The Price of Liquidity: Implied Volatility of Automated Market Maker Fees

An automated market maker (AMM) provides a method for creating a decentralized exchange on the blockchain. For this purpose, individual investors lend liquidity to the AMM pool in exchange for a stream of fees earned from its operations as a market maker. Within this work, we reinterpret the loss-versus-rebalancing as the implied fee stream generated by an AMM so that a risk-neutral investor is indifferent in the decision of providing liquidity. With this implied fee structure, we propose a novel fixed-for-floating swap on the fees generated by an AMM in order to quote the implied volatilities and implied correlations of digital assets. We apply this theory to realized fees in different markets to empirically validate the relevance of the deduced fee-based volatility.