Source-linked AI summary
Viable Pool Sizing for On-Chain FX Liquidity: Amplification, Capital, and Resilience
Ryan Fang, Ivan Bardziyan, Jessica Wang, Mayank Anand
TL;DR
The paper asks how institutional on-chain FX pools should jointly choose amplification and capital to meet slippage, profitability, and shock-resilience requirements. It combines StableSwap mechanics with a Merton jump-diffusion and LVR-based profitability analysis to map viable (A, TVL) configurations. The results identify a capital-scaling rule, thin A-invariant returns, and a practical amplification ceiling imposed by reserve drain and tail slippage.
Problem
Institutional on-chain FX liquidity must simultaneously provide sub-2-bps slippage, balance-sheet-scale capital efficiency, and resilience to macro-driven one-sided flows.
Method
The paper maps the joint (A, TVL) space using StableSwap mechanics, a Merton jump-diffusion FX process, and LVR-based profitability analysis under shock experiments.
Results
Viability requires TVL/Q ≈1000/A; at minimum viable size ROC is ≈0.054% per horizon and A-invariant, while high-A pools face severe reserve drain and tail slippage.
Takeaways & Limitations
For Q = $100,000 and 2-bps slippage, the viable institutional range is A ∈[100, 200] with TVL ∈[$5M, $10M].
Takeaways & Limitations
The model assumes constant volatility and independent jumps, although FX volatility can cluster and jumps may correlate with liquidity conditions.
Abstract
from arXiv · showhide
Financial institutions deploying on-chain FX liquidity face a joint design problem: how much capital to commit, and how to configure the pool, to remain both competitive on trading costs and profitable as a liquidity provider? The StableSwap mechanism (Egorov, 2020) interpolates between constant-product (CPMM) and constant-sum (CSMM) market makers (Port and Tiruviluamala, 2022) via an amplification factor A, but neither extreme suits institutional FX: CPMM pools require excessive capital and generate high impermanent loss; CSMM pools are capital-efficient near the peg but drain rapidly under adversarial flow. Using a Merton jump-diffusion price process (Merton, 1976) and the loss-versus-rebalancing (LVR) framework (Milionis et al., 2022), we map the joint (A, TVL) space to identify configurations that satisfy all three institutional requirements: competitive slippage, positive return, and shock resilience. Minimum viable pool size scales approximately as TVL/Q = 1000/A; ROC at that minimum is thin (about 0.054% per horizon) and independent of A; low-A pools (A <= 10) suffer slippage exceeding 200 bps under a 10x shock, while high-A pools (A >= 500) suffer reserve drain up to 60%, establishing both a capital floor and a practical amplification ceiling.
1 Introduction
Institutional on-chain FX venues must jointly control slippage, capital commitment, and resilience to macro-driven one-sided flows. StableSwap frames this as selecting viable (A, TVL) pairs rather than optimizing one metric.
- 1 Introduction: Wholesale FX venues targeting institutional flow must offer slippage within 2 bps, balance-sheet-scale capital, and resilience to macro shocks.Relevant shocks include rate decisions, data releases, and geopolitical events that drive large one-sided flows.
- 1 Introduction: No single CPMM–CSMM extreme satisfies low slippage, capital efficiency, and shock resilience simultaneously.CPMMs provide liquidity across prices but have high slippage and impermanent loss, whereas CSMMs are near-zero-slippage near the peg but drain when rates move.
- 1 Introduction: StableSwap interpolates between CPMM and CSMM behavior through amplification A, concentrating liquidity near a target rate while retaining price recovery under reserve imbalance.This mechanism provides the design spectrum evaluated in the paper.
- 1 Introduction: The institutional design problem is to identify jointly viable (A, TVL) pairs rather than optimize a single metric.The fee is fixed at 1 bp, leaving amplification A and total value locked as the design variables.
- 1 Introduction: Higher-A capital-efficiency gains are offset by shock fragility, with the two constraints binding in different parameter-space regions.The result motivates analyzing capital and resilience jointly.
2 Related Work
The paper builds on established AMM mechanisms, LP-cost theory, and FX modeling to study StableSwap liquidity for near-pegged institutional pairs.
- 2 Related Work: Prior work established the constant-product AMM baseline, introduced StableSwap, and characterized the CPMM–CSMM tradeoff.The paper positions its mechanism within this progression.
- 2 Related Work: The analysis uses the LVR framework for LP costs and extends it to fee-bearing pools through prior work.This supplies the profitability perspective for the pool evaluation.
- 2 Related Work: High-A StableSwap is described as conceptually analogous to tick-based concentrated liquidity but purpose-built for near-pegged pairs without manual range management.The comparison distinguishes the studied mechanism from general-pair concentrated liquidity.
- 2 Related Work: FX prices are modeled using a Merton jump-diffusion process within the paper’s related methodological context.The process combines continuous FX dynamics with discrete macro discontinuities.
3 Methodology
The methodology normalizes FX reserves around an oracle price, evaluates StableSwap’s amplification-dependent mechanics, and simulates rebalancing, repegging, profitability, and shocks under explicit viability criteria.
- 3.1 Pool Mechanics: StableSwap operates on equal-unit normalized reserves using an oracle reference price p∗, so liquidity centers on the correct cross-rate when the oracle is accurate.Updating p∗ recenters the invariant without changing raw reserves.
- 3.1 Pool Mechanics: The invariant spans constant-product behavior as A →0 and constant-sum behavior as A →∞, with near-linear pricing near balance and stronger curvature as reserves skew.Figure 1 illustrates the corresponding geometry across amplification values.
- 3.1 Pool Mechanics: Each trade pays a 1 bp fee, while net trade size executes against the invariant and slippage is computed from pre- and post-trade AMM prices.The fee matches the tight end of institutional inter-dealer FX spreads.
- 3.1 Pool Mechanics: Near equilibrium, curvature implies minimum depth scales as TVL/Q ∝1/A, with an empirical constant of approximately 1000 calibrated from bisection results.The calibrated relationship holds within 5% across tested amplification values.
- 3.2 Rebalancing, Repegging, and Profitability: A rebalancing bot compares AMM price with spot and executes a price-alignment trade when the deviation exceeds transaction cost.The trade captures the arbitrage spread net of gas cost, while repegging separately updates the oracle after material drift.
- 3.2 Rebalancing, Repegging, and Profitability: Gross margin combines fee revenue and arbitrage capture, and ROC is defined as gross margin Π divided by TVL over the simulation horizon.The framework therefore evaluates both trading income and capital usage.
- 3.3 Market Simulation: The market simulation uses a Merton jump-diffusion spot process with specified diffusion and jump parameters, plus elevated parameters and periodic one-sided shocks for resilience testing.The resilience experiment injects 5×, 10×, and 20× Q shocks every 50 steps.
- 3.4 Model Assumptions and Viability Metrics: The model assumes a sole LP, fixed 1 bp fees, zero latency, accurate spot at repegging, uninformed flow, and constant gas cost.These assumptions define the simulated operating environment.
4 Results
The results map the trade-off between amplification, capital required for low slippage, profitability, and resilience. Minimum viable depth declines with A, while ROC depends mainly on TVL/Q and high-A pools become more vulnerable under shocks.
- Minimum viable pool size: 952× at A = 10 and 10× at A = 1000: minimum TVL/Q is inversely proportional to A for ≤2 bps slippage.These ratios correspond to approximately $95M and $1M, respectively, for Q = $100,000.
- Minimum viable pool size: TVL/Q ≈1000/A near equilibrium because marginal price curvature scales as 1/A.The approximation breaks down under large shocks.
- Return on capital: 0.054% per horizon: ROC at minimum viable TVL for A = 100, approximately a $10M pool.ROC falls monotonically with pool size because fee revenue is fixed by trade volume while the TVL denominator increases.
- Return on capital: ≈0.054% at TVL/Q = 100×: pools with A = 100 and A = 1000 yield identical ROC, showing that profitability is determined by TVL/Q rather than A alone.Higher A reduces capital required to reach a given TVL/Q without improving yield.
- Resilience under adversarial shocks: 8 bps mean at A = 500 and A = 1000: maximum slippage falls through A = 200, then plateaus with high-variance tail runs.The plateau reflects the transition toward CSMM-like behavior, with unbounded price impact outside the efficient range.
- Resilience under adversarial shocks: 0.59 imbalance at A = 1000 versus 0.28 at A = 200, indicating substantially greater reserve skew at higher amplification.Values above 0.5 indicate that over half the pool is drained to one side.
5 Discussion
The viable region balances slippage-driven capital needs against shock resilience and profitability. Moderate amplification, rather than maximum capital efficiency, satisfies the joint constraints.
- Viable region: TVL/Q ≥1000/A is required for slippage, while resilience imposes an amplification ceiling near A = 200.At higher A, reserve imbalance becomes operationally thin under a 10× shock.
- Practical sizing: A ∈[100, 200] with $5M–$10M TVL is viable for Q = $100,000 under the stated constraints.This range combines the slippage requirement with the resilience threshold.
- The CSMM ceiling: At A = 1000, a single $1M shock triggers the CSMM-like vertical region in the majority of runs.Further one-sided trades then extract value at the pool’s expense.
- Profitability: 1 bp fee revenue yields approximately $5,400 gross margin, or 0.054%, on a $10M pool per horizon at minimum viable size.Revenue depends on trade frequency and notional, so insufficient order flow cannot justify locked capital.
- Practical sizing: At A = 500, capital halves but resilience fails; at A = 10, shock resistance requires approximately $95M TVL.The two configurations illustrate the capital-efficiency versus resilience trade-off.
6 Limitations
The analysis is bounded by simplified market, liquidity, rebalancing, and oracle assumptions. These limitations may make reported resilience and profitability differ from live institutional deployments.
- Shock analysis: Figure 5 varies A under 5×, 10×, and 20× shocks at $10M TVL, with imbalance crossing 50% near A = 500.The caption reports increasing imbalance above A = 200.
- Shock analysis: Figure 6 compares maximum slippage across shock sizes and $10M versus $100M TVL, showing a high-A plateau with increasing tail-run variance.The plateau accompanies transition toward constant-sum behavior.
- Rebalancing: Zero-latency rebalancing may understate realized slippage because block delays and mempool competition can let arbitrageurs extract LVR first.The bot may arrive late in practice.
- Rebalancing: Fixed gas costs may understate operational risk because congestion can make rebalancing unprofitable and allow the pool to drift from spot.Dynamic gas modeling is left for future work.
- Flow model: The simplified flow model omits autocorrelation, order fragmentation, and macro-driven informed flow, which would affect slippage and profitability.These features are present in real institutional flow.
- FX price process: The Merton jump-diffusion assumes constant volatility and independent jumps, excluding volatility clustering and liquidity-correlated jumps.Alternative specifications such as Heston or SABR are left for future comparison.
- Adversarial setting: Periodic adversarial shocks may understate vulnerability because sophisticated attackers could target oracle-lag or low-liquidity windows.Reported resilience metrics are therefore lower bounds on vulnerability.
- Oracle: Oracle manipulation, latency, and failure are not modeled, although a compromised oracle could drain the pool by shifting p∗ adversarially.This is a separate unmodeled attack surface.
7 Conclusion
On-chain FX liquidity is viable within a bounded (A, TVL) region. Capital efficiency improves with A, but shock resilience becomes the binding constraint at high amplification.
- 7 Conclusion: TVL/Q ≈1000/A, while ROC at minimum size remains positive, thin at approximately 0.054%, and A-invariant.For Q = $100,000 and 2-bps slippage, the viable range is A ∈[100, 200] with $5M–$10M TVL.
- 7 Conclusion: A ≥500 pools suffer reserve drain exceeding 40% and elevated tail slippage under adversarial flow.Thus, high-A capital efficiency is constrained by shock resilience.
Glossary
The glossary defines the AMM mechanisms, sizing and risk variables, pricing references, rebalancing concepts, and FX shock model used in the paper.
- Core mechanisms: AMM means a smart-contract exchange that uses a mathematical invariant to set prices and execute trades without an order book.
- Core mechanisms: CPMM uses xy = k, producing high price impact while preventing complete pool drainage.
- Core mechanisms: CSMM uses x + y = k, offering near-zero peg slippage but allowing complete drainage under one-sided flow.
- Core mechanisms: StableSwap interpolates between CPMM and CSMM through amplification factor A.
- Core mechanisms: A controls liquidity concentration: higher values are CSMM-like near the peg, while lower values are CPMM-like across the full range.
- Sizing variables: TVL is the aggregate USD value of pool assets and the primary capital-sizing variable.
- Sizing variables: D is the StableSwap liquidity invariant solved in normalized reserve units at each step.
- Pricing and operations: The oracle price p∗ is an off-chain FX reference used to normalize reserves and repegged when drift exceeds θpeg = 0.1%.