## From Par to Pressure: Liquidity, Redemptions, and Fire Sales with a Systemic Stablecoin

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### 1. Introduction — Overview, risks, and empirical signals
- Stablecoins (SCs) considered: fiat-backed SCs backed by financial assets closely tied to fiat currency; unbacked and algorithmic designs described as “inherently unviable.”
- Usage trends and systemic footprint:
  - SCs increasingly used for cross-border payment flows, not just crypto trading.
  - Market shares (mid-2025): the two largest SCs are 64 and 22 percent.
  - Largest stablecoin issuers’ holding share in U.S. treasury bills is 1.7 percent by mid-2025.
  - Nearly 70 percent of countries are developing regulatory frameworks for SCs.
- Key systemic-risk channels and implications:
  - New conduit for liquidity pressure and runs spilling into capital markets, especially sovereign bond markets.
  - Reserve portfolios link redemptions to bond market liquidity and yields, creating dynamics similar to MMFs but operating 24/7/365 and cross-border.
  - Amplified classic concerns: first-mover advantage, fire sales, dilution of remaining holders.
  - New concerns: market impact, digital currency substitution, monetary sovereignty and transmission, especially with large foreign-denominated coins.
  - SCs may meet FSB G-SIB-like criteria (size, interconnectedness, substitutability, cross-jurisdictional activity, complexity) despite not being banks.

### 3. The Economics of Stablecoins — channels, mechanics, and broader implications
- Asset composition and linkages:
  - Typical holdings: cash reserves at banks and MMFs, sovereign bonds, reverse repo lending to banks and NBFIs (incl. MMFs).
  - Sovereign bond markets are the primary common exposure; redemptions can trigger bond sales → depressed prices → amplified solvency and liquidity pressures system-wide.
- Liquidity transformation and market frictions:
  - SCs issue liabilities redeemable on demand perceived as “safe” while holding assets that are not perfectly liquid under stress.
  - Redemption frictions: minimum sizes, operational lags, KYC, fees, banking hour constraints.
  - SCs lack access to deposit insurance or lender-of-last-resort; par maintained via arbitrage rather than institutional guarantee.
- Reverse repos vs outright bonds:
  - Reverse repos: cash lent against collateral; cash locked until repo unwinds; in stress counterparties may not honor repayment → liquidity risk.
  - Outright longer-dated bonds: typically less liquid, greater market-price volatility when sold.
- 24/7 redemptions vs market hours:
  - Sovereign bond and repo markets close overnight/weekends; large redemptions can be concentrated when markets reopen, amplifying price impacts.
- Systemic amplification and broader macro effects:
  - Endogenous redemption → fire-sale → market feedback loops can produce self-fulfilling destabilizing spirals affecting sovereign debt and repo markets.
  - Reserve concentration at few custodians introduces single-name wholesale deposit run risk; two-way feedback possible between SCs and custodians.
  - Remuneration dynamics: direct or indirect remuneration to SC holders increases store-of-value appeal and could draw deposits from banks/MMFs; non-remuneration is state-dependent in effectiveness.
  - Sovereign–stablecoin nexus: domestic SC issuance can shift sovereign debt demand toward shorter-term bonds, shorten maturity structure, and raise rollover frequency and interest-rate sensitivity.
  - Cross-border external demand for a domestic SC can appreciate the home currency and prompt asymmetric monetary responses.
- Financial integrity and capital-flow considerations:
  - SCs can facilitate circumvention of capital controls, exacerbate capital flight, and strain domestic banking systems in crises.
- Market structure risks and potential benefits:
  - Network effects can produce market tipping and dominance by systemic SC providers.
  - Benefits include faster/cheaper payments, reduced transaction costs, potential improvements in remittances and trade settlement.
- Policy responses prompted:
  - Development of CBDCs or tightly supervised domestic SCs to preserve monetary sovereignty and capture digital payment efficiencies.

### 3.3 Parallels to Investment Funds — MMF analogies and regulatory lessons
- Structural parallels with MMFs:
  - Both offer liabilities redeemable at short notice and invest in short-term, imperfectly liquid assets, producing liquidity transformation and first-mover advantages.
  - Run dynamics map closely to MMF episodes (2008, March 2020).
- Heterogeneity and analogs:
  - Fiat-backed SCs with only short-dated public instruments resemble government MMFs; riskier asset mixes resemble prime MMFs.
- Systemic spillovers:
  - MMFs are major investors in sovereign bills, commercial paper, and repo markets; SCs scaled to large size could exert similar or larger pressures due to 24/7 cross-border redemption.
- Regulatory tools from MMFs informative for SCs:
  - Liquidity requirements, redemption fees and gates, swing pricing.
  - Empirical note: swing pricing used for 71 percent of assets under management in Luxembourg-domiciled funds (2022 survey).
- Competitive and demand dynamics:
  - Tokenized MMFs and government bond funds can offer yield-bearing alternatives.
  - Empirical pattern: SC market size declines after monetary policy tightening while prime MMF assets rise.

### 4.3 Counterfactual Design Simulations — model setup, baseline, scenarios, and principal findings
- Scenarios simulated alongside a baseline:
  - Capital requirements (raise initial asset-liability ratio (ALR) above 100 percent).
  - Minimum cash reserve ratio (RR).
  - Redemption gates (cap daily redemption rate as a percentage of outstanding liabilities).
  - Lower durations for bond holdings (reduce portfolio Macaulay duration below baseline).
- Calibration objectives and illustrative targets:
  - ALR counterfactual: increased so probability of cumulative redemptions and fire sales at end of 30-day horizon equals 5 percent (baseline: around 50 percent with ALR=1 in T0).
  - RR counterfactual: fire sale probability targeted to 5 percent at end-horizon.
  - Redemption-gate and lower-duration calibrated to match mean cumulative redemption rate of the RR scenario.
  - Simulation: 5,000 rounds up to a 30-day horizon; initial cash reserve ratio assumed at 0.5 percent (distinct from baseline where cash ratio in T0 is zero percent).
- Baseline parameterization (exact values preserved):
  - Bond portfolio Macaulay duration = 0.5 (years).
  - Modified convexity = 0.8 (years^2).
  - Bond yield process (base noise): current annualized yield to maturity of short-term bonds i0 = 0.04.
  - Long-run average bond yield i_lr = 0.04.
  - Mean reversion speed i_speed = 20 (per year; =20 implies half-life of shocks of about 9 days).
  - Diffusion parameter i_sigma = 0.07 (annualized standard deviation).
  - Redemption function steepness kappa = 2 (>1 for convex).
  - Max daily redemption rate f_max = 0.25.
  - Bond market price impact primary slope lambda = 0.05.
  - Shape parameter alpha = 0.75 (<1 for concave).
  - Dependence on duration gamma = 0.5 (>0 for meaningful price and yield response to change in D).
- Baseline initialization (Figure 8 illustration):
  - Total assets and total liabilities initialized at 1,000 (currency units).
  - Bond portfolio market value in T0 = 995 (currency units); cash balance = 5 (currency units).
  - ALR in T0 = 1.
- Major comparative findings:
  - Capital (ALR) and cash-reserve (RR) designs deliver the broadest stabilization: lower likelihood and severity of de-pegs, redemptions, and fire sales, and dampened bond market feedback.
  - Redemption gates and lower duration provide consistent but milder mitigation, moderating intensity rather than frequency.
  - ALR > 1 most effectively reduces end-horizon events: ALRs < 1, cumulative redemptions > 0, and cumulative fire sales > 0.
  - RR buffers absorb outflows up to roughly 2 percent cumulative redemptions (flat relation in that range) before bond sales resume.
  - ALR > 1 and RR compress fire-sale vs yield-shift outcomes and halve 1 percent tail metrics relative to baseline for tail risk metrics shown.
  - Redemption gates delay and stagger sales (shift distribution furthest right); lower duration flattens price-impact sensitivity and modestly delays sales.
  - Mechanism distinction: solvency (capital) and liquidity (cash) buffers are preventive; redemption gates and duration adjustments are mitigating.
- Robustness and sensitivity:
  - Conclusions robust to wide parameter variation (redemption elasticities, market impact parameters).
  - Sensitivity tests (concave redemption function vs convex, convex vs concave bond price impact) do not overturn conclusions.
- Suggested model extensions (selected):
  - Make redemption–solvency sensitivity endogenous to gates; model exogenous news triggers; simulate continuous-time (dt < 1/252) to capture 24/7 dynamics; multi-entity networks; multi-country extensions with FX dynamics.

### 5. Design Implications — nine design questions, recovery/resolution, and common elements
- Nine core design questions and condensed policy guidance (exact language and numeric ranges preserved where given):
  1. Capital requirements?
     - Consider ALR floors (e.g., 1.01–1.05) with size-linked surcharges; phase in for entrants; restrict distributions until buffers are met; avoid procyclicality.
  2. Minimum cash reserve requirements?
     - Reduce fire-sale risk; mainly lower fire-sale frequency rather than redemption probability; diversify placements; consider central bank deposits (interest-bearing) and international coordination.
  3. Distribution of cash reserves across holding institutions?
     - Consider minimum diversification rules (e.g., no more than a certain percentage per bank group) or tiered ratios between banks and the central bank; ensure segregation and bankruptcy remoteness.
  4. Role of redemption gates?
     - Smooth redemptions, limit fire-sale spillovers; too strict gates may spur pre-emptive runs; distinguish issuer-level vs system-wide activation; use clear triggers and complementary tools.
  5. Maximum duration limits on bond holdings?
     - Shorter maturities reduce valuation and solvency risk; codify existing short-duration practice to deter maturity extension.
  6. Ban on interest-bearing wrappers?
     - Prohibit issuer/affiliate/third-party implicit remuneration if preserving payment function is priority; if yield offered, require separate regulated product.
  7. Prohibit lending to nonfinancial private sector?
     - Keeps reserves liquid and low-risk; lending would make issuer akin to a bank requiring banking regulation.
  8. Prevent monopoly formation?
     - Build interoperability ex ante; apply antitrust and merger review; consider CBDC as public benchmark; pursue international coordination.
  9. Access to standing central bank facilities?
     - Can support at-par redemption promise; access should be collateralized with high-quality assets and paired with prudential regulation to avoid moral hazard.
- Recovery and resolution:
  - Dedicated recovery and resolution frameworks needed for systemic SCs; ordinary corporate bankruptcy is too slow to prevent contagion.
- Common elements across national frameworks:
  - Capital requirements (fixed minima or risk-weighted); reserve asset eligibility rules (bank deposits, government securities, possibly MMFs or reverse repos with liquidity/credit/maturity criteria); explicit limits on maturity transformation (maximum maturities or weighted average maturity limits).
- Model findings revisited:
  - Model links redemptions to issuer solvency and bond market prices to bond sales; useful for inferring capital and liquidity requirements to target tail probabilities, akin to bank capital frameworks.
  - Solvency and liquidity buffers act as preventive stabilizers; gates and duration limits mitigate intensity and timing once stress occurs.
- Systemic considerations and structural effects:
  - SCs scaled to systemic size can interweave with financial markets, triggering run–fire-sale–market feedback loops affecting sovereign bond and repo markets.
  - Distinctions from MMFs: 24/7 global retail access, no formal backstops, continuous par redemption in secondary markets, lack of central-bank access so far.
  - Potential macro-financial structural effects: shortening sovereign debt maturities, a growing sovereign–stablecoin nexus, and digital currency substitution that may undermine monetary sovereignty and policy transmission.

### Annex 3 — Model variables, ratios, and parameter definitions (selected)
- Endogenous stock variables (end-of-period):
  - L — Stablecoin balance (liability of issuer, book value).
  - B — Bond portfolio (market value).
  - B_par — Bond portfolio (par/book value).
  - R — Cash reserves.
  - U — Emergency debt (additional liabilities if B and R depleted).
- Endogenous flows and metrics:
  - i — Bond yield (annualized yield to maturity).
  - f$ — Redemption flow (monetary terms).
  - b$ — Fire sale flow (monetary terms).
  - π — Fire sale price impact (decimal; e.g., −0.1 = −10%).
  - Δi_fire — Fire sale yield impact (decimal; e.g., 0.01 = 1 p.p.).
- Ratios and derived metrics:
  - ALR — Asset-liability ratio = (R + B)/L.
  - RR — Cash reserve ratio = R/L.
  - f redemption flow rate = redemption flow over pre-redemption stablecoin balance.
  - b fire sale flow rate = fire sale flow relative to pre-sale bond portfolio size.
- Initialization parameters and structural parameters listed (names preserved): L0, RR0, ALR0, i0, D (Macaulay duration), χ (modified convexity), σ (diffusion), τ (mean reversion speed), i_lr, κ (redemption steepness), f_max, λ0 (sales impact parameter), α (shape of price impact), γ (dependence on duration).

*Source: IMF Working Paper — From Par to Pressure: Liquidity, Redemptions, and Fire Sales with a Systemic Stablecoin (selected sections: 1; 3; 3.3; 4.3; 5; Annex 3).*

### 1. Introduction ........................................................................................................

### 1. Introduction

### Overview and motivation
- Stablecoins (SCs) — specifically fiat-backed SCs backed by financial assets closely tied to fiat currency — may scale from a niche crypto tool to a mainstream means to hold and move monetary value.
- Unbacked and algorithmic designs keep proving “inherently unviable.”
- Fiat-backed SCs are increasingly used for cross-border payment flows—not just crypto trading.
- As issuers grow, they would hold more sizeable pools of financial assets (deposits, short-term sovereign bonds, reverse repo lending), increasing their footprint in financial markets and raising resilience and interplay concerns with markets.

### Key systemic-risk channels and implications
- Large-scale SCs introduce a new conduit for liquidity pressure and runs to spill over into capital markets, especially sovereign bond markets.
- Reserve portfolios link user redemptions to bond market liquidity and yields, creating liquidity dynamics and run risks similar to money market funds (MMFs) but operating 24/7/365, cross-border, and at near-instant speed.
- Classic concerns amplified: first-mover advantage, fire sales, and dilution of remaining holders.
- New concerns: market impact, digital currency substitution, monetary sovereignty and transmission, particularly if large foreign-denominated coins take root.
- SCs may meet the Financial Stability Board’s (FSB) G-SIB-like criteria (size, interconnectedness, substitutability, cross-jurisdictional activity, complexity) even though issuers are not banks; cross-border reach is inherent and overall complexity may rise through entity diversity or crypto ecosystem integration.

### Empirical signals highlighted in the chapter
- Selected data (Figure 1) corroborate SC relevance:
  - The SC market shares of the currently two largest SCs (USDT in [G] and USDC in [H]) are 64 and 22 percent, in mid-2025.
  - The largest stablecoin issuers’ holding share in U.S. treasury bills is growing, at 1.7 percent by mid-2025.
  - Nearly 70 percent of countries are developing regulatory frameworks for SCs at present.
- SCs exhibit much higher implied velocity (use as transaction conduits) and cross-border flows at levels comparable to unbacked crypto.
- Largest SCs’ asset compositions include short-term bonds, reverse repo exposures, MMF holdings, and deposits (panels [G] and [H] summarized).

### Principal policy-design “dials” and their modeled effects
- The paper analyzes how design dials map to outcomes, with outcomes including redemption frequency and intensity, fire sale frequency and intensity, and bond market volatility and yield shifts. Design dials examined include:
  - Capital requirements
    - Raise the SC issuer’s asset–liability ratio above unity, lowering likelihood of de-pegging, redemptions, fire sales, and adverse market feedback.
    - Work on both likelihood and severity margins; solvency requirements are a potent headline design choice.
    - Asset–liability ratios above unity could be achieved by reinvesting bond interest income proceeds so that the market value of the bond portfolio exceeds liabilities.
  - Cash reserve requirements
    - In isolation, would not alter the probability of redemptions much, but when redemptions occur, higher cash reserves absorb them first so fewer bonds need to be sold, mitigating adverse market feedback.
    - A higher cash reserve share lowers the SC issuer’s bond market footprint and thereby reduces fire sale-induced price impacts.
  - Redemption gates (or limits)
    - Reshape the temporal profile of outflows, giving markets space to digest bond sales and policymakers time to possibly intervene.
    - Staggered liquidations can dampen non-fundamentals-driven panic dynamics, possibly reducing adverse feedback.
    - May spur pre-emptive redemption dynamics if investors anticipate activation and seek to redeem ahead of binding constraints.
- Complementarity of design dials:
  - Capital (excess assets) most potently reduce likelihood and severity of instability.
  - Cash reserves reduce likelihood of bond sales and associated adverse market feedback.
  - Redemption gates help flatten liquidity pressures if they occur.

### Conceptual scope and modeling approach
- The paper discusses the financial economics of a fiat-backed SC of a hypothetical systemic scale, emphasizing interconnectedness with financial market entities, forms of credit, market, and liquidity risk, and a run–fire-sale–market feedback.
- Also discusses beyond-short-term consequences: changing sovereign debt maturity structure, a growing sovereign–stablecoin nexus, and digital currency substitution.
- Provides a simple, structural model of a systemic SC issuer that holds bonds and cash reserves to analyze how design dials map to outcomes.
- The model features two-way feedback between an SC issuer and the markets it invests in, explicit run dynamics, and counterfactual design simulations to quantify effects of specific design choices.

### Structure of the paper (as previewed)
- Section 2: literature review.
- Section 3: conceptual discussion of the financial economics of SCs.
- Section 4: model and counterfactual design simulations.
- Section 5: detailed design considerations.
- Section 6: conclusions.
- Annex 1: compares SCs with MMFs.
- Annex 2: outlines alternative technical SC formats and their economic logics.
- Annex 3: contains further model details.

*Source: IMF Working Paper — 1. Introduction (From Par to Pressure: Liquidity, Redemptions, and Fire Sales with a Systemic Stablecoin).*

### 3.  The Economics of Stablecoins

### 3.  The Economics of Stablecoins

### 3.1   The Financial Economics of Stablecoins
- A fiat-backed SC arrangement is linked to the financial system via direct exposures and common holdings of sovereign bonds; issuers’ balance sheets expand with intermediate SC holdings and potential store-of-value motives (Figure 2).
- Typical SC asset composition includes cash reserves at banks and MMFs, sovereign bonds, and reverse repo lending to banks and NBFIs (incl. MMFs), creating direct asset-liability links across sectors (Fig. 1 [H-G] and Fig. 2).
- Sovereign bond markets are the primary common exposure; SC redemptions can trigger bond sales that depress prices, erode valuations across holders, and amplify solvency and liquidity pressures system-wide.
- SC issuers perform liquidity transformation similar to investment funds/MMFs: they issue liabilities redeemable on demand and perceived as “safe,” while holding assets that are liquid but not perfectly so, especially under stress.
- Deviations from par arise because SCs operate in a segmented and frictional market where only selected participants can access the issuer:
  - Redemption limitations: minimum sizes, operational lags, KYC procedures, fees, and banking hour constraints.
  - Secondary markets clear on momentary supply and demand; arbitrage restores the peg but requires time and balance sheet capacity.
  - Result: temporary discounts or premia emerge that would not occur for cash or bank deposits.
- SCs lack universal access to redemption into deposit money, lack a lender of last resort, and do not feature deposit insurance—par value is maintained via arbitrage rather than institutional guarantee.
- Reverse repurchase agreements (reverse repos) as reserve holdings:
  - Represent lending cash against collateral (typically government bonds, possibly longer-term).
  - Collateral is legally transferred to the issuer and subject to obligation to be returned at repo maturity; selling collateral can breach contract unless a right-of-use clause exists and exposes issuer to replacement-cost and market-liquidity risks.
  - Cash lent is locked until repo unwinds; reverse repos are liquid only if maturities are very short, e.g., overnight.
  - In systemic stress, repo counterparties may not honor repayment obligations, creating liquidity risk for SC issuers.
- Differences between outright bond holdings and reverse repos:
  - Outright longer-dated bonds often less liquid than short-dated instruments and expose issuer to greater market-price volatility when sold to meet redemptions.
  - In reverse repos the underlying collateral is typically longer-term; borrower default can leave the issuer holding longer-term bonds to dispose of in adverse conditions, inheriting liquidity and price-impact risks.
  - Short-maturity repos minimize liquidity risk when they unwind smoothly but failure scenarios resemble forced liquidation of longer-term bonds.
- Structural mismatch from 24/7/365 redemptions vs. market hours:
  - Sovereign bond and repo markets close overnight and on weekends with limited off-hours liquidity.
  - Large redemption waves may be met initially with prefunded cash-like reserve buffers but can result in concentrated asset sales when markets reopen.

### 3.2   Systemic Amplification Channels and Broader Implications
- Systemic scaling: risks scale if SCs attain systemic relevance, especially globally, due to continuous and global operation of digital platforms enabling redemptions outside business hours and jurisdictions.
- Endogenous redemptions–fire-sale–market feedback loop (Figure 4):
  - Redemptions force asset (bond) sales → depressed bond prices and higher yields → weakened SC issuer solvency → eroded user confidence → further redemptions.
  - Once redemptions reach a critical scale, self-fulfilling destabilizing spirals can extend to sovereign debt markets and other bond holders.
  - Repo and money market disruptions can occur as counterparties adjust haircuts or funding terms.
- Distribution and concentration of cash reserves:
  - If reserves are placed with one or a few banks (or MMFs), concentration risk arises: custodian failure or distress impairs issuer’s ability to honor redemptions.
  - Diversification across multiple banks/MMFs reduces single-name risk but introduces coordination and cross-jurisdictional supervisory dependence.
  - From banks’/MMFs’ perspective, large concentrated placements create single-name wholesale deposit run risk and higher liquidity requirements (LCR-type metrics).
  - Two-way feedback: a run on the SC could propagate to its custodians and vice versa.
- Store-of-value competition and remuneration dynamics:
  - SC issuers holding funds outside banking system or with few banks may induce bank funding pressure.
  - Investment in MMFs can channel wholesale funding to specific larger banks.
  - Direct remuneration by an SC issuer would make SC a rate-bearing asset and could draw deposits away from banks and MMFs, increasing SC footprint in sovereign bond markets.
  - Indirect remuneration (third-party wrappers) can also strengthen store-of-value motives and undermine bans on issuer-paid yield (GENIUS example cited).
  - Non-remuneration limits store-of-value appeal; in positive interest-rate environments bank deposits and MMF shares are more attractive, while in low or negative rate environments SCs may become more attractive—state-dependence of non-remuneration’s effectiveness is important.
  - Interest on SCs, if present, would likely move with market rates, reducing state-dependent in- and outflow dynamics.
- Absence of stabilizing overlays magnifies vulnerabilities:
  - Banks benefit from deposit insurance and lender-of-last-resort facilities; MMFs operate with redemption gates, fees, and portfolio constraints.
  - SCs may operate without such buffers, and technological features (always-on redemption, global accessibility) combined with institutional gaps (lack of contingent liquidity support) enable individual redemption decisions to escalate into market-moving fire sales.
- Sovereign-stablecoin nexus and debt market effects:
  - Domestic SC issuance can shift sovereign debt demand composition toward shorter-term bonds (liquid, low-duration assets), shortening maturity structure and increasing rollover frequency and interest-rate sensitivity.
  - External demand for a domestic SC represents net new inflow into domestic sovereign debt concentrated in shorter-term tenors, temporarily easing sovereign funding conditions.
  - A surge in external demand for a domestic SC would likely appreciate the SC’s home currency, affecting trade competitiveness and possibly prompting foreign central banks to tighten policy; the home country may lean against appreciation through rate cuts, creating asymmetric monetary adjustments and policy coordination challenges.
- Distinction of risks by time horizon:
  - Short-term, high-frequency liquidity risks: redemption surges, fire sales, market feedback unfolding over hours or days (model focus of the paper).
  - Slower-moving cyclical dynamics: interest rate-driven inflows/outflows over cycles.
  - Structural changes: gradual shifts in consumer preferences, new SC supply, and structural shifts in incumbent financial system over months or years.
- Longer-term structural risks:
  - Unintended digital currency substitution and weakening of domestic monetary policy transmission.
  - Loss of seigniorage income for central banks/sovereigns and reduced ability to steer inflation/economic dynamics if economic cycles are not synchronized with SC home country.
- Capital flow, AML/CFT, and capital flight considerations:
  - SCs can facilitate circumvention of capital controls via cross-border, peer-to-peer transactions, weakening capital flow measures unless aligned with robust AML/CFT regimes and regulation of SC issuers/service providers.
  - SCs may exacerbate capital flight during economic or political instability, straining domestic banking systems, heightening exchange rate volatility, and triggering liquidity stress that may require central bank intervention; outcomes include higher interest rates, increased debt service burdens, defaults, unemployment, and economic contraction.
- Market structure and concentration risks:
  - Strong network effects, economies of scale in payments, and data advantages can lead to market tipping and dominance by systemic SC providers, allowing extraction of monopolistic rents and amplifying spillover risks from operational or governance failures.
- Potential benefits:
  - Faster and cheaper payments, reduced transaction costs and settlement delays in domestic transactions and cross-border remittances.
  - Wider SC usage can facilitate international trade and reduce reliance on correspondent banking chains; in some economies SC-driven dollarization may enhance monetary stability and import purchasing power.
- Policy responses:
  - SC-induced structural changes around monetary sovereignty and policy transmission may prompt central banks to develop CBDCs or tightly supervised domestic SCs to preserve monetary sovereignty, safeguard financial stability, and maintain effective monetary policy transmission while capturing digital payment efficiency gains.

*IMF Working Paper — From Par to Pressure: Liquidity, Redemptions, and Fire Sales with a Systemic Stablecoin*

### 3.3   Parallels to Investment Funds

### 3.3   Parallels to Investment Funds

### Structural parallels to money market funds (MMFs)
- Fiat-backed SCs share structural features with open-end investment funds, most directly with MMFs: both offer investors liabilities redeemable at short notice and at par or near-par while holding portfolios of ostensibly safe and liquid securities.
- Liquidity transformation in both creates a first-mover advantage: early redeemers obtain full value while remaining investors bear fire sale losses and impaired asset values.
- The run dynamics observed in MMFs during the 2008 financial crisis and the March 2020 COVID-19 pandemic map closely onto risks potentially facing large SC arrangements.
- Contrast with equity or real estate funds: those funds give investors a pro rata claim on fluctuating market-value shares rather than a fixed at-par claim.

### Heterogeneity across SC structures and MMF analogs
- Fiat-backed SCs may resemble government MMFs when reserves consist only of short-dated public-sector instruments.
- When issuers hold riskier, less liquid, or opaque assets, SC structures are instead akin to prime MMFs, with correspondingly higher run-risk.
- Portfolio concentration in sovereign and money market instruments creates a channel through which fund-specific runs can propagate into broader market stress.
- SCs scaled to large size would concentrate reserves in similar assets as MMFs and could exert pressures of comparable magnitude, amplified by 24/7, cross-border redemption.

### Systemic market spillovers
- MMFs are major investors in sovereign bills, commercial paper, and repo markets; sudden MMF asset sales can disrupt markets.
- SCs, if scaled, could concentrate reserves in similar assets and thereby transmit fund-specific runs into broader market stress via portfolio concentration and 24/7 redemption accelerants.

### Policy responses and design implications drawn from MMF experience
- Regulatory tools applied to MMFs that are directly informative for SC design include:
  - liquidity requirements and minimum holdings of daily and weekly liquid assets;
  - redemption fees and gates (with redemption gates noted as removed in the U.S. in 2024);
  - swing pricing to internalize redemption costs (swing pricing is widely used in the UK and other European countries; a 2022 survey by the Association of the Luxembourg Fund Industry found that swing pricing is used for 71 percent of assets under management in Luxembourg-domiciled funds).
- For SCs, analogous measures that could be considered:
  - limits on eligible assets;
  - liquidity buffers in cash;
  - redemption frictions;
  - dynamic pricing mechanisms that prevent par redemption in stress.
- Objectives differ: MMF regulation emphasizes investor protection and market stability, whereas systemic SCs may be treated as payment infrastructures subject to the Principles for Financial Market Infrastructures (PFMI), reflecting additional objectives related to payment integrity, operational resilience, and monetary sovereignty (CPMI-IOSCO, 2022).
- The MMF experience demonstrates that instruments designed to appear “safe” can generate systemic risk without adequate guardrails; stabilizing design is therefore relevant for SCs.

### Competitive landscape and demand dynamics
- Developments in the fund space may affect SC demand: the emergence of tokenized MMFs and government bond funds creates yield-bearing alternatives with similar technological features.
- The at-par promise and convenience of SCs might outweigh regular portfolio reallocations in a low-interest rate environment, but demand for zero-yielding SCs could structurally decline in higher interest rate environments (Bibow, 2025).
- Empirical pattern noted: SC market size declines after monetary policy tightening, while prime MMF assets rise (short-term corporate debt holdings) (Aldasoro et al., 2025b).

*IMF Working Paper — From Par to Pressure: Liquidity, Redemptions, and Fire Sales with a Systemic Stablecoin — Section 3.3.*

### 4.3   Counterfactual Design Simulations

### 4.3   Counterfactual Design Simulations

### Counterfactual scenarios and calibration
- Four counterfactual scenarios were simulated alongside a baseline to compare design levers:  
  - Capital requirements (raising the initial asset-liability ratio (ALR) to a level above 100 percent).  
  - Minimum cash reserve ratio (RR) as a liquidity requirement.  
  - Redemption gates (cap daily redemption rate, defined as a percentage of outstanding SC liabilities).  
  - Lower durations for bond holdings (reduce portfolio Macaulay duration below baseline).  
- Calibration objective: make impacts quantitatively comparable across scenarios. Example calibrations:  
  - The ALR was increased to a level that implies the probability of cumulative redemptions and fire sales at the end of the 30-day horizon equals 5 percent (instead of around 50 percent in the baseline, with its ALR=1 in T0).  
  - For the RR counterfactual, the fire sale probability was targeted to 5 percent at end-horizon.  
  - Redemption-gate and lower-duration counterfactuals were calibrated to match the mean cumulative redemption rate of the RR scenario (since they do not notably influence the probability of redemptions and fire sales).  
- Illustration in Figure 8: 5,000 simulation rounds up to a 30-day horizon; initial cash reserve ratio assumed at 0.5 percent (distinct from the baseline where the cash ratio in T0 is zero percent).

### Baseline parameterization (Table 1)
- Bond portfolio: Macaulay duration = 0.5 (years).  
- Modified convexity = 0.8 (years^2).  
- Bond yield process (base noise): current annualized yield to maturity of short-term bonds i0 = 0.04.  
- Long-run average bond yield i_lr = 0.04.  
- Mean reversion speed i_speed = 20 (per year; =20 implies half-life of shocks of about 9 days).  
- Diffusion parameter i_sigma = 0.07 (annualized standard deviation).  
- Redemption function steepness kappa = 2 (>1 for convex).  
- Max daily redemption rate f_max = 0.25.  
- Bond market price impact primary slope lambda = 0.05.  
- Shape parameter alpha = 0.75 (<1 for concave).  
- Dependence on duration gamma = 0.5 (>0 for meaningful price and yield response to change in D).

### Baseline initialization (Figure 8 illustration)
- Under the illustrative run in Figure 8: total assets and total liabilities (SC balance outstanding) initialized at 1,000 (currency units).  
- Bond portfolio market value in T0 = 995 (currency units); cash balance = 5 (currency units).  
- Since assets equal liabilities in T0, residual equity is zero and the asset-liability ratio is therefore 1 in T0.

### Major comparative findings from the counterfactual simulations
- Overall summary: capital (ALR) and cash-reserve (RR) designs deliver the broadest stabilization—lowering both likelihood and severity of de-pegs, redemptions, and fire sales, and dampening bond market feedback. Redemption gates and lower duration provide consistent but milder mitigation, moderating intensity rather than frequency.
- Distributions and event likelihoods:  
  - End-horizon ALR distribution shifts most visibly upward in the higher-ALR-at-T0 counterfactual; other design variants also raise lower tails and tighten distributions.  
  - ALR > 1 most effectively reduces the likelihood of adverse events: end-horizon ALRs < 1, cumulative redemptions > 0, and cumulative fire sales > 0.  
  - Cash-reserve counterfactual produces modest feedback to ALRs, still high redemption probabilities, and lower fire sale probability (cash buffers absorb withdrawals first).  
  - Redemption-gate and lower-duration designs leave event probabilities broadly unchanged, indicating their stabilizing power operates mainly through timing and valuation sensitivity rather than event frequency.
- Redemption vs fire sales relationship:  
  - In non-RR cases (cash reserves zero), there is near one-to-one correspondence between cumulative redemptions and fire sales—every redemption must be met through bond sales.  
  - ALR > 1 tightens dispersion around that line (smaller and less variable redemption–fire-sale episodes).  
  - In the RR case, relation is flat up to roughly 2 percent cumulative redemptions (cash reserves absorb outflows up to that level), then bond sales resume and the 45-degree slope re-emerges at a lower level than baseline.
- Fire sales vs yield shifts and market yield feedback:  
  - ALR > 1 and RR buffers compress the cloud of fire sales vs fire sale-induced yield shifts, dampening incidence and magnitude of yield spikes.  
  - Redemption gates curb extreme outliers by limiting daily sales, but slightly raise yield-per-event ratio as delayed sales occur in higher-yield conditions.  
  - Lower-duration design flattens the slope: duration adjustment in the price-impact function reduces yield shifts per unit sale and shifts overall market yield effects down.
- Tail risk and timing:  
  - ALR > 1 and RR buffers halve 1 percent tail metrics relative to baseline for tail risk metrics shown (relative reduction explicitly stated as “halve 1 percent tail metrics relative to baseline”).  
  - Redemption gates and lower duration trim upper-percentile extremes.  
  - ALR > 1 and RR extend the median time to first bond sales; redemption gates shift the distribution furthest right (sales occur later and more gradually). Lower duration causes a modest delay via smaller mark-to-market shocks.
- Mechanism distinctions:  
  - Solvency (capital) and liquidity (cash-reserve) buffers act as preventive stabilizers (reducing frequency and severity).  
  - Redemption gates and duration adjustments serve as mitigating mechanisms once stress materializes (moderating intensity and timing).

### Robustness checks and sensitivity
- Robustness: conclusions are robust to wide parameter variation (redemption elasticities, market impact parameters, and other parameters from Annex 3). Direction of effects and relative magnitudes across counterfactuals remain stable.  
- Specific sensitivity tests: assuming a concave redemption function (instead of convex) and a convex bond price impact function (instead of concave) did not overturn conclusions.

### Suggested model extensions (eight examples)
1. Make the redemption–solvency sensitivity (f_max and/or κ in eq. 5) endogenous to the presence/tightness of redemption gates to capture possible pre-emptive redemptions.  
2. Augment the redemption function to allow exogenous triggers (e.g., social-media-mediated news), news about material losses in flow terms, expectations thereof, or an asset-liability ratio shortfall relative to a regulatory minimum; make redemption propensities a function of levels/changes of interest rates.  
3. Model redemption gates to resemble real-world designs more closely (e.g., gates triggered when liquid asset or net-asset-value metrics fall below thresholds).  
4. Allow continuous-time or non-business-day simulation (dt < 1/252) to capture 24/7 trading and redemption and analyze weekend dynamics and uninterrupted market access.  
5. Add a slow-moving flow component tied to the interest-rate environment (e.g., rate differentials vs. bank deposits/MMFs) to capture gradual portfolio reallocation and cyclical dynamics.  
6. Model issuer portfolio rebalancing and maturity management decisions endogenously (issuer can shorten/lengthen duration or shift between cash/bills/reverse repos).  
7. Consider a multi-entity network (multiple SCs, banks, central bank, MMFs) to assess cross-entity contagion and amplification through balance sheet links and common exposures; distinguish deposits at commercial banks versus the central bank.  
8. Multi-country extension with explicit capital flows and FX dynamics to assess dynamics for emerging market economies and design choices limiting foreign-currency-denominated SCs domestically.

*Italic source: IMF Working Paper section "4.3   Counterfactual Design Simulations" (figures and tables referenced within).*

### 5.  Design Implications

### 5.  Design Implications

### Overview
- Discussion structured along nine questions (Table 3) to inform SC design choices from a financial economics perspective, with the objective of maintaining domestic and global monetary stability.
- Several design features imply costs or foregone income for an SC issuer while strengthening issuer stability and the broader ecosystem.
- Capital and liquidity requirements may affect competitiveness and incentivize regulatory arbitrage or off-shoring, highlighting the need for cross-jurisdictional coordination.

### Nine design questions and design choices
- 1. Should capital requirements for SC issuers be considered?
  - Rationale: Strengthens solvency and confidence, lowering the likelihood and severity of redemptions, fire sales, and market spillovers.
  - Comments:
    - Consider asset-liability ratio (ALR) floors (e.g., 1.01–1.05) with size-linked surcharges; phase in for entrants.
    - Restrict distributions until buffers are met.
    - Residual equity (assets exceeding liabilities) can be built organically by reinvesting income in bonds.
    - Avoid procyclicality through stable, through-the-cycle calibration.
    - Coordinate internationally to prevent regulatory arbitrage.

- 2. Should minimum cash reserve requirements be considered?
  - Rationale: Lowers fire-sale risk by meeting redemptions first with cash, reinforcing liquidity and user confidence.
  - Comments:
    - Cash reserve requirements mainly reduce fire-sale frequency, not redemption probability.
    - Conditional fire sale severity remains elevated if not paired with capital requirements.
    - Diversify placements across banks and, possibly, central bank.
    - Ensure segregation and bankruptcy remoteness at banks.
    - Interest-bearing central bank deposits would imply interest income for SC issuer.
    - A cash deposit requirement at banks may, if deposits pay low or zero interest, imply less income generating capacity for the SC issuer.
    - Coordinate internationally to avoid migration to regimes with less stringent requirements.

- 3. If cash reserve requirements are used, should their distribution across holding institutions (banks vs. central bank) be regulated?
  - Rationale: Diversified placement avoids concentration risk, distortions, and funding asymmetries, supporting stability and smoother monetary policy transmission.
  - Comments:
    - Consider minimum diversification rules (e.g., no more than a certain percentage of reserves per bank group) or tiered placement ratios between banks and the central bank.
    - When banks receive more wholesale deposits from SC issuer (and may lose retail deposit liabilities), they may then rotate from longer-term to short-term sovereign debt investments (duration matching).
    - Beyond diversification across banks and the central bank, consider diversification across instruments and markets to reduce concentrated market, liquidity, and credit risk, and adverse feedback into core markets.

- 4. What role may redemption gates play for SC and market stability?
  - Rationale: Help smooth redemptions and limit fire sale spillovers to markets.
  - Comments:
    - Too strict gates may spur pre-emptive runs and reduce transactional utility and the perceived “moneyness” of the SC.
    - Distinguish issuer-level from system-wide activation.
    - Use clear triggers, notice periods, or swing pricing as complementary tools.

- 5. Should maximum duration limits be imposed on stablecoin bond holdings?
  - Rationale: Shorter maturities reduce valuation and solvency risk, weakening redemption–fire-sale loops.
  - Comments:
    - Shorter-term bonds are more liquid, reducing price and yield impact in fire sale scenarios.
    - A shift to shorter-term sovereign funding could raise sovereign rollover and rate-risk exposure.
    - SCs already hold short-duration bonds, so limits would largely codify practice but remain useful to deter future yield-driven maturity extensions.

- 6. Should interest-bearing wrappers (i.e., mechanisms that pass reserve yield to stablecoin holders) be banned?
  - Rationale: Preserve payment function of stablecoins, avoiding rate competition and implied store-of-value competition for bank deposits and MMFs.
  - Comments:
    - If the regulator decides to prohibit remunerated SCs, issuer, affiliate, or third-party yield programs and implicit remuneration schemes should be banned.
    - If yield is offered, require a separate, non-par investment product regulated under fund or securities rules to maintain neutrality with banks and MMFs.
    - Consider measures to prevent excessive rent-seeking by SC issuer in positive interest rate environment (see #8 below).
    - By limiting store-of-value competition, reduce the systemic footprint of the SC issuer in bond markets.

- 7. Should stablecoin issuers be prohibited from lending to the nonfinancial private sector?
  - Rationale: Reserves more liquid and low-risk, safeguarding par convertibility and avoiding overlap with the banking system’s credit and hence money creation role.
  - Comments:
    - Lending would turn SCs into money-creating entities (assuming its liabilities, SCs, would serve the functions of money and be used as such).
    - If ever allowed, it may occur in a separate, capitalized vehicle; otherwise imply the issuer becomes a bank and is subject to ordinary banking regulation (solvency and liquidity).
    - Align with e-money and MMF precedents.
    - Coordinate internationally to prevent offshore regulatory arbitrage.

- 8. How may regulation prevent monopoly formation or dominance by a single systemic stablecoin domestically or globally?
  - Rationale: A dominant stablecoin could extract rents, entrench network effects, and pose systemic and monetary-sovereignty risks.
  - Comments:
    - Recognize network effects and economies of scale favor concentration.
    - Build interoperability ex ante to allow competition, as ex-post remedies are hard once dominance emerges.
    - Apply antitrust and merger review, consider CBDC as a public benchmark, and pursue international coordination.

- 9. Should stablecoin issuers have access to standing central bank facilities?
  - Rationale: Access can support at-par redemption promise, thereby reducing run risk, contagion, and adverse market feedbacks.
  - Comments:
    - May be considered when SCs would become a widely used public good.
    - Access to standing facilities would be collateralized with high-quality assets and conservative haircuts.
    - To avoid moral hazard, access can be paired with full prudential regulation.
    - Cross-border SCs require coordinated home–host arrangements.

### Recovery, resolution, and operational risk
- A dedicated recovery and resolution framework complements prudential design considerations.
- Even an SC with sound financial design remains vulnerable to governance or operational failures (major cyber-attacks or internal fraud).
- For a systemic entity, ordinary corporate bankruptcy proceedings are too slow and ill-equipped to prevent financial contagion.
- A resolution framework gives a designated authority tools to intervene, maintain critical functions, and wind down the entity in an orderly manner.
- Further details of such resolution frameworks are beyond the scope of this paper.

### Common elements across national frameworks
- As of today, national regulatory frameworks pursue a set of common design elements while differing in implementation details. Common elements include:
  - (i) capital requirements, with some jurisdictions considering explicit capital buffers calibrated as fixed minima or on a risk-weighted basis;
  - (ii) reserve asset eligibility rules permitting bank deposits and government securities and, in some frameworks, also allowing investments in MMFs or reverse repurchase agreements—provided criteria for liquidity, credit quality, and maturity are met;
  - (iii) explicit limits on maturity transformation achieved through maximum maturities for individual holdings or limits on the portfolio’s weighted average maturity.

### Model findings and implications for monetary and financial stability
- The model captures SC-related amplification channels and can be used to assess different SC designs.
  - Key functions: one relating SC redemptions to SC issuer solvency; one making bond market prices a function of bond sales.
  - The model can simulate counterfactual SC design scenarios (capital and liquidity requirements of different kinds) to outcomes (run frequency and intensity, fire sale frequency and intensity, and bond market feedback).
  - The model can be used to reversely infer an SC issuer’s capital and liquidity requirements to target certain tail probabilities, akin to bank capital frameworks.
- Design-related comparative outcomes:
  - Capital and cash-reserve designs deliver the broadest stabilization: lowering the likelihood and severity of de-pegs, redemptions, and fire sales, as well as bond market feedback.
  - Redemption gates and lower duration offer consistent but milder mitigation, moderating intensity rather than frequency.
  - Overall, solvency and liquidity buffers act as preventive stabilizers while redemption gating serves as a mitigating mechanism once stress materializes.
- Broader measures on competition and interoperability can curb monopoly formation and safeguard monetary sovereignty.
- Parallels to investment-fund regulation: tools such as liquidity buffers, gates, fees, and swing pricing have proven effective elsewhere and could be adapted to SCs.

### Structural effects and systemic considerations
- Fiat-backed stablecoins scaled to systemic size would be interwoven with financial markets and can trigger self-reinforcing run–fire-sale–market feedback loops that transmit stress into sovereign bond and repo markets.
- Key economic linkages and risks:
  - Balance sheet linkages and exposures to credit, market, and liquidity risk.
  - Contagion potential from common asset holdings and endogenous interplay with markets.
  - Direct and indirect connections to banks, MMFs, and sovereign debt markets via holdings of cash, repos, and sovereign bonds.
  - Liquidity risk from maturity mismatches and 24/7 redemption against markets that close overnight and on weekends.
  - Endogenous feedback loops if the issuer has a sizeable bond market footprint, amplified by connections to other financial entities and common exposures.
- Distinctions from MMFs:
  - SCs operate with 24/7 global retail access and no formal backstops; MMFs have business-hour redemption and regulatory liquidity safeguards.
  - SCs circulate in payment systems, redeem continuously at par or near-par in secondary markets, and rely on self-held reserves without central-bank access so far.
  - MMFs redeem into brokerage cash, settle on T+0/T+1 schedules, and operate under post-crisis reforms mandating liquidity buffers and restricting risky investments.
- Potential macro-financial structural effects:
  - Shortening of sovereign debt maturities where a dominant global SC develops in a jurisdiction’s currency, raising rollover and interest rate risk.
  - Growing sovereign-stablecoin nexus.
  - Digital currency substitution for non-SC-dominant economies, potentially undermining monetary sovereignty and policy transmission and prompting local SCs, CBDCs, or SC-specific capital controls.

### Annex insights (summaries provided in the chapter)
- Annex 1: Stablecoins vs. Money Market Funds
  - Both fiat-backed SCs and MMFs hold redeemable liabilities and invest in short-term, imperfectly liquid assets, exposing them to liquidity transformation and run risk.
  - Key distinctions include:
    - SC liabilities: tokens redeemable at par, transferable peer-to-peer, circulate in secondary markets; redemption 24/7, platform-based, instant settlement at par; no backstops; direct links to sovereign bond markets, repo, and banks.
    - MMF liabilities: shares redeemable at NAV, held in brokerage accounts; redemption limited to market hours, typically T+0 or T+1; some implicit/explicit support; links to short-term funding markets.
  - MMF experience shows asset composition matters: CNAV vs. VNAV and limits on asset types (e.g., public debt only for CNAV in some jurisdictions).

- Annex 2: Types of Stablecoins
  - Taxonomy and brief characteristics:
    - 1. Fiat-backed stablecoins: backing includes cash, bank deposits, short-term government bonds, reverse repos. Economics: liquidity transformation and run risk. Fragility: redemptions → reserve liquidation → market impact → feedback to solvency → redemptions.
    - 2. Crypto-collateralized stablecoins: backing by over-collateralized crypto assets; economics hinge on collateral volatility; fragility through procyclical liquidation spirals.
    - 3. Algorithmic stablecoins (unbacked or partially backed): rely on algorithms and incentive mechanisms; economics resemble peg-credibility problems; fragility from confidence loss and absence of reserve buffers.
    - 4. Commodity-backed stablecoins (e.g., gold-backed): backing by physical commodities; economics tied to commodity prices; fragility like exchange-traded products, with custody and liquidity risks.
    - 5. Hybrid or synthetic stablecoins: mix of fiat assets, crypto collateral, derivatives; risk profile depends on design and can inherit weaknesses of constituent models.

*IMF WORKING PAPERS From Par to Pressure: Liquidity, Redemptions, and Fire Sales with a Systemic Stablecoin — Chapter 5, “Design Implications”*

### Annex 3: Model Variables and Parameters

### Annex 3: Model Variables and Parameters

### Endogenous model variables (stocks, all end-of-period)
- 1 퐿 — Stablecoin balance  
  - Liability of stablecoin issuer, at book value
- 2 퐵 — Bond portfolio (market value)  
  - Asset of stablecoin issuer, measured at market value
- 3 퐵୰ୣ୤ — Bond portfolio (par/book value)  
  - Value of bonds held, reflecting only sales, not revaluation, during the simulation; needed when endogenizing the fire sale impact parameter (휆)
- 4 푅 — Cash reserves  
  - Deposit-like reserve holdings, e.g., at banks or a central bank
- 5 푈 — Emergency debt  
  - Additional liabilities possibly incurred, if 퐵 and 푅 were depleted, under stress

### Endogenous model variables (flows and related)
- 6 푖 — Bond yield  
  - Annualized yield to maturity of the bond portfolio
- 7 푓$ — Redemption flow  
  - In monetary terms
- 8 푏$ — Fire sale flow  
  - In monetary terms
- 9 휋 — Fire sale price impact  
  - Decimal, i.e., -0.1 means -10% (means a 10% drop in price)
- 10 ∆푖௙௜௥௘ — Fire sale yield impact  
  - Decimal, i.e., 0.01 means a 1 p.p. (100 bps) shift in yield

### Other metrics, including ratios, as a function of endogenous model variables
- . 퐴퐿푅 — Asset-liability ratio  
  - (푅+퐵)/퐿
- . 푅푅 — Cash reserve ratio  
  - 푅/퐿
- . 푓 Redemption flow rate  
  - Redemption flow (푓௧) over pre-redemption stablecoin balance (퐿௧ି)
- . 푏 Fire sale flow rate  
  - Fire sale flow (푏௧) relative to pre-sale bond portfolio size (퐵௧ି)

### Parameters for initialization
- 1 퐿଴ — Initial stablecoin balance  
  - Book value
- 2 푅푅଴ — Initial cash reserve ratio  
  - Initial cash-like reserve stock implied as 푅଴ = 푅푅଴ × 퐿଴
- 3 퐴퐿푅଴ — Initial asset-liability ratio  
  - Initial bond holding implied as 퐵଴ = 퐵଴୰ୣ୤ = 퐴퐿푅଴ × 퐿଴ − 푅଴
- 4 푖଴ — Initial bond yield  
  - Annualized interest rate at the onset; decimal, i.e., 0.01 means 1%

### Parameters
- 5 퐷 — Macaulay duration  
  - Bond portfolio’s Macaulay duration in years
- 6 휒 — Modified convexity  
  - Bond portfolio’s convexity in years-square
- 7 휎 — Diffusion parameter  
  - Three parameters relevant for the stochastic interest rate process (“base noise”, see eqs. 1 and 2).
- 8 휏 — Mean reversion speed
- 9 푖௅ோ — Long run mean of 푖
- 10 휅 — Steepness of redemption rate response  
  - Two parameters relevant for the function that relates the redemption flow rate 푓 to the stablecoin issuer’s asset-liability ratio (see eq. 5).
- 11 푓୫ୟ୶ — Max daily redemption rate
- 12 휆଴ — Sales impact parameter  
  - Three parameters relevant for the function that relates the bond market price impact to the stablecoin issuer’s bond sales into the market (see eq. 13).
- 13 훼 — Functional shape of price impact
- 14 훾 — Dependence on duration

*Annex 3: Model Variables and Parameters — From Par to Pressure: Liquidity, Redemptions, and Fire Sales with a Systemic Stablecoin*

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_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026005-source-pdf.pdf_