论文标题
流动性提供商在几何平均市场中的回报
Liquidity Provider Returns in Geometric Mean Markets
论文作者
论文摘要
几何平均做市商（G3MS）（例如Uniswap和Balancer）包括由以下规则定义的一类流行的自动化营销商（AMM）：每个交易前后AMM的储备必须具有相同的（加权）几何平均值。本文将恒定重量G3MS已知的几个结果扩展到了G3MS的一般情况，并具有随机变化和潜在的随机权重。这些结果包括投资者为G3MS提供流动性而获得的流动性池（LP）股票的回报和无契约价格。使用这些表达式，我们展示了如何创建LP股份复制金融衍生品的收益的G3M。所得的树篱是与模型无关的，并且对于衍生合同的衍生合同，其收益功能满足弹性约束。这些策略允许LP股票复制各种交易策略和财务合同，包括标准选择。因此，G3MS被证明能够通过LP股份中的被动职位来重现各种主动交易策略。
Geometric mean market makers (G3Ms), such as Uniswap and Balancer, comprise a popular class of automated market makers (AMMs) defined by the following rule: the reserves of the AMM before and after each trade must have the same (weighted) geometric mean. This paper extends several results known for constant-weight G3Ms to the general case of G3Ms with time-varying and potentially stochastic weights. These results include the returns and no-arbitrage prices of liquidity pool (LP) shares that investors receive for supplying liquidity to G3Ms. Using these expressions, we show how to create G3Ms whose LP shares replicate the payoffs of financial derivatives. The resulting hedges are model-independent and exact for derivative contracts whose payoff functions satisfy an elasticity constraint. These strategies allow LP shares to replicate various trading strategies and financial contracts, including standard options. G3Ms are thus shown to be capable of recreating a variety of active trading strategies through passive positions in LP shares.
