Exploring the Dynamics of Liquidity Pools: A Mathematical Approach

Automated market making for crypto tokens is an extremely attractive and efficient way to establish decentralized exchanges. An inevitable prerequisite for this type of market is the willingness of participants to provide liquidity. Except in the case of two correlated pairs, providing liquidity is often sub-optimal. In fact, one often faces significant opportunity cost commonly referred to as impermanent loss. Prevailing transaction fee levels, even with levered positions, are often insufficient to compensate for the opportunity costs incurred. Marketability and exchangeability are essential prerequisites for attributing value to many crypto tokens. Therefore, when issuing fiat tokens for the viability of intriguing business models, one ends up with the chicken-or-the-egg causality dilemma: how to achieve sustainable incentives to the liquidity provision for an abstract good whose intrinsic value is defined solely by that liquidity system? This talk derives and discusses useful formulas for the quantitative risk management in the context of automated market makers. In addition, order size and pool size dependent transaction costs are proposed that may incentivize the desired level of liquidity.