译文/Translated：
今天我要介绍一个新的代币挂钩算法，它能带来高流量、减少价差，同时，就算抵押品价值减少，它也能有效地防止违约。我们的算法是高度过度担保的空头头寸，它和Bancor算法一起，对多头和空头头寸提供了流量。我们用价格馈源来引导市场，但是它的影响仅限于出现长期偏离的时候，以免出现做市商滥用。
背景
2013年比特股引入了BitUSD的概念，这是由BTS代币支持的“智能币”，它瞄准了美元价值。BitUSD在想利用BTS做杠杆人和想保持价格稳定的人之间创建订单簿。为了给购买BitUSD的人提供流量，BitUSD持有人可以在多日延迟之后强制平仓至少抵押的空头头寸。这就创造了一个有效的追加保证金，保证BitUSD买家的代币总是价值一美元的BTS。为了避免违约，如果价值馈源低于最低保证金要求，最低抵押头寸可能也会被强制平仓。
BitUSD体系的主要问题是缺少流量，发行的BitUSD太少，以及市场价差。做市商需要运行交易机器人，实现在内部订单簿上移动订单。尽管BitUSD持有人能获得一定的流量，短期头寸并不能保证一定有流量。最后，万一最小抵押头寸不能获得保证，那么整个市场都受到黑天鹅事件的影响。一旦如此，这种挂钩体系就会永久崩塌，最终在BitUSD和BTS上就会产生固定交易费用。
BitUSD供应量很少、价差很高，这主要由几个原因：BitUSD不是因为激励机制产生的、低流量风险大（如果没有不合理的下滑就不能补偿）、突然要求增加保证金、运行安全的做市商机器人难度大。
像这样利用各类过度担保头寸和提出保证金要求的项目还有很多，但是它们都和BitUSD有同样的问题。
传统的衍生市场采用“期货交易”，即允许人们提供抵押品、在未来某个固定的时间以固定的价格进行结算。这些期货合约都是可替代的、可以在一定时间内进行交易，但是因为有期限问题以及结算/转仓要求，它们并不适合用来创建挂钩代币。
Bancor算法提供了两个资产间的自动流量，同时保证再狡猾的交易者都不能窃取其储备金。不管Bancor算法执行的订单数量和种类有多少，当资产组价格回到原点时，该算法总是能产生利润。一般的Bancor做市商是两个“连接器”间的接力（Relay），这两个连接器代表了相等的市场价值的结余。该算法成功地在诸如EOS RAM等市场上提供了自动流量。
挂钩算法
挂钩算法的基本概念是挂钩代币是空头对多头的服务。该服务要求空头为挂钩代币提供流量。如果(市场)对挂钩代币产生需求，那么对于交易提供者来说，做市商赚的交易费用就是有利可图的，即使是在相对萧条的市场也是如此。
其它的挂钩算法让卖空者相互竞争而不是促成合作，从而实现把挂钩货币服务带向市场的目标。在这样的算法中，空头相互竞争，回补和抵押头寸，担心被空头挤压。
而我们算法的前提是：如果有人愿意稍长时间地在某质押资产（如EOS）上使用杠杆，那么他就能因为促进EOS和某可替代地挂钩资产（如USD）的做市活动而获利，这个挂钩资产应该能够在一定的偏差值间瞄准某个价格馈源。
我们的算法不会让用户创建独立的空头，我们会创建一个全局空头，让用户在这个全局空头中购买和出售份额。在中间没有发生其它交易的情况下，在空头中购买和出售份额是中性且可逆的过程（减去交易费用）。杠杆不是主要动力，交易费用才是在空头中购买份额的动力。这就是说，400%甚至以上的超额担保是可行的，卖空者只要在质押资产中稍微使用杠杆就有机会赚取交易费用。
做市商首先是通过在合约中存入质押品形成。合约会在做市商（MMS）中形成代币并将代币交给初始的存入方。比如说，假定质押品是EOS，挂钩代币是美元，代币要追踪24小时内的EOS对应美元的中位数。
目标准备金率比如是400%。基于4倍准备金的原则，75%的存入的EOS会被归为超额质押，25%会放在权重50%的Bancor Relay连接器。此时，自动化的做市商合约就会产生一定数量的USD代币给第二个Bancor Relay 连接器提供资金，这样，EOS的市场价值和USD连接器结余都等于价格馈源的初始价值。
初始状态下，做市商在连接其中拥有100%的USD，因此没有任何净流量（必须购买回来的USD）。MMS的账面价值等于连接器中的EOS价值加上超额质押的EOS减去任何连接器中出售的流通中的USD。初始设置之后，任何人都可以从做市商手上购买USD，MMS持有人就有了未来必须回购的负债。Bancor Relay算法的数学性质说明，用户从做市商手上购买USD之后，报价将会上升。如果每个人都购买USD然后重新出售，那么连接器最终将回到初始状态。任何交易费用将会带来连接器结余的EOS净增长。
这个设定以及400%的储备金目标，我们可以看到，实际储备金和USD的比值将会远远超过400%。如果要低于400%（没有市场价格变化），整个USD连接器只能买断，这就会推动USD价格无限上涨。实际上，随着多头USD多头数量减少，做市商会主动提高购买USD的多头成本。
做市商提供的现货价值等于EOS和连接词余额中的USD比值。当现货价格和价格馈源偏差超过可接受的幅度（如+/-2%）超过可接受的时间（如24小时），那么做市商会根据市场情况执行以下几个动作：
SPOT = price of USD according to Bancor
FEED_USD = price of a federal reserve note in EOSif( SPOT > FEED_USD )
if( Excess Collateral < 3x EOS Connector )
then slowly move EOS Connector to Excess (lowering SPOT)
else
then slowly add new USD to Connector (lowering SPOT)else if( SPOT < FEED_USD )
if( excess collateral )
then gradually buy USD using excess collateral
and destroy it (raising SPOT)else do nothing
该算法的目标是把状态移动到更加接近初始状态，即Bancor余额多3倍的超额质押以及USD连接器中100%的USD。只要还有流通的USD，很明显想要实现连接器中100%的USD都是不可实现的，但是当EOS价值远远高过USD时，流通供给的百分比会下降。
质押品转移或USD发行速度目标应该是在一段目标时间内（如一小时）实现可接受的范围内的价格修正。理论上来说，交易者在购买和出售USD的时候应该假定该USD等于1美元，因为他们有信心他们在短期内是可以以1美元的价格销售该USD。这就是说，当EOS和USD的相对价格稳定的时候，做市商不需要依靠价格馈源修正实时价格，Bancor算法对抗操控的机制能够保护连接器结余不至于被非法转移给交易者。
设置参数的时候，如馈源偏移、修正率、价格修正开始前的延期等，很重要的一点是尽量减少积极干预做市商的必要性频率。如果确实需要干预，那么也应该是逐步干预。市场参与者不应该抢在做市商之前获益。
该算法的结果是形成挂钩资产，该资产对应24小时的中位数而不是瞬间价值。只有24小时做市商中位数远远大于24小时实际市场中位数的时候，它才会主动地修改挂钩。当实际市场下跌的时候，我们希望交易者能够利用Bancor算法刻意领跑24小时的中位数，这样地领跑会防止出现Bancor连接器的强制修正，除非是遇到延时过长的情况。中位数价格变化越慢，做市商面临的风险就越低，但是挂钩的USD和实际USD的偏差就越小。受馈源影响，让Bancor算法能够有更大的偏移（如5%）还能够减少人为干涉价格的影响。人为干预越少，价格馈源瞬间准确度的相关性越小。
购买和出售MMS代币
任何人在任何时候都可以利用新的EOS购买MMS和USD的组合。该机制运行的原理是维持Bancor连接器中MMS，EOS，USD的比例并再加入新的EOS之后维持流通中的USD。个人用户会获得MMS和流通中的USD对应的新增EOS的1%。USD和EOS也会被加到连接器和超额储备金中。用户就可以出售USD获得EOS，以此反复或就持有相应超额的USD或EOS。
出售MMS代币需要提供等于“流通中的USD*出售的MMS/供应的MMS”的USD。这和他们在第一时间用EOS购买MMS（减去任何交易费用）可以获得的USD数量。
这个过程可以被看作是分割和连接相同的空头头寸。只要你能控制空头头寸的所有未偿债务，你就可以解除它、收回所有质押品。这个过程的关键是保持不变性：用质押物购买/出售做市商，或购买/出售做市商以获得质押物不会改变MMS，EOS，USD和流通中的USD的比例。如果你想出售做市商（MMS）1%的份额，你就必须购买和涵盖1%的流通中的USD。不幸的是，你只能从做市商本身购买流通中的USD，这样，流量就一直存在了。
市场交易费用
用户购买和出售USD，EOS，和MMS的时候会产生交易费用。该费用是一个收入流，最终会给持有MMS的人带来资本收益。波动性越大，交易越多，交易费用也就更多。这些费用不断对做市商进行资产重组，而不需要被杠杆方整体进行任何投入。不管市场环境如何，被扛杆的一方不可能减少他们的质押物，也不可能部逐渐增加抵押品。如果初始质押率很高，如4倍，质押物要比交易费用增加速度快75%。
黑天鹅
黑天鹅指做市商无法维持USD的价值接近价格馈源。当没有超额质押的时候，这就会发生。这种情况下，做市商还会继续运作，但是USD的价格将会根据馈源发生浮动。敏锐的观察家很可能就会考虑把连接器一端的USD转移，从而维持价格，但是我们不建议这么做，因为这种情况下，人们会争相挤兑连接器中剩下的EOS。没有超额质押价格就会产生浮动，这样，想早退场的人就要为流量支付溢价，而进行中的交易会对剩下各方进行资产重组。
即使是在黑天鹅事件中，交易费用代表的收入流会刺激各方提供质押物、为做市商提供资金。假使质押资产（如EOS）未来也没有恢复价值的可能，挂钩资产（如USD）的持有人也会以市场定价获得连接其中剩下的EOS的相应份额。
和其它系统不同，黑天鹅事件不是特例，市场有无缝、自然的恢复方法重新恢复挂钩。
假设没有超额质押物，做市商会被重新配置，防止出售MMS代币的同时获得还能在用EOS购买MMS的时候获得10%的折扣。这就对做市商进行了资产重组，给新MMS持有人的利益就比先前一个多。一旦超额质押能够恢复，MMS就可以按照上述方式重新出售。超额质押什么时候用完、折扣大小如何，这些都是变量，我们可以调整这些变量减少完全耗尽的风险、提高激励机制、快速对市场进行资产重组，而不用过度惩罚先前的MMS持有人。
价格馈源
要产生可信任的价格馈源方法很多；但是，要获得更好的结论，我们有这么一些建议。挂钩代币可以追踪任何价格馈源，包括诸如30天移动平均值在内的人工馈源。一般的价格馈源会去追踪实时现货价格，但是对于安全的做市商来说，这种预期是不现实的。价格变化越慢，维护挂钩就越容易，因为市场参与者有时间调整。
我建议，挂钩应该瞄准24小时中位数价格而不是瞬时价格。这会减少挂钩偏移的频率和程度，还不会影响到USD作为美元替代品的价值。实际上，它会把一些日期内波动风险转移到USD持有人（偏离平均值）身上，同时对冲USD持有人面临的长期波动性风险。
我们还需要在市场上做一些实验才能最终判定价格馈源的反应性和做市商因为波动的盈利能力变化之间最合适的平衡是怎么样的。
其它价格修正方法
用户使用算法的时候，他们是把Bancor价格从馈源上推得要么更远，要么更近。此时，应该需要一个动态交易费用，交易把Bancor价格从馈源上推得远，动态费用越高。这就让MMS持有人能够增加利润，也能保证市场操作者不会和价格馈源有太大的偏移。
结论
相比如BitUSD这样的系统，我们的挂钩机制能够激励资产产生，在向提供质押品的卖空者提供交易费用的时候，我们的机制还能带来流量，又能为卖空者避开大量的流量风险。此外，算法为市场双方都提供了等量的流量，而BitUSD只为市场一方提供强制结算。交易费用不断对市场进行资产重组，让市场能够从价格变化导致的损失中恢复过来。只要交易费用带来的收入高于质押资产价值下跌额，系统就能保持偿付能力和维护流量。我们相信这个机制能够对所有参与者获得最大的效用，同时还能减少危险。
注意：本文提到的经济安排可能（不）符合您所在地的法律法规。请在使用本文提到的方法前咨询专业的法律顾问。实际的表现情况还受制于各类因素，包括应用和选择的配置参数。本文提到的想法和观点是我自己的想法，和我的员工无关。
原文/Original：
Today I introduce a new token pegging algorithm that provides high liquidity and narrow spreads, while being robust against default in the event collateral loses value over time. The basis of our algorithm is a heavily over-collateralized short position combined with the Bancor algorithm to provide liquidity to both long and short positions. A price feed is utilized to guide the market, but its influence is limited to situations where there is a prolonged deviation so as to protect the market maker from abuse.
Background
In 2013 BitShares introduced the concept of BitUSD, a “smart coin”, backed by BTS tokens, which was designed to track the value of the dollar. BitUSD operated by creating an order book between those who wanted leverage on the BitShares token (BTS) and those who wanted price stability. To provide liquidity for those who purchased BitUSD, BitUSD holders were allowed to force-settle the least-collateralized short position at the price feed after a multi-day delay. This created an effective margin-call and assured buyers of BitUSD that their token was always worth about a dollar worth of BTS. To prevent default, the least collateralized short position could also be force closed if the price feed fell below the minimum margin requirements.
The primary problem with the BitUSD approach is the lack of liquidity, the limited supply of BitUSD available, and the market spread. Market makers were required to operate trading bots that move orders on the internal order book. While the BitUSD holders were provided liquidity, the short positions were not guaranteed liquidity. Lastly, the entire market is subject to a black-swan event when the least collateralized position is unable to be covered. When this happens the peg is permanently broken and a fixed exchange rate is established between BitUSD and BTS.
The lack of incentive create BitUSD, the risks of low liquidity (unable to cover without unreasonable slippage), unexpected margin calls, and difficulty in running safe market making bots meant the supply of BitUSD was small and the spreads were high.
There have been many other projects that utilize variations of over-collateralized positions and margin requirements. All of them suffer similar problems to BitUSD.
Traditional derivative markets implement “futures trading” which allows people to post collateral and settle at a price feed at a fixed point in the future. These futures contracts are fungible and can be traded for a certain time, but due to the expiration and required settlement / rollover they are not suitable for creating a pegged token.
The Bancor algorithm provides automated liquidity between two assets while protecting its reserves from being lost to sophisticated traders. Regardless of the number and kind of orders executed against the Bancor algorithm, the algorithm always generates a profit when the price of the asset pair returns to its original starting point. A typical Bancor market maker is known as a relay which has two “connectors” which represent balances of equal market value. This algorithm has been successful at providing automated liquidity in markets such as the EOS RAM market.
The Pegging Algorithm
This pegging algorithm is based upon the concept that a pegged token is a service provided by the shorts to the longs. This service requires the shorts to provide liquidity for the pegged token. If there is demand for the pegged token then trading fees earned by the market maker should be profitable for the service provider even if the market is relatively flat.
Other pegging algorithms pit shorts against each other rather than facilitate their cooperation for the purpose of bringing a pegged currency service to the market. In these other algorithms shorts compete to cover and collateralize their positions and are worried about short squeezes.
The premise of our algorithm is that those willing to be slightly leverage-long in a collateral asset (such as EOS), can make money by facilitating market making activities between EOS and a fungible pegged asset, (e.g. USD), whose value is designed to track a price feed within an allowed deviation range.
Instead of users creating independent short positions, our algorithm creates one global short position and allows users to buy and sell stake in this global position. Buying and selling stake in the short position is a neutral and reversible process (minus trading fees) provided no other trades occur in between. Instead of leverage being the primary motive, trading fees are the motive for buying stake in the position. This means that a target of 400% over collateralization or higher is viable allowing shorts to be only slightly-leveraged in the collateral asset so that they have the opportunity to earn trading fees.
The market maker is initially created by depositing collateral into the contract. The contract will create tokens in the market maker (MMS) and give them to the initial depositor. For the sake of example, we will assume the collateral is EOS and that the pegged token is USD and is designed to track the 24hr median EOS dollar price.
A target reserve ratio is decided upon, for example 400%. Based upon a 4x reserve ratio, 75% of the EOS deposited would be set aside as excess collateral, and 25% would be placed into a Bancor Relay connector with weight of 50%. At this time the automated market maker contract will create a number of USD tokens to fund a second Bancor Relay connector such that the market value of EOS and USD connector balances are the same at the initial value of the price feed.
In the initial condition the market maker owns 100% of the USD in its connector and therefore has no net liability (USD it must buy back). The book value of the MMS is equal to the value of the EOS held in the connector plus the excess collateral EOS and minus any circulating USD sold from the connector. After this initial setup anyone can buy USD from the market maker which establishes a future buy-back liability on the MMS holders. The mathematical properties of the Bancor Relay algorithm mean that as users buy USD from the market maker the offer-price will increase. If everyone who bought USD then sold it back then the connectors would end up in their initial condition. Any fees charged on the trades would result in a net increase in EOS held in the connector balance.
Given this setup and a 400% reserve target, we can demonstrate that the actual reserves vs sold USD will be far in excess of 400%. In order to get down to 400% (without market price changes) the entire USD connector would have to be bought out which would push the USD price to infinity. In effect, the market makers automatically raise the cost of buying a long USD position as the supply of available long USD positions decreases.
The spot-price offered by the market maker is equal to the ratio of EOS to USD held in the connector balances. When the spot price deviates from the feed price by more than an acceptable margin (e.g. +/- 2%) for more than an allowed period of time (e.g. 24 hours), then the market maker will do one of the following actions depending upon market conditions:
SPOT = price of USD according to Bancor
FEED_USD = price of a federal reserve note in EOSif( SPOT > FEED_USD )
if( Excess Collateral < 3x EOS Connector )
then slowly move EOS Connector to Excess (lowering SPOT)
else
then slowly add new USD to Connector (lowering SPOT)else if( SPOT < FEED_USD )
if( excess collateral )
then gradually buy USD using excess collateral
and destroy it (raising SPOT)else do nothing
The goal of this algorithm is to always move the state closer to the initial condition of having 3x more excess collateral than Bancor balance and 100% of USD in the USD connector. It is obviously impossible to achieve 100% USD in the connector while there is circulating USD, but the circulating supply can decrease in percentage terms when the value of EOS rises significantly relative to USD.
The rate at which collateral is moved or USD issued should target a price correction to the within the acceptable range within a targeted period of time (e.g. 1 hour). In theory traders should buy and sell USD as if it were worth about 1 dollar because they have confidence that they will always be able to sell it for about 1 dollar in the near future. This means that when relative price for EOS and USD is stable that the market maker will not have to rely on the price feed to correct the real time price and the security of the Bancor algorithm against manipulators protects the connector balances from being lost to traders.
When configuring parameters such as allowed deviation from feed, rate of correction, and delay until start of price correction it is critical to minimize the frequency of needing active intervention into the market maker and when intervention is needed, that intervention is slow and gradual. Market players shouldn’t be able to front-run the market maker’s moves for profit.
The result of this algorithm is a pegged asset which follows an 24-hr median value instead of an instantaneous value. It only actively corrects the peg when 24-hr median of the market maker is significantly greater than the 24-hr median of the real market. When the real market jumps we want traders to interact with the Bancor algorithm to speculatively front-run the 24-hr median. This front-running prevents the forced adjustment of the Bancor connectors from occurring except in prolonged cases. The slower the median-price moves the less risk to the market maker, but the greater deviation between pegged USD and real USD. Giving the Bancor algorithm the ability to deviate by a larger percent (say 5%) also minimizes artificial interaction with pricing due to feeds. The less artificial interaction the less relevant the instantaneous accuracy of the price feeds become.
Buying and Selling MMS Tokens
Anyone at any time may contribute new EOS to buy a combination of MMS and USD. This works by maintaining the ratio of MMS, EOS, USD in Bancor connector and USD in circulation after adding new EOS. The individual receives MMS plus a percent of the newly created USD proportional to the USD in circulation. USD and EOS are also added to connectors and excess reserves. Users can then sell the USD for EOS and repeat the process or simply hold excess USD or EOS.
Selling MMS tokens requires providing a number of USD equal to USD_circulating * MMS_Sell / MMS_Supply. This is the same quantity of USD they would have received when buying MMS with EOS in the first place (minus any trading fees charged).
This process can be viewed as splitting and joining identical short positions. Once you control all outstanding debt of your short position you can unwind it and get all the collateral back. The key to the process is maintaining the invariant that someone buying or selling the market maker with/for collateral does not change the ratio of MMS, EOS, USD, and USD circulating. If you want to sell 1% stake in the market maker (MMS) then you must also buy and cover 1% of circulating USD. Fortunately, you can buy circulating USD from the market maker itself so there is always liquidity.
Market Trading Fees
As users buy and sell USD, EOS, and MMS a trading fee is charged. This fee represents a revenue stream that results in capital gains to those holding MMS. The higher the volatility the more trading occurs and the more fees are generated. These fees continuously recapitalize the market maker without requiring any input from those who are collectively leveraged. Regardless of market conditions it isn’t possible for those who are leveraged to reduce their collateral or fail to gradually top it up. With a high initial collateral ratio, eg 4x, the collateral would have to fall by 75% faster than trading fees accumulate.
Black Swans
A black swan is any event where the market maker is unable to maintain the value of USD near the price feed. This occurs when the excess collateral is gone. When this happens the market maker will continue to function but the price of USD will float independent of the feed. Astute observers will likely consider removing USD from one side of the connector to maintain the price, but this is unadvisable as it would create a run on the remaining EOS in the connector. By letting the price float once the excess collateral is gone, those who want to exit early pay a premium for the liquidity and ongoing trading will recapitalize the remaining parties.
Even during a black swan, the revenue stream represented by trading fees incentivizes parties to provide collateral and fund the market maker. In the event the collateral asset, (e.g. EOS), has no expectation of future recovery of value, then holders of the pegged asset (e.g. USD) will get a fair share of remaining EOS in the connector at market determined prices.
Unlike some other systems, a black swan event is not a special case and the market has a seamless and natural recovery method to restore the peg.
In the event excess collateral is gone, the market maker could be configured to prevent selling of MMS tokens while simultaneously allowing the buying of MMS with EOS for a 10% discount. This recapitalizes the market maker giving benefit to the new MMS holders over the prior holders. Once excess collateral is restored MMS could be sold again as described above. The exact point of excess collateral depletion and the magnitude of the discount are variables that can be adjusted to minimize the risk of complete depletion and maximize the incentive rapidly recapitalize the market without overly punishing prior holders of MMS.
Price Feeds
There are many different ways to produce a trusted price feed; however, there are some recommendations for better results. A pegged token can track any price feed, including artificial feeds such as a 30-day moving average. Typical price feeds attempt to track instantaneous spot prices, but this expectation is unrealistic for safe market makers. The slower prices change the easier it is for a peg to be maintained because market participants have more time to adjust.
It is my recommendation that pegs target the 24hr median price rather than the instantaneous price. This will reduce the frequency and magnitude of deviations from the peg without undermining the value of the pegged USD as a dollar alternative. In effect, it transfers some of the intraday volatility risk to the USD holder (deviation from the mean) while still hedging the USD holder against long-term volatility.
Some experimentation in the market will be required to determine the proper balance between reactivity of price feed and profitability of the market maker due to volatility.
Alternative Price Correction Measures
When traders interact with the algorithm they are either pushing the bancor price further from the feed, or closer to the feed. It should be possible to have a dynamic fee on trades that grows higher the further the trade would push the bancor price from the feed. This allows MMS holders to increase profits and discourages manipulators from causing excessive deviation from the price feed.
Conclusion
Compared to systems like BitUSD, our pegging approach incentivizes asset creation and liquidity by providing trading fees to the shorts who post collateral while effectively eliminating the majority of liquidity risks of the shorts. Furthermore, this algorithm provides equal liquidity to both sides of the market where BitUSD only provided forced-settlement to one side of the market. Trading fees continuously re-collateralize the market and enable it to recover from losses due to changing prices. So long as income from trading fees is greater than the average fall in the value of the collateral asset the system can remain solvent and liquid. We believe this approach maximizes the utility to all participants while minimizing risks.
Note: The economic arrangements described in this post may or may not be subject to regulations in your jurisdiction. Please seek professional legal opinions before engaging in economic arrangements described. Actual performance will depend upon many factors including implementation and selected configuration parameters. The ideas and opinions expressed above are my own and not those of my employer.
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