The math behind the thesis.
Four papers formalize the mechanics PGTs rely on: how to price LP risk, how to hedge it, and how to package it into an instrument that protects holders. This is the rigor under the preferred-token argument.
View All Papers on SSRNThe papers
Evaluating Liquidity Provision Strategies for Automated Market Makers
Why it matters for preferred tokens: 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
Why it matters for preferred tokens: 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
Why it matters for preferred tokens: 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
Why it matters for preferred tokens: 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 the mechanical stack underneath preferred tokens. Paper 01 establishes when LPing creates value instead of hidden drag. Paper 02 makes LP risk isolatable and priceable. Paper 03 makes that risk hedgeable and tradeable. Paper 04 packages the primitives into a protected instrument. PGT is the first preferred token built from that progression: collateral-backed downside protection, full upside, and protocol-owned liquidity.