Written by | Banach

Time | 2021.01.24

Produced | NEST fans (nestfans.com) authorized by the author to publish

Produced | NEST fans (nestfans.com) authorized by the author to publishWhen you develop DEX, the essence is to design a trading operator

, this operator can be linear or nonlinear. Similarly, when you design an interest rate operator, you are essentially designing a transaction operator. There is also a difference between linear and nonlinear. But this difference is not easy for most people to understand.The meaning of linearity means that when we complete the transaction, we useequilibrium price, the transaction is just a simple linear transformation of the asset portfolio at this price. Why is it linear at this time, because the equilibrium price theory is used to accept the no-arbitrage assumption. In this case, reasonable financial transactions are linear. If there is a nonlinear result, such as STP = Y, T is nonlinear , then the obtained Y is an unpriced asset portfolio, or an asset portfolio with arbitrage opportunities.

In principle, the transaction model of the oracle machine is used, and its transaction operator should be linear, otherwise it will be arbitraged. From another perspective, as long as the market is complete and pricing is effective, only linear trading operators will have no arbitrage.But a linear representation of a feature:Any pool is equal and the operator cannot be tokenized, because it is exactly the same after being copied.

It needs to be mentioned here that the so-called agreement captures value on the chain and tokenization is two expressions of the same concept, that is, this agreement has the ability to build a new equilibrium. If it is only a linear transformation on the existing equilibrium (for No arbitrage, that's all), it is impossible to capture value. Imagine that when each asset on the chain accepts a given equilibrium price, these assets complete transactions, which are equivalent in any contract, and do not need to be completed in the specified contract, because these transactions are simple If there is a linear transformation, it is impossible for any transaction contract or transaction operator to capture value and tokenize it. Without considering automatic hedging, copying a CoFiX contract can complete the same function as CoFiX. It doesn't matter which contract the so-called liquidity is dispersed in (regardless of GAS), the chain is a complete In the open world, linear transformation means equivalent everywhere.It is different if a non-linear trading operator is used. At this time, according to the above analysis, there is no need for an oracle.Non-linear operators try to accomplish three things: pricing, trading, and depositing value (tokenization).

Since the non-linear trading operator is more open in design, it can in principle be designed as a scale-related self-reinforcing property to accumulate value (CoFiX does not need this. For how to tokenize CoFiX, see the trigger operator later). It brings about several problems: one is that when the market is gradually complete, the nonlinear trading operator essentially fits the linear operator in a very small transaction scale; the other is that when the market is not complete, the nonlinear trading operator Are the design, cost and efficiency of the trading operator adequate? The third is who will provide the non-linear value input? Will this value input gradually be lost under the competition of linear transaction operators?As mentioned earlier, when the market is complete, the arbitrage-free transaction is linear. Therefore, when the nonlinear operator completes the transaction, its rationality depends entirely on the effectiveness of the market. Once the market is complete enough, then the non-linear transaction algorithm Subcontracts are essentially fitting linear operators in extremely small intervals.，We see that many AMMs currently adopt the so-called fixed product trading model, XY = K, which is a typical scale-related nonlinear trading operatorThat is, only when the pool of market makers is large enough, partial simulation of linear transactions becomes possible, that is, if the trading object of AMM is a complete market, its core significance lies in the effectiveness of the post-fitting of the scale effect (the arbitrage loss is small), this effectiveness is not very essential,

In comparison, CoFiX is more essential and natural.The reason for this,It is because many people want to put pricing power on the chain, which is an illusion, because when the market is complete (simply speaking, the supply and demand are extremely huge, and no one can manipulate the market), the advantages of centralized exchanges are very obvious, or more essentially, every behavior on the chain is after the auction The gap between this and the demand for pricing trading services is too large. Pricing trading is an extreme activity. Even normal centralized exchanges have the highest requirements for computing storage and communication, not to mention the discreteness and auction attributes on the chain. This cannot be used for efficient pricing in a complete market. What about an incomplete market? For example, those tail assets that everyone often talks about? new project? At this time, the core problem is not being arbitraged, or there is no such validity testing and demand,The demand at this time should be to form prices quickly and at low cost and complete a large number of transactions. The constraints are mainly two costs: the cost of quickly forming prices, and the cost of completing larger-scale transactions.

Note that the cost here is not marketing cost or traffic cost, but the endogenous cost of a pure transaction operator. Taking a transaction operator such as XY = K as an example, this cost includes the correlation between the cost formed in the AMM fund pool and the slippage Here, this endogenous cost and efficiency distinguish the value of various trading operators.In addition, an important issue is that these nonlinear trading operators combine pricing and trading at the same time, and they also need to withstand the competition of linear trading models that accept oracles (price operators). Under this competition, at least Transaction efficiency is completely incomparable:The trading efficiency of trading operators under the oracle far exceeds that of non-linear trading operators.

The remaining comparative advantages are pricing cost and efficiency, which can be studied in depth and comprehensively, but linear operators are intuitively superior.Continue to discuss the third problem of nonlinear trading operators,value input problem. This problem is also very fatal,From the perspective of a complete market, there must be a large number of small transactions (fitting linear operators) to input value, so as to compensate for the arbitrage loss of nonlinear operators when the equilibrium price fluctuates

, this constraint is very strict, because a large number of small demands (relative to the AMM pool, or the pool is large enough, all ordinary transactions are relatively small) will often be eliminated from the market due to the increase in the marginal cost on the chain, equal to In the long run, it is not conducive to the survival of operators on this chain. If the market is highly incomplete, and there are indeed a large number of traders who do not care about price slippage, then any nonlinear operator can fulfill this transaction requirement, and the important thing here is to complete as many transactions as possible (price insensitive) , which turns into a quasi-linear model. For example, in the transaction of stable coins, the XY = K model has to be changed to reduce the nonlinear characteristics, which is not conducive to the precipitation value.From the above three characteristics, the nonlinearity of transaction operators is not a valuable direction, or in the protocol group that deposits decentralized value on the chain, non-linear transaction operators are not what we are looking for That type of non-linear operator: trading should not do this

. What is interesting is that the interest rate operator mentioned earlier is also a trading operator. This operator is slightly different from pure secondary market transactions. This difference stems from the difficulty of interest rate arbitrage: there is not enough term structure trading market for You go to realize the arbitrage. This is why many people think that lending on the chain is more reliable than trading, not because of any essential reason, but because of the effectiveness or difficulty of arbitrage. At present, the interest rate market on the blockchain is very thin, and the transaction has not reached the point of being effective. At this time, there is no good interest rate oracle machine. Therefore, there is a certain value in pricing interest rates with non-linear operators, but this value It is an expedient measure, not an essential innovation.Non-linear trading operators can also be improved. This improvement needs to introduce recursive information, that is, capture some valuable components in historical transaction information, thereby reducing the risk of arbitrage, this part of the current market research is very little, but many people have realized that the so-called impermanent loss of the current DEX can be reduced based on the combination of recursive operators and nonlinear trading operators. These ideas are not difficult.