Liquidity Providers Greeks and Impermanent Gain

Paper: arXiv 2302.11942

Authors: Niccolò Bardoscia, Alessandro Nodari

Abstract

In traditional finance, the Black & Scholes model has guided almost 50 years of derivatives pricing, defining a standard to model any volatility-based product. With the rise of Decentralized Finance (DeFi) and constant product Automated Market Makers (AMMs), Liquidity Providers (LPs) are playing an increasingly important role in markets functioning, but, as the recent bear market highlighted, they are exposed to important risks such as Impermanent Loss (IL). In this paper, we tailor the formulas introduced by Black & Scholes to DeFi, proposing a method to calculate the greeks of an LP. We also introduce Impermanent Gain, a product that LPs can use to hedge their position and traders can use to bet on a rise in volatility and benefit from large market moves.

Complexity vs Empirical Score

• Math Complexity: 6.0/10
• Empirical Rigor: 3.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents an innovative adaptation of Black-Scholes Greeks to Automated Market Maker (AMM) liquidity provision and introduces a new hedging primitive (‘Impermanent Gain’). While mathematically sound and conceptually novel for DeFi, it lacks extensive empirical backtesting and historical data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Hedge LP Impermanent Loss & Model DeFi Risk"] --> B["Input: Black-Scholes Model & AMM Mechanics"]
    B --> C["Tailor Black-Scholes Formulas to Constant Product AMMs"]
    C --> D["Derive LP Greeks (Delta, Gamma, Vega)"]
    D --> E["Design 'Impermanent Gain' Derivatives"]
    E --> F["Outcomes: Precise Risk Modeling & New Volatility Hedging Product"]