Source: Perpetual Protocol (formerly: Strike Protocol)
Mable, Multicoin Capital
A brief history of AMM
In the DeFi domain, automated market makers (AMM) are used to describe protocols or applications that use mathematical functions to determine asset prices and then facilitate the exchange of two or more assets. The most famous example of AMM is Uniswap, a decentralized exchange (DEX) that USES a constant function of x * y = k for token exchange.
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To learn more about AMM, read:Explore innovative ways for automated market makers (AMM)".
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Since Bancor launched AMM on the chain in 2017, there have been some significant improvements in different aspects of AMM:
Uniswap (2018) : THE first AMM to achieve meaningful trading volumes and kick off the AMM wave in DeFi. Uniswap is largely due to its simplicity. Curve (2019) : The first asset manager optimized for a stable asset basket. Balancer (2020) : The first AMM that enables a liquidity pool creator to customize weights between two or more assets in a single pool. Bancor V2 (2020) : The first dynamic asset management to mitigate liquidity pool losses by realizing the losses of Bancor LP (& NBSP; AMM) to introduce dynamic weight into the liquidity pool. Bancor also allows you to provide liquidity to only one side of the pool. Blackholeswap (2020) : The first AMM that could handle transactions that exceeded its current liquidity through the use of an excess supply of Compound or other lending agreements.
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Building on this chain of innovation, we are proud to share the new AMM: Virtual Automated Market Maker (" vAMM "), created by the Permanent Agreement.
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Current limitations of AMM: Leverage, short positions, and Volatile Losses (IL)
Although there has been a great deal of innovation in this area, all the improvements mentioned above have focused on servicing scrip swaps, meaning that each new approach applies only to swaps and not to derivatives, such as permanent contracts.
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Permanent contracts are the most popular product for cryptocurrency traders. Because derivatives often involve some kind of leverage, it is difficult to make them compatible with AMM's current design. However, there are several ways. For example, one way to enable leverage and short selling through AMM is to encourage liquidity providers to offer tokens (= 1 times leverage) in the AMM pool and allow traders to borrow assets with the required leverage. You can learn more about this method here. However, the disadvantages of this approach are: 1) liquidity providers suffer high permanent losses and 2) open positions are constrained by the size of the pool.
Permanent protocol solution: Virtualize AMM
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To address the current limitations of AMM, Perpetual Protocol introduces a new approach called "virtual AMM" that fundamentally expands the scope of AMM applications and enables permanent contracts for the first time.
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For those unfamiliar with perpetuities: A perpetuity is a derivative similar to a futures contract but without a maturity date. For a conventional futures contract (such as WTI), the contract price gradually converges with the spot market price of the underlying asset as the maturity date approaches. For permanent contracts, the most effective method used in the industry to bring their prices in line with the spot market is the "financing rate". You can read our documentation or this FTX Help Center article for more information about how the money works.
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The vAMM of the permanent protocol USES the same x * y = K constant product formula as Uniswap. As implied in the "virtual" part of vAMM, no actual asset pool (k) is stored within the vAMM itself. Instead, the real assets are stored in the smart contract vault, which manages all vAMM collateral. In contrast to traditional AMM, the permanent protocol USES vAMM as the price discovery mechanism, but is not used for spot transactions.
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This is an example showing how vAMM runs in the background:
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1. Before creating a vAMM on the blockchain, the creator sets the number of virtual assets stored in the vAMM. Assuming that the ETH price is traded at 400 DAI, the creator can set the initial number of ETH and DAI at a vAMM ratio of 1-400. For simplicity, let's assume that the creator sets the initial state of the vAMM to 100 vETH and 40,000 vDAI.
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2. Trader Alice wants to take 100 DAI as collateral for a ETH 10 times the length:
Alice keeps 100 DAI in the permanent Agreement vault, which is the smart contract for the permanent agreement, as described above.

The permanent protocol credits vAMM with 1,000 vDAI (10 times the leverage of 100 DAI) from Alice, who then calculates the number of vETH received by Alice based on the constant function (x * y = k).
The permanent protocol record Alice is now 2.4390244 vETH, and the status in this vAMM is 97.5609756 vETH and 41000 vDAI.

3. Trader Bob then USES 100 DAI as collateral to make a 10 times short ETH, which means:
Bob has 100 DAI's in the same vault.

The permanent agreement will put Bob's -1,000& NBSP; VDAI credits the vAMM, which in return computes the number of negative vETH received by Bob according to the constant function (x * y = k).
Permanent protocol record Bob has now shorted 2.4390244 vETH, and the status within this vAMM is now 100 vETH and 40,000 vDAI.

VAMM's unique attributes require no working capital provider
Because of the independence of the path, the Treasury always has enough collateral to repay all traders who transacted with vAMM (assuming that all uncollateralized assets are successfully liquidated before bankruptcy). In contrast to the traditional AMM where liquidity comes from the liquidity provider providing assets to facilitate transactions, vAMM's liquidity comes directly from a vault located outside of vAMM. In other words, the liquidity provider is not needed to bring liquidity to the vAMM: the trader provides liquidity for each order.
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Since there is no need for a liquidity provider in the vAMM, there is no volatile loss in the first place.
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Periodic price adjustment
VAMM itself is a separate cash settlement market. To bring vAMM market prices close to the base index would require an increase in the financing rate, similar to the financing payments for permanent contracts on a central limit order (CLOB) exchange. For example, the following is the fund payment formula for FTX:

Funds are paid to encourage arbitrageurs to keep the market price as close as possible to the base index and to let the vAMM market track the base index.
The permanent agreement USES a formula for financing rates similar to FTX's, allowing new derivatives markets to trade with leverage while closely tracking the underlying indices.
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Management of slippage
For vAMM, similar to traditional AMM, traders suffer fewer slippage when K is high - but the similarities end there.
For conventional AMM, the only way to increase the K value is 1) to encourage more liquidity providers to provide more liquidity, or 2) to increase transaction fees and recoup transaction profits to provide more liquidity.
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Instead, in vAMM, because the value of k is set manually by the vAMM operator at startup, you can arbitrarily increase or decrease K at any time, even if vAMM is created, to help the market respond to the latest situation. That being said, although the vAMM operator has such authority, he/she cannot transfer funds kept in the safe. VAMM operators will be the first version of the permanent protocol team, after which the transition to THE DAO structure will take place.
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Although the first version of the Permanent Protocol will set K manually, over time we want to set K algorithmally. For example, K can be set as a function of volume, open interest, payment of funds, volatility, and other variables.
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Setting the value of K is a delicate balancing act. If K is too low, the natural users of the protocol will have too many slippage points and will not want to trade in the system. However, if K is too high, the arbitragee will not have enough capital to keep the vAMM price in line with the underlying index price.
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As we learn more about how users use the system in production, we will move the "permanent protocol" from manual selection of K to algorithmic selection.
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conclusion
Above, we introduced how vAMM works and several unique attributes of vAMM. Permanent agreement is the first implementation vAMM, currently in Ropsten test online at https://ropsten.perp.exchange .
The original link: https://medium.com/@perpetualprotocol/a-deep-dive-into-our-virtual-amm-vamm-40345c522eeb
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