Volatility and Liquidity Provider Payoffs in Automated Market Makers

Summary

The document derives a preliminary formula for the expected fee cash flow earned by liquidity providers on decentralized exchanges. It assumes efficient markets, geometric Brownian price movements, and the absence of arbitrage. In this formulation, trading volume is no longer treated as an external input to fee calculations; instead, it depends on the asset’s volatility and the liquidity available.

The authors report that the resulting volume relationship is close to linear in underlying asset volatility. They discuss whether securitized liquidity-fee cash flows could therefore function as a volatility product. This is a theoretical derivation under simplifying assumptions, not evidence that fee income reliably tracks volatility in actual pools. The supplied description gives no empirical validation, implementation details, or treatment of practical factors such as changing liquidity, fee tiers, and adverse selection, which could affect realized provider payoffs.

Key ideas

• The paper formulates expected liquidity provider fee cash flow for automated market makers.
• Its derivation assumes geometric Brownian prices, efficient markets, and zero arbitrage.
• Trading volume is modeled as depending on volatility and available liquidity.
• The derived relationship between volume and asset volatility is described as near-linear.
• Securitized fee cash flows are proposed as a possible volatility product, without empirical validation in the supplied description.

Tags

# Liquidity Provision Payoff on Automated Market Makers


# Liquidity Provision Payoff on Automated Market Makers









The standard approach for compensating liquidity providers on many decentralized exchanges (DEX) for serving as counter-party to swaps is through charging a small percentage of fees. The expected payoff from the cash flow of this mode of market making has yet to be mathematically formulated in terms of volatility in the existing literature. We provide here a preliminary derivation of the payoff formula, by making the standard set of assumptions for efficient markets, namely geometric Brownian price movements and zero arbitrage. Trading volume, conventionally taken as an exogenous variable for fees calculation, becomes a function of volatility and available liquidity in this formulation. In doing so, we show that it is a near-linear function of the volatility of the underlying risky asset. Since hedging instruments with such a property are highly sought after, we discuss the potential of securitizing the cash flow of liquidity fees to serve as a volatility product in its own right.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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