Performance Guarantees for Permissionless Lending (arXiv (Cornell University))

Summary

• The paper introduces a permissionless asynchronous lending protocol offering fixed-rate, fixed-duration loans with mathematical performance guarantees [p.1].p.1
• Participants engage in tâtonnement-like dynamics via competing interest-rate offers to discover market rates without relying on a central authority [p.1].p.1
• Under independent and identically distributed Gaussian log-valuation returns, exact expressions are derived for borrower liquidation and lender repayment shortfall probabilities [p.2].p.2
• Daily BTC-USD return data from September 7, 2021 to September 6, 2026 is evaluated to fit Gaussian, Student-t, and symmetric stable Paretian distributions [p.19].p.19
• For an example 30-day loan with a 6.00% annual interest rate and ρ = 1.20, the symmetric stable Paretian model yields a 34.55% 30-day liquidation probability [p.20].p.20
• Within the same 30-day example, the fitted Gaussian model yields a liquidation probability of 31.03% and a repayment shortfall probability of 0.90% [p.20].p.20

Key insights

1. Existing pool-based permissionless lending protocols lack formal risk guarantees and expose users to arbitrary rate settings and manipulation risks [p.1].p.1
2. Fixed-rate peer-to-peer lending contracts eliminate interest rate volatility and third-party manipulation throughout the duration of the loan [p.2].p.2
3. Trustless protocol execution necessitates over-collateralization where collateral value exceeds the borrowed loan principal [p.2].p.2
4. Defining health factors relative to accrued debt rather than terminal maturity value provides an adaptive and less conservative risk measure [p.9].p.9
5. Avoiding frequent liquidations requires collateral values to appreciate geometrically faster than accrued debt [p.16].p.16
6. Lender repayment shortfall occurs only when collateral value falls below accrued debt at the time liquidation is triggered [p.17].p.17
7. AIC and BIC model selection criteria both favor the Student-t distribution over Gaussian and symmetric stable Paretian distributions for daily BTC-USD returns [p.20].p.20
8. Heavy-tailed distributions like Student-t and symmetric stable Paretian project higher short-term liquidation risks than Gaussian models due to tail risk [p.20].p.20