Liquidity-Saving Mechanisms for 24/7 Instant Payment Systems: Rolling Liquidity Bounds, Certified Offsetting, and an Open Benchmark (Zenodo)

Summary

• The authors establish the first analytical bounds on liquidity for 24/7 instant payment systems where payments must be settled within a delay cap T.p.1
• For a 1-minute delay cap, simulations show that at most 0.55% of liquidity remains available for any engine to save, and no more than 0.73% across 81 synthetic configurations.p.1
• Max-value settlement (MVS) is proven to be strongly NP-hard even when every bank balance is zero, ruling out an FPTAS unless P = NP.p.2
• Without an end-of-day reset, the worst 24-hour liquidity window required 3.5× the worst calendar-day lower bound in simulation models.p.1
• Simultaneous batch netting is mathematically proven to always perform as well as or better than any linear payment ordering.p.1
• In a time-indexed MIP test on 270 small instances, the theoretical liquidity floor was exactly attained in 255 instances (94.4%).p.4

Key insights

1. Liquidity floors equal the traditional real-time gross settlement bound at T = 0 and decrease as the delay cap T increases.p.1
2. Short delay caps severely limit potential liquidity savings, leaving a maximum possible saving bound of 0.73% for 1-minute caps and 2.9% for 5-minute caps across tested configurations.p.4
3. The theoretical minimum liquidity floor is not always attainable in practice, as shown by a two-bank, four-payment counterexample.p.1
4. Settling a payment batch simultaneously using netting dominates any payment reordering heuristic, executing in linear time O(|β| + n).p.6
5. Rolling liquidity bounds designed for 24/7 payment flows are proven to be ordered, monotone, and consistent with classic daily bounds.p.1
6. On simulated core-periphery business days, offsetting engines eliminate all unsettled value at the end of the day.p.4
7. Quantum annealing reordering heuristics are rendered unnecessary whenever simultaneous batch netting is permitted.p.5