Rethinking Cryptocurrencies: Liquidity and Valuation

Abstract

In this paper, we integrated the literature on constant function market makers (CFMMs), a recent invention on the blockchain, with the broader field of monetary economics to arrive at a novel framework for explaining cryptocurrency prices and utility in terms of their liquidity profile with goods. CFMMs utilize invariant curves for constant time determination of the exchange ratio between tokens. By defining liquidity in terms of invariant curves of liquidity pools, we were able to empirically show how access to liquidity impacts the utility of risk-averse traders in face of volatile market movements. Additionally, we developed an augmented model of Walrasian auction in which the arbitrage of CFMMs is considered and included in the market clearance equation. We introduced tokens as a means of purchasing claim to liquidity, and developed approximate equilibrium solvers to calculate token prices based on the Gale-Nikaido-Debreu lemma, assuming rational expectations. We showed that token prices are positively impacted by the amount of locked liquidity. Additionally, we posited how factors such as skewness of liquidity and circulation of tokens may affect token price. Our empirical results were inconclusive, and we suggested modifications to our market model that may resolve the issues. Lastly, we included supplementary discussions about liquidity on CFMMs that serves to motivate further exploration of the topic. We also appended a brief commentary on the expected utility of liquidity provision, particularly the path dependence of liquidity fees.