Viable Pool Sizing for On-Chain FX Liquidity: Amplification, Capital, and Resilience
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.