Dynamic Curves for Decentralized Autonomous Cryptocurrency Exchanges

Abstract

One of the exciting recent developments in decentralized finance (DeFi) has been the development of decentralized cryptocurrency exchanges that can autonomously handle conversion between different cryptocurrencies. Decentralized exchange protocols such as Uniswap, Curve and other types of Automated Market Makers (AMMs) maintain a liquidity pool (LP) of two or more assets constrained to maintain at all times a mathematical relation to each other, defined by a given function or curve. Examples of such functions are the constant-sum and constantproduct AMMs. Existing systems however suffer from several challenges. They require external arbitrageurs to restore the price of tokens in the pool to match the market price. Such activities can potentially drain resources from the liquidity pool. In particular dramatic market price changes can result in low liquidity with respect to one or more of the assets and reduce the total value of the LP. We propose in this work a new approach to constructing the AMM by proposing the idea of dynamic curves. It utilizes input from a market price oracle to modify the mathematical relationship between the assets so that the pool price continuously and automatically adjusts to be identical to the market price. This approach eliminates arbitrage opportunities and, as we show through simulations, maintains liquidity in the LP for all assets and the total value of the LP over a wide range of market prices.

Composing Networks of Automated Market Makers

“…To make this presentation selfcontained, we list some informal, common-sense axioms any practical AMM should satisfy, and then restate these informal requirements as more precise mathematical properties. These properties mirror prior proposals [5,8,17], with some adjustments to encompass higher-dimensional AMMs (those that trade more than two kinds of assets), and to facilitate later introduction of composition operators.…”

“…AMMs are increasingly being integrated with external price information oracles. For example, Krishnamachari et al [17] describe a family of AMMs capable of adjusting their curves in response to reported price changes. In future work, we plan to investigate composition for AMMs that make use of oracle services..…”

A theory of Automated Market Makers in DeFi

“…We conjecture that the invariants in [3,19] are incentive-consistent. The work [22] proposes a dynamic constant product invariant, parameterized by oracle prices: the invariant is adjusted dynamically based on the oracle price feed, thus reducing the need for arbitrage transactions at the cost of lower fee accrual. AMMs with virtual balances have been proposed [2] and implemented [6,7], where the swap rate depends, besides the current funds balances in the AMM, on past actions.…”

“…AMMs with virtual balances have been proposed [2] and implemented [6,7], where the swap rate depends, besides the current funds balances in the AMM, on past actions. This, similarly to [22], aims to minimize the necessity for arbitrage transactions to ensure the local AMM swap rate tends towards the exchange rates. Our model can be extended to capture dynamic funds invariants and virtual balances.…”

G3Ms:Generalized Mean Market Makers

“…Moreover, a trading function defined by means of a (weighted) geometric mean gives rise to a CFMM [7] closely related to the constant product CFMM. Alternately, instead of exploiting a constant product or geometric mean trading function, constant sum or arithmetic mean trading functions can also be used to define a CFMM, resulting in a constant sum or arithmetic mean CFMM [6].…”