The Theoretical Foundations of Protected Liquidity
Four papers. One framework. The mathematical basis for turning LP tokens into hedgable, structurable financial instruments — and the research that underpins everything Exchequer builds.
View All Papers on SSRNWhitepapers
Evaluating Liquidity Provision Strategies for Automated Market Makers
The problem it solves: LPs had no rigorous way to know when providing liquidity actually beats holding. This paper gives them the answer.
LP tokens behave like a log-normal asset carrying a –σ²/8 convexity drag. The paper derives the precise yield threshold — y > σ²/8 — that an LP must clear to outperform a simple hold position. This benchmark is now widely referenced across DeFi risk analysis.
View on SSRN →The LP Forward Contract: Quantifying Liquidity-Position Risk in DeFi
The problem it solves: There was no way to isolate and price LP risk separately from LP yield. This paper creates the instrument to do it.
Introduces the LP Forward — a contract that strips yield from price exposure, allowing impermanent loss to be priced as an explicit premium using Black-Scholes. Decomposes any LP position into a price-risk leg and a yield leg, giving hedging desks the building block they need.
View on SSRN →Liquidity Position Options: Transforming DeFi with Novel Risk Management Primitives
The problem it solves: LPs had no way to cap their downside or express a view on LP volatility. This paper introduces the options to do both.
Defines LP calls and puts, proves that a power-½ transformation unlocks closed-form Black-Scholes pricing, and establishes LP put-call parity: CLP – PLP = FLP. Opens the door to volatility trading and structured products on liquidity positions.
View on SSRN →A Novel Financial Instrument for DeFi: Liquidity Protection Notes
The problem it solves: Protocol liquidity programs bleed tokens through emissions with no downside protection and no LP loyalty. This paper designs the fix.
The LP Note packages a zero-coupon bond, LP options, and boosted yield into a single instrument delivering ~75% principal protection. Funded by recycling project treasury tokens rather than inflationary emissions, LP Notes convert mercenary capital into sticky, project-aligned liquidity depth.
View on SSRN →How the Papers Connect
These four papers form a deliberate progression: Paper 01 establishes when LPing creates value. Paper 02 makes LP risk isolatable and priceable. Paper 03 makes LP risk tradeable. Paper 04 packages everything into a product that aligns protocol and LP incentives. This is the theoretical stack behind Exchequer's Protected Growth Tokens and LP Notes. Every product we ship is built on this framework.