Research
On-Chain Liquidity Engineering
The quantitative research behind PGT. Four papers building an end-to-end LP derivatives stack — from impermanent-loss benchmarks to fully structured protection notes. Zero inflationary emissions.
View All Papers on SSRNWhitepapers
Evaluating Liquidity Provision Strategies for Automated Market Makers
LP tokens behave like a log-normal asset with half the spot drift and a –σ²⁄8 convexity penalty. Liquidity provision only beats HODLing when pool yield clears that hurdle.
Defines “volatility drag” and gives the simple rule y > μ/2 + σ²/8 for expectation parity (or y > σ²/8 risk-adjusted) between LPing and HODLing.
The LP Forward Contract: Quantifying Liquidity-Position Risk in DeFi
Shows LP spot – LP forward = fair cost of farming yield; makes impermanent-loss insurance an explicit premium.
Defines the forward, derives closed-form price, and decomposes any LP into “price risk” + “yield leg”. Perfect building block for hedging desks.
Liquidity Position Options: Transforming DeFi with Novel Risk Management Primitives
LP options let LPs cap impermanent loss or sell volatility; establishes LP put-call parity CLP – PLP = FLP.
Options pave the way for volatility trading & structured notes on LP risk, mirroring TradFi equity-derivative markets.
A Novel Financial Instrument for DeFi: Liquidity Protection Notes
LP Notes recycle project treasury tokens to fund principal protection, moving “mercenary liquidity” to locked, project-owned depth.
Explains collateral mechanics and why LP Notes outperform classic liquidity-mining on both cost and TVL stickiness.
Ready to protect
your community?
Deploying on Ethereum and Arbitrum. Get early access, explore the research, or talk to our team.