A Brief Review of the Price Discovery Procedures of AMM
The AMM-based trading paradigm is popular in DeFi world, largely because it provides an extremely easy way to organize liquidity for trading. Whereas the traditional way, i.e. orderbook, requires high expertise from the liquidity providers (i.e. the market makers). The easiness of liquidity-providing for trading is a revolutionary property of AMM. It does not just have financial but also social significance. However, this is beyond the scope of our current discussion. We will only focus on the technical part of finance. The core function of AMM is price discovery. From an epistemological perspective, the price discovery of AMM is a process of obtaining knowledge (i.e. the prices). Therefore, AMM can be categorized per their price discovery procedures.
- Ab intus without a priori knowledge: the regular AMMs like constant product market makers (CPMM), e.g. Uniswap V2 or Balancer, determine their prices completely by the local transactions.
- Ab intus with a priori knowledge: the stableswap of Curve V1 is largely similar to CPMM except it adopts the a priori knowledge that price=1.
- Guided by external information: AMMs like PMM, e.g. DODO, depend on oracle price input as a guide to its price discovery.
The choice of specific AMM type largely depends on the trading characteristics. First of all, if there is some a priori knowledge, it is better to adopt it and hence take the second approach (ab intus with a priori knowledge). Curve has become the dominant AMM for stablecoins mainly because it makes good use of the a priori knowledge about the price and thus achieves a superb financial efficiency. However, what the stableswap of Curve deals with is a very special scenario. In more general cases, a priori knowledge is usually unavailable. For general cases, if the price discrepancy with external markets is not a major concern, then the first type of AMM would be an elegant solution. This is usually the case when an AMM has authority or dominance in the price discoveries across all markets. For spot trading, it is usually so for those “long-tail” pairs, which are primarily (or even solely) traded on a single AMM, e.g. Uniswap. However, when an AMM does not dominate the price discoveries across all markets, then the price discrepancy with external markets becomes a problem. For the first type of AMM, there is no “built-in” mechanism to synchronize the price with external markets. Instead, such synchronization is handled by a “plug-in” mechanism: traders take arbitrage and consequently converge the price to external markets. In general, such a “plug-in” mechanism is financially inefficient compared to built-in mechanisms. The so-called “impermanent loss” is the cost for such inefficiency. In other words, the AMM (or it’s really the liquidity providers) pays the arbitrageurs to synchronize the prices at the cost of “impermanent loss”. Therefore, when an AMM has neither a priori knowledge nor dominance of price discoveries across all markets, the third approach, i.e. adopting guide by external information, might be a pragmatic choice.
There are two special cases worthy of special discussion.
Curve V2 extends its application to non-stablecoins by introducing an “internal oracle” to dynamically repeg the stableswap curve. The knowledge about “repegging” (given by “internal oracle”) is learned from past experiences (a posteriori but ab intus), rather than a priori. So the AMM of Curve V2 for non-stablecoins belongs to the first category.
Uniswap V3 adopts a very special external mechanism to optimize the price synchronization: range orders. When LPs provide liquidity with specified “ranges”, they implicitly bring in a lot of external market information to guide the price discovery, which substantially enhances the financial efficiency of the price synchronization. In other words, instead of solely depending on the arbitrageurs, Uniswap V3 lets the liquidity providers help synchronize the price, at zero cost. (Our discussion is from a financial perspective so gas cost is not in consideration.) However, similar to the orderbook paradigm, this requires relatively high expertise from the liquidity providers. Such a dependency on the guide by external information makes Uniswap V3 more of a third-type AMM.
We are especially interested in the case of derivative trading, where price synchronization with external markets is a core issue. For derivative trading, what is happening in external markets is a major concern, simply because the value of a derivative depends on the underlier price, by definition. Therefore, the third approach might play a more important role in derivative trading.
It is noted that some of the DeFi derivative trading protocols do choose the first approach and leave the price synchronization to the external arbitrage mechanism. While such an arbitrage mechanism would eventually synchronize the price, it is rather inefficient. This is the major problem for such derivative AMM (or called vAMM in some applications).
In a few weeks, we are rolling out AMM-based everlasting options as part of Deri Protocol. We choose to base our implementation on the Proactive Market Making framework, which is a prudent choice after a thorough review and analysis of the existing AMM types. In this article we explains our rationale behind our AMM choice: as a representative of the third type of AMM, the price discovery of PMM converges to the external markets much faster than the first approach (the regular AMM).
About Deri Protocol
Deri Protocol is a decentralized protocol for users to exchange risk exposures precisely and capital efficiently. It is the DeFi way to trade derivatives: to hedge, to speculate, to arbitrage, all on chain. This is achieved by liquidity pools playing the roles of counterparties for users. With Deri Protocol, risk exposures are tokenized as NFTs so that they can be imported into other DeFi projects for their own financial purpose. Having provided an effective on-chain mechanism to exchange and hold risk, Deri Protocol has minted one of the most important blocks of the DeFi infrastructure.
