereign Bond Holdings by Large Euro Area Banks: AFS + HFT (In percent of total sovereign exposures under AFS and HFT 1/): Italy 16%, Spain 16%, Germany 12%, France 12%, Netherlands 5%, US 9%, Other 30%.

*Source: IMF staff analysis from the referenced chapter content*

### 5. Country/maturity-specific regimes and non-regime-switching variances with volatility

### 5. Country/maturity-specific regimes and non-regime-switching variances with volatility

### Assumptions and stress-test setup
- Time of liquidation is one day; all banks sell the same share of their sovereign bond holdings in one day.
- All banks need to sell 5 percent of their sovereign bond holdings of the largest five sovereign exposures in their CBC to offset negative funding gaps from the liquidity stress test.
- No pecking order in fire sales is assumed.
- Implementation shortfall is assumed to be 50 percent (following Cont and Schaanning (2017)).
- For specifications with volatility variables:
  - US VIX is assumed to increase to 23.9 percent (as in the recent US Fed scenario for stress testing).
  - Respective market volatility indexes for the five countries are assumed to increase by two standard deviations from their values observed at the end of Q1 2018.
- The accompanying Excel file (see Appendix III description) allows entry of granular assumptions about sales of each security (by type and maturity) for each bank.
- Precise optimal sales strategy estimation is beyond the scope of the paper; supervisory data could be used by central banks or supervisors to derive loss-minimizing strategies given granular holdings and daily liquidity shortages.

### Haircut estimation method and key properties
- Haircuts are calculated based on fire sales of 5 percent of bond holdings.
- The Markov regime-switching models (models (1) and (6) with regime-switching variances) are used; they are estimated with Matlab (see Appendix IV for Matlab program description).
- Haircuts are based on the total amount sold and thus reflect differences in:
  - The estimated price impact.
  - Holdings of different types of sovereign assets (volume effect).
- Regime behavior:
  - Price impact (market liquidity) exhibits significant binary or regime-switching behavior.
  - The model allows haircuts to change with the total amount of assets (in each asset class) sold by all banks at the same time, instead of assuming constant haircuts.
  - Market volatilities (global and country-specific) are included as additional regime-switching variables to simulate stress-regime and non-stress-regime haircuts under different volatility scenarios.
- Empirical regularities observed:
  - Haircuts on Italian and Spanish sovereign bonds are typically higher than those on Dutch, French, and German sovereign bonds, particularly in stress regimes—mainly due to higher estimated price impact even after controlling for higher variances during stress in specification 1.
  - Volume effects can make haircuts on “safe” bonds (e.g., German bonds) higher if banks hold and thus sell larger absolute amounts of those bonds, given the assumption of equal percentage sales (5 percent).
  - Specification 3 (common regimes) suggests “flight to quality” effects:
    - Italian and Spanish haircuts in the stress regime are generally higher than in the non-stress regime (except zero- to three-year Italian bonds).
    - Dutch, French, and German bond haircuts in the stress regime are generally lower than in the non-stress regime.
- Statistical significance and model comparisons:
  - Estimated haircuts are statistically significantly different between stress regimes and non-stress regimes in most specifications.
  - In all specifications with country/maturity-specific regimes, haircuts in stress regimes tend to be statistically significantly higher than in non-stress regimes.
  - Specifications with non-regime-switching variances (specifications 2 and 5) typically produce much higher haircuts than specifications with regime-switching variances (specifications 1 and 4), mainly due to higher volatilities in stress regimes.
  - Regression statistics suggest specifications with regime-switching variances tend to have better goodness of fit than those with non-regime-switching variances; specifications 1 and 4 are generally preferable to specifications 2 and 5.
- Example of statistical distinction:
  - The estimated 95-percent confidence interval for the haircut ratio of German sovereign bonds with residual maturity of four to six years in specification 2 is [0.2%, 0.3%] for the non-stress regime and [1.7%, 2.0%] for the stress regime.

### Impact on banks’ capital (CET1 / CAR)
- Loss realization and valuation treatment:
  - Losses on sales are assumed realized immediately (with a 50 percent implementation shortfall).
  - Fair value of remaining (unsold) assets classified as Available for Sale and Held for Trading are affected by the full amount of haircut.
  - Risk-weighted assets (RWAs) are not reduced because sovereign bonds in the exercise are treated as zero-risk weighted exposures (following Capital Requirement Regulation (CRR) under European law).
- Impact calculation (definition):
  - CET1 CAR after shock for bank i and specification M:
    - CET1_CAR_i_shocked;M = CET1_CAR_i_initial − L_losses_i_M / RWA_i
    - Where CET1 is Core Equity Tier I capital for bank i; L_losses_i_M denotes losses for bank i and specification M as in equation (7).
- Results for assumed 5 percent sale (Table 2 median CET1 ratios before and after asset liquidation):
  - CET1 CAR before asset liquidation (median by bank type):
    - G-SIB: 12.72
    - Internationally active: 14.29
    - Domestic focus: 14.29
  - CET1 CAR after asset liquidation:
    - specification 1, stressed: 12.29 (G-SIB), 13.99 (Internationally active), 13.57 (Domestic focus)
    - specification 1, non-stressed: 12.69, 14.26, 14.24
    - specification 2, stressed: 10.93, 13.23, 11.50
    - specification 2, non-stressed: 12.57, 14.20, 14.06
    - specification 3, stressed: 12.60, 14.18, 14.02
    - specification 3, non-stressed: 12.59, 14.22, 14.11
    - specification 4, stressed: 12.22, 13.97, 13.58
    - specification 4, non-stressed: 12.70, 14.28, 14.29
    - specification 5, stressed: 11.35, 13.31, 12.20
    - specification 5, non-stressed: 12.49, 14.15, 13.96
- Key quantitative findings:
  - The impact of direct (asset liquidation) and indirect (asset valuation) losses is more severe during periods of financial turbulence.
  - The largest stressed/non-stressed difference is observed in specification 2: a 152-bp difference between the impact on banks’ CET1 ratio in the stress regime and in the non-stress regime (weighted average of banks in the sample), with the stress regime being more severe.
    - The 95-percent confidence interval for this impact difference is between 141 bps and 162 bps.
  - Higher market volatility leads to higher haircuts and subsequent losses.
- Heterogeneity by bank business model and diversification:
  - Banks with higher shares of their own sovereign bonds suffer higher losses compared to banks with diversified liquid asset holdings.
  - Domestic-focused banks show the largest stressed/non-stressed differences due to higher domestic sovereign bond shares and lower asset diversification.
  - Large international banks and G-SIBs have more diversified liquid asset portfolios and show lower fire-sale impact on CET1, including smaller stressed vs. non-stressed differences.
- Use of heatmap to illustrate stress-parameter uncertainty:
  - A heatmap (Figure 12) summarizes results across the five specifications and shows sensitivity to model choice and volatility assumptions.
  - Guidance: if a stress-testing scenario includes shocks to market volatility, a system-wide liquidity squeeze, and changes in central bank collateral frameworks, stressed haircuts are more appropriate than non-stressed haircuts.

### Conclusions, policy implications, and potential extensions
- Conclusions:
  - Fire sales in stress periods can lead to statistically significantly higher price impacts than in non-stress periods.
  - Haircuts are highly non-linear and much higher during stress periods than during non-stress periods.
  - Estimated stress-regime haircuts are more suitable for systemic events; non-stress haircuts are more appropriate for idiosyncratic events.
  - Using stress-regime haircuts can significantly reduce banks’ capital ratios compared to using non-stress haircuts; the magnitude depends on the total amount of assets fire-sold by all banks and on market volatility scenarios.
  - The fire-sales channel is an important component in stress tests and can lead to additional depletion of banks’ capital buffers.
- Policy implications:
  - Stress testers should account for different market liquidity regimes and consider regime-switching behavior when estimating haircuts for stress tests.
  - Stress testers can compare CET1 impacts from fire-sales models with CET1 numbers from solvency stress tests without fire-sales loops, and link CET1 impacts to macro variables (e.g., credit growth, interest rates) to estimate potential second-round effects on the real economy.
  - Supervisors may use granular supervisory data to derive bank-specific, loss-minimizing sales strategies in practice.
- Potential extensions and future work:
  - Model the pecking order and sequencing of asset fire sales (which assets are sold first under systemic vs. idiosyncratic stresses).
  - Incorporate the time horizon of fire sales and how prices evolve when large amounts are liquidated over different time horizons.
  - Extend the model to simulate haircuts for fire sales triggered by non-bank financial institutions (money market mutual funds, insurance companies, pension funds) and allow for stabilizing demand by such institutions.
  - Incorporate second-round contagion effects among financial institutions, including price effects and network effects across bilateral exposures; ignoring interbank feedback may lead to underestimation of losses.
  - Use the reduced-form model to calibrate general-equilibrium models that include the number of market participants, liquidity constraints, and cross-exposures.
- Operational note:
  - The model could be incorporated into FSAP-style macroprudential stress tests as a module estimating haircuts from marketable asset fire sales and could also be used to model funding costs in stressful situations.

*Source: IMF staff estimates and authors’ calculations from “5. Country/maturity-specific regimes and non-regime-switching variances with volatility” (wpiea2019250-print-pdf).*

### REFERENCES

### wpiea2019250-print-pdf - REFERENCES (Selected appendices and methodological notes)

### Market liquidity measures (Appendix I)
- Amihud (2002) measure:
  - Defined as the ratio between the absolute value of daily returns and daily trading volume of a frequently traded security.
  - Interpreted as the daily price change associated with one dollar of trading.
  - Typically used for frequently traded securities whose trading volumes are net zero (for example, stocks).
- Market depth:
  - Captures the quantity dimension of market liquidity—ease of trading large amounts.
- Security-level price impact measure:
  - Defined as the slope coefficient of a regression of price change on a signed order flow (buyer-initiated trades minus seller-initiated trades).
  - Measures the average price impact of a one-unit (net) trading volume; represents the marginal cost of trading an additional unit of quantity.
  - Assigns “signs” to trades, making it suitable for modeling haircuts for asset fire sales (most asset fire sales are seller-initiated).
  - Can be calculated for less frequently traded securities (for example, bonds).
  - Requires transaction-level data.

### Funding costs, solvency-liquidity interactions, and nonlinearity (Appendix II)
- Key interactions and mechanisms:
  - Declines in CAR (capital adequacy ratio) may increase banks’ funding costs.
  - Funding liquidity shocks from tightened funding conditions can cause funding shortages in cash flow–based liquidity stress tests.
  - Tightening funding conditions can shrink funding volumes and increase funding costs; banks with high asset encumbrance typically have lower secured wholesale funding costs and higher unsecured funding costs.
  - Banks with solvency concerns can experience larger declines in available funding volume and higher increases in funding costs (closure of unsecured funding markets, higher withdrawals of wholesale deposits, additional margin calls for repos and derivatives).
  - Solvency and liquidity shocks interact and amplify each other’s effects; integrated frameworks are important.
- Empirical magnitudes reported:
  - Schmitz and others (2017): a 1 percent decrease in regulatory capital ratios leads to a decrease in funding costs of 1.05 percent. Higher funding costs reduce the capital ratio: an increase of funding costs by 1 percent reduces CAR by 0.3 percent on average.
  - Aymanns and others (2016): a 1 percentage point decline in CAR leads to a 0.02 percentage-point increase in average funding costs, and a 0.04 percentage-point increase for wholesale funding costs.
- Practical modeling choices:
  - Funding costs can be modeled across dimensions: domestic vs. foreign currency, by tenure, and by instrument type. If unavailable, use total funding costs as ratio of interest expenses over interest rate-sensitive liabilities.

### Use of Markov regime-switching models to obtain stressed funding costs (Appendix II)
- Rationale:
  - Funding costs exhibit non-linearity under stress; Markov regime-switching regressions are an alternative to linear regressions used to derive stressed funding costs.
  - Implemented by IMF staff for liquidity-solvency stress tests in the 2017 Japan FSAP.
- Application to large Japanese banks:
  - Large Japanese banks rely heavily on wholesale sources for foreign currency funding (Aldasoro and others 2018).
  - The amount of banks’ funding in US dollars accounts for less than 25 percent of their total funding in all currencies system wide.
  - Most US dollar funding (versus yen funding) comes from unsecured corporate funding, repos, and FX swaps; many FX swaps are rolled over and repriced every three to six months.
  - Short repricing windows allow linking liquidity pressures to new prices of funds in both USD and JPY during market stress and to the evolution of banks’ CAR.
- Liquidity risk premium and observed episodes:
  - Analysis indicates deterioration in USD/JPY swap market liquidity in 2016 increased the liquidity risk premium and pushed up US dollar funding cost, despite some recovery in 2017.
  - “Liquidity risk premium” is defined as the impact of market liquidity on US dollar funding cost.
- Modeling structure and drivers:
  - The Markov regime-switching model captures two main drivers of market-wide US dollar funding cost: changes in the three-month LIBOR in USD (from macro scenarios) and liquidity stress in the USD/JPY swap market (bid-ask spread of the three-month USD/JPY swap).
  - Assumptions for scenario mapping:
    - Baseline and moderate adverse scenarios: no deterioration in market liquidity in USD/JPY swap market; the main driver of USD funding cost projection is three-month LIBOR in USD.
    - Severe adverse scenario: liquidity risk premium in USD/JPY swap market switches from tranquil to stress regime due to more rapid tightening in US monetary policy, significantly pressuring USD funding cost.
- Specified Markov regime-switching model (as presented):
  - ∆FFC_t_USD = β0_k + β1 ∙ ∆LIBOR_t + β2_k ∙ LCS_t + ε_t_k
    - where t denotes time and k indicates the liquidity regime.
    - ∆LIBOR_t is the change in the 3-month LIBOR in USD.
    - LCS_t is the bid-ask spread of the three-month USD/JPY swap contract (market liquidity measure) and is the only regime-switching variable in the model, except the constant β0_k which also varies across regimes.
  - Notes:
    - Three-month LIBOR in USD is used because most FX swap contracts used by banks are rolled over and repriced every three to six months.
    - USD funding cost is calculated from the three-month USD/JPY swap cost.
  - The use of Markov regime-switching to identify liquidity risk premium regimes follows Acharya and others (2013), IMF (2015), and Flood and others (2015).

### Program and templates for haircut and CAR estimation (Appendix III)
- Components of the proposed framework:
  1. Matlab-based program for haircut estimation using trading data.
  2. Excel tool for market haircut calculation based on aggregate amounts sold and CAR estimation.
- I. MATLAB program:
  - Matlab programs estimate the Markov regime-switching models (1) and (6) with regime-switching variances.
  - Programs are built upon the MS_Regress Matlab package developed by Perlin (2014).
  - Alternative specifications with non-regime-switching variances can be estimated using Stata’s built-in Markov regime-switching package.
- II. Excel tool (tabs and functionalities):
  - Results_Stressed tab:
    - Summary of stress testing results (CAR before and after liquidity shock and difference vis-à-vis no shock) as a heatmap (bank-by-bank) and by each type of model (version handles haircuts for up to 12 models; expandable).
    - Summary of haircuts on assets based on the amount of securities banks sell collectively (percentages from 100 million value of securities sold).
  - Charts tab:
    - Produces Box-Whisker charts for banks’ CAR.
  - Stress parameters tab (user inputs scenario parameters), sub-categories:
    - Liquidity stress input: percentage of assets sold by each bank, by security type, and residual maturity of securities (expandable with appropriate holdings and daily trading data).
    - Assumptions about revaluation of bonds: if “Yes”, all bonds (AFS, HFT, HTM, FVPL, FVOCI, FVAC) are repriced using new haircuts; if “No”, only AFS, HFT, FVPL, FVOCI are repriced.
    - Assumptions about implementation shortfall parameter: default value is 50 percent; tester can choose any value between 0 and 100.
    - Scenarios: linking haircuts with market volatility. Option to generate stressed haircuts conditional on market volatility. Current version takes into account only one stressed period. Two types of volatility data may be entered: global VIX (US) and country VIX (as residuals of the VIX equation linking each country VIX with US VIX).
  - Haircuts_regressions tab:
    - Input tab for haircuts estimated using various econometric models (up to 12 different models).
  - Exposures tab:
    - User enters data about banks’ exposures to securities.
  - Scenario1_VIX and Scenario2_VIX tabs:
    - Calculate haircuts based on VIX scenarios (no user input needed).
  - CAR_data tabs (before shocks and 1-12):
    - Calculate CAR data used for Box-Whisker charts (no user input needed).
  - Total_amount_sold tab:
    - Calculates amount of securities sold by all banks and amount left on balance sheet (used to reprice remaining securities under stressed haircuts).
  - CAR tab:
    - Calculates CAR before shocks and for each model; stress tester enters total assets, liabilities, capital, and RWAs for each bank.

*Italic: Source — wpiea2019250-print-pdf (REFERENCES and Appendices I–III).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019250-print-pdf.pdf_