Research

The math behind the thesis.

Four papers formalize the mechanics Liquidity Preferred relies on: how to price LP risk, how to hedge it, and how to package it into a primitive that protects holders. This is the rigor under the preferred-token argument.

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The papers

y > σ²/8

Evaluating Liquidity Provision Strategies for Automated Market Makers

Jan 2023 · 8 pp.

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.

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F = 2D√S · e^−σ²τ/8

The LP Forward Contract: Quantifying Liquidity-Position Risk in DeFi

Feb 2023 · 7 pp.

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.

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C − P = F

Liquidity Position Options: Transforming DeFi with Novel Risk Management Primitives

Mar 2023 · 8 pp.

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.

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N = Z + C − P + (1+β)Y

A Novel Financial Instrument for DeFi: Liquidity Protection Notes

Mar 2023 · 6 pp.

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.

This paper packages a zero-coupon bond, LP options, and boosted yield into a single instrument for principal protection. Funded by recycling project treasury tokens rather than inflationary emissions, the structure converts mercenary capital into sticky, project-aligned liquidity depth.

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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 primitive. Liquidity Preferred is built from that progression: collateral-backed downside protection, full upside, and protocol-owned liquidity.

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