0090-VAMM-automated_market_maker.md

Automated Market Maker Framework

Summary

The automated market maker (AMM) framework is designed to allow for the provision of an on-chain market making methodology which automatically provides prices according to a simple set of rules based on current market data. These rulesets are not created with the expectation of providing any profit nor of remaining solvent under any specific conditions, and so should be limited to conceptually simple setups. The initial methodology follows a concentrated-liquidity style constant-function market setup, with configurable maximum and minimum price bounds.

An automated market maker is configured at a per-key level, and is enabled by submitting a transaction with the requisite parameters. At this point in time the protocol will move committed funds to a sub-account which will be used to manage margin for the AMM. Once enabled, the configuration will be added to the pool of available AMMs to be utilised by the matching engine.

Each party may have only one AMM configuration per market, and both Spot and Futures markets are eligible, with the behaviour differing slightly for each.

Process Overview

The configuration and resultant lifecycle of an automated market maker is as follows:

• Party funds a key which will be used by the strategy with desired token amounts.
• Party submits a transaction containing configuration for the strategy on a given market. This will contain:
  • Amount of funds to commit
  • Price bounds (upper, lower, base)
  • Margin ratios at upper and lower bound (ratio for leverage at bounds. Reciprocal of leverage multiplier e.g. 0.1 = 10x leverage)
• Additionally, the transaction should contain data related to the setup of the position but which does not need to be stored:
  • Maximum slippage (%), used for rebasing position when creating/updating vAMM
• Once accepted, the network will transfer funds to a sub-account and use the other parameters for maintaining the position.
• At each block, the party's available balance (including margin and general accounts) for trading on the market will be checked. If the total balance is 0 the vAMM configuration will be stopped.
• The party is finally able to cancel the vAMM through a few different methods. They can choose to either set it into a mode in which it will only reduce position, eventually cancelling when/if the position reaches 0, or choose to give up the existing position and associated required collateral.

Sub-Account Configuration

Each main Vega key will have one associated sub account for a given market, on which an AMM may be set up. The account key should be generated through a hash of the main account key plus the ID of the market to generate a valid Vega address in a predictable manner. Outside of the AMM framework the sub-accounts are treated identically to any other account, they will have the standard associated margin/general accounts and be able to place orders if required as with any other account. The key differentiator is that no external party will have the private key to control these accounts directly. The maintenance of such an account will be performed through a few actions:

• Creation: A sub-account will be funded when a user configures an AMM strategy with a set of criteria and a commitment amount. At this point in time the commitment amount will be transferred to the sub-account's general account and the AMM strategy will commence
• Cancellation: When the vAMM is cancelled the strategy specified will be followed:
  • For futures, either any positions associated with the vAMM will be abandoned and given up to the network liquidation engine to close out, along with any associated required collateral, or the vAMM will be set into a mode in which it can only reduce position over time.
• Amendment: Updates the strategy or commitment for a sub-account

Interface

All AMM configurations should implement two key interfaces:

• One taking simply the current state (position and total funds) and a trade (volume, side) and returning a quote price. This should also handle a trade of volume = 0 to return a notional fair price
• The second taking (position, total funds, side, start price, end price) should return the full volume the AMM would trade between the two prices (inclusive).

AMM Configurations

Initially there will only be one option for AMM behaviour, that of a constant-function curve, however there may be others available in future. As such, the parameters pertaining to this model in particular should be passed in their own structure such that the creation message is similar to:

{
  commitment,
  market,
  slippage_tolerance_percentage,
  proposed_fee,
  concentrated_liquidity_params: {
    base_price,
    lower_price,
    upper_price,
    leverage_at_upper_bound,
    leverage_at_lower_bound,
  }
}

Concentrated Liquidity - Futures

The Concentrated Liquidity AMM is a market maker utilising a Uniswap v3-style pricing curve for managing price based upon current market price. This allows for the market maker to automatically provide a pricing curve for any prices within some configurable range, alongside offering the capability to control risk by only trading within certain price bounds and out to known position limits.

The concentrated liquidity market maker consists of two liquidity curves of prices joined at a given base price, an upper consisting of the prices above this price point and a lower for prices below it. At prices below the base price the market maker will be in a long position, and at prices above this base price the market maker will be in a short position. This is configured through a number of parameters:

• Base Price: The base price is the central price for the market maker. When trading at this level the market maker will have a position of 0. Volumes for prices above this level will be taken from the upper curve and volumes for prices below will be taken from the lower curve.
• Upper Price: The maximum price bound for market making. Prices between the base price and this price will have volume placed, with no orders above this price. This is optional and if not supplied no volume will be placed above base price. At these prices the market maker will always be short
• Lower Price: The minimum price bound for market making. Prices between the base price and this will have volume placed, with no orders below this price. This is optional and if not supplied no volume will be placed below base price. At these prices the market maker will always be long
• Commitment: This is the initial volume of funds to transfer into the sub account for use in market making. If this amount is not currently available in the main account's general account the transaction will fail.
• Leverage at Bounds: The exact volume scaling is defined by the position at the upper and lower prices. To determine this the commitment must be compared with what leverage that might allow at the price bounds. Using this parameter allows them to set a value such that position = remaining funds * leverage at bound*, however with the restriction that commitment must still be >= initial margin. This parameter should be optional. There is a separate parameter for each potential bound.
  • Upper Bound Leverage: leverage_at_upper_bound
  • Lower Bound Leverage: leverage_at_lower_bound

Note that the independent long and short ranges mean that at base price the market maker will be flat with respect to the market with a 0 position. This means that a potential market maker with some inherent exposure elsewhere (likely long in many cases as a token holder) can generate a position which is always either opposite to their position elsewhere (with a capped size), thus offsetting pre-existing exposure, or zero.

Additionally, as all commitments require some processing overhead on the core, there should be a network parameter market.amm.minCommitmentQuantum which defines a minimum quantum for commitment. Any create or amend transaction where commitment / asset quantum < market.amm.minCommitmentQuantum should be rejected.

Creation/Amendment Process

Creation

Futures

A Concentrated Liquidity AMM has an inherent linkage between position and implied price. By configuration, this position is 0 at base price but non-zero above and below that (assuming both an upper and lower bound have been provided), however it is possible to configure an AMM such that this base price is far from the market's current mark price. In order to bring the vAMM in line with where it "should" be the vAMM will determine whether the order book is currently able to synchronise the vAMM and reject the transaction if not

1. If the AMM's base price is between the current best bid and best ask on the market (including other active vAMMs) it is marked as created and enters normal quoting with no trade necessary.
2. If the AMM's base price is below the current best bid and the AMM has an upper range specified, then the vAMM would need to become short in order to synchronise with the market. In order to do this, the protocol will query each price level in turn starting from best bid and:
   1. At each level:
      1. Check the full volume available across all limit orders and other vAMMs at this price and every higher bid (store a running cumulative volume in order to track this).
      2. Check the volume required for the incoming vAMM to have a fair price at that level.
      3. If the volume required is less than the full cumulative volume including this level, place a single order on the market for the volume required at the previous price level, with a price equal to the current price level. e.g. With:
         • best bid at 10 USDT
         • Cumulative volume at 8 USDT equal to 4 contracts
         • Bid offers for 4 contracts at 7 USDT
         • And a vAMM which would be short 5 contracts for a fair price at 8 USDT and short 4 contracts at 7 USDT
         • Enter a limit order to sell 5 contracts for 7 USDT into the order book and allow it to match.
   2. If a price level is reached such that the current price is more than the max slippage specified away from the best bid, reject the transaction.
   3. If there is no upper range specified, it is marked as created immediately.
3. If the AMM's base price is above the current best ask and the AMM has a lower range specified, then the vAMM would need to become short in order to synchronise with the market. Follow an identical process as above but instead on increasing price levels from best ask
   1. If there is no lower range specified, it is marked as created immediately.

Amendment

Futures

A similar process is followed in the case of amendments. Changes to the upper, lower or base price, or the commitment amount will affect the position implied at a certain price, meaning that the market maker may need to enter an aggressive trade to synchronise. In general, the behaviour above will be followed. As the vAMM may be currently holding a position, the existing position should be compared to that required at both sides (best bid/ask) of the order book to determine whether buying or selling is necessary. If the current position is between that required at best bid and best ask the amendment succeeds without requiring a trade.

If reducing the commitment amount then only funds contained within the AMMs general account are eligible for removal. If the deduction is less than the general account's balance then the reduced funds will be removed immediately and the AMM will enter single-sided mode as specified above to reduce the position. If a deduction of greater than the general account is requested then the transaction is rejected and no changes are made.

Cancellation

Futures

In addition to amending to reduce the size a user may also cancel their AMM entirely. In order to do this they must submit a transaction containing only a field Reduction Strategy which can take two values:

• Abandon Position: In this case, any existing position the AMM holds is given up to the network to close as a liquidation. This is performed in two steps:
  • All funds in the AMM's general account are transferred back to the party who created the AMM.
  • The position is marked as requiring liquidation and is taken over by the network through the usual liquidation processes. All funds in the margin account are transferred to the network's insurance pool as in a forced liquidation
• Reduce-Only: This moves the AMM to a reduce-only state, in which case the position is reduced over time and ranges dynamically update to ensure no further position is taken. As such:
  • If the AMM is currently short, the lower bound is removed
  • If the AMM is currently long, the upper bound is removed
  • The upper/lower bound (if the AMM is currently short/long) is then set to the AMM's current fair price. In this mode the AMM should only ever quote on the side which will reduce it's position (it's upper/lower bound should always be equal to the current fair price belief).
  • Once the position reaches 0 the AMM can be cancelled and all funds in the general account can be returned to the creating party
  • This acts similarly to the mode when an AMM is synchronising, except that the position will be closed in pieces as the price moves towards the base price rather than all at once at the nearest price.

Note that, whilst an Abandon Position transaction immediately closes the AMM a Reduce-Only transaction will keep it active for an uncertain amount of time into the future. During this time, any Amendment transactions received should move the AMM out of Reduce-Only mode and back into standard continuous operation.

Determining Volumes and Prices

Although AMM prices are not placed onto the book as orders it is necessary to be able to be able to quote prices for a given volume, or know what trading volume would move the fair price to a certain level.

The volume to offer at each price level is determined by whether the price level falls within the upper or lower price bands alongside the market maker's current position. In order to calculate this, use the concept of Virtual Liquidity from Uniswap's concentrated liquidity model, corresponding to a theoretical shifted version of the actual liquidity curve to map to an infinite range liquidity curve. The exact mathematics of this can be found in the Uniswap v3 whitepaper and are expanded in depth in the useful guide Liquidity Math in Uniswap v3. Here will be covered cover only the steps needed to obtain prices/volumes without much exposition.

The AMM position can be thought of as two separate liquidity provision curves, one between upper price and base price, and another between base price and lower price. Within each of these, the AMM is buying/selling position on the market in exchange for the quote currency. As the price lowers the AMM is buying position and reducing currency, and as the price rises the AMM is selling position and increasing currency.

One outcome of this is that the curve between base price and lower price is marginally easier to conceptualise directly from our parameters. At the lowest price side of a curve (lower price in this case) the market should be fully in the market contract position, whilst at the highest price (base price in this case) it should be fully sold out into cash. This is exactly the formulation used, where at base price a zero position is used and a cash amount of commitment amount. However given that there is likely to be some degree of leverage allowed on the market this is not directly the amount of funds to calculate using. An AMM with a commitment amount of X is ultimately defined by the requirement of using X in margin at the outer price bounds, so work backwards from that requirement to determine the theoretical cash value. Next calculate the two ranges separately to determine two different Liquidity values for the two ranges, which is a value used to later define volumes required to move the price a specified value.

One can calculate a scaling factor that is the smaller of a multiplier specified in the commitment (leverage_at_bounds, either upper or lower depending on the side considered) or the market's worst case margin option. If leverage_at_bounds for the relevant side is not set then the market's worst case initial margin is taken automatically

$$ r_f = \min(l_b, \frac{1}{ (f_s + f_l) \cdotp f_i}) , $$

where $l_b$ is the sided value leverage_at_bounds (upper ratio if the upper band is being considered and lower ratio if the lower band is), $f_s$ is the market's sided risk factor (different for long and short positions), $f_l$ is the market's linear slippage component and $f_i$ is the market's initial margin factor.

A few components are needed to calculate the target position at the bounds, which will be used to generate a liquidity value for each curve. First, in order to calculate the average entry price for the full volume traded across the range one can calculate this liquidity, or $L_u$ value, for a range assuming a position of $1$ at the bounds (as the average entry price is invariant to scaling of volume across the curve)

$$ L_u = \frac{\sqrt{p_u} \sqrt{p_l}}{\sqrt{p_u} - \sqrt{p_l}} , $$

where $p_u$ is the price at the top of the range (upper price for the upper range and base price for the lower range) and $p_l$ is the price at the bottom of the range (base price for the upper range and lower price for the lower range). This gives the two L values for the two ranges. With this the average entry price can be calculated as

$$ p_a = L_u \sqrt{p_u} (1 - \frac{L_u}{L_u + \sqrt{p_u}}) , $$

where $p_a$ is the average execution price across the range and other values are as defined above. With this, the volumes required to trade to the bounds of the ranges are:

$$ P_{v_l} = \frac{r_f b}{p_l (1 - r_f) + r_f p_a} , $$

$$ P_{v_u} = \frac{r_f b}{p_u (1 + r_f) - r_f p_a} , $$

where $r_f$ is the short factor for the upper range and the long factor for the lower range, b is the current total balance of the vAMM across all accounts, $P_{v_l}$ is the theoretical volume and the bottom of the lower bound and $P_{v_u}$ is the (absolute value of the) theoretical volume at the top of the upper bound. The final $L$ scores can then be reached with the equation

$$ L = P_v \cdot \frac{\sqrt{p_u} \sqrt{p_l}}{\sqrt{p_u} - \sqrt{p_l}} = P_v L_u, $$

where $P_v$ is the virtual position from the previous formula, $p_u$ and $p_l$ are as defined above. This gives the two L values for the two ranges.

Fair price

From here the first step is calculating a fair price, which can be done by utilising the L value for the respective range to calculate virtual values for the pool balances. From here on y will be the cash balance of the pool and x the position.

1. First, identify the current position, P. If it is 0 then the current fair price is the base price.
2. If P != 0 then calculate the implied price from the current position using the virtual position $P_v$ which is equal to $P$ when $P > 0$ or $P + P_{v_u}$ where $P < 0$.
3. The fair price can then be calculated as

$$ p_f = \frac{\sqrt{p_u}}{P_v \cdotp \sqrt{p_u} \cdotp \frac{1}{L} + 1}^2 , $$

where $p_u$ is base price when $P > 0$ or upper price when $P < 0$.

Price to trade a given volume

Finally, the protocol needs to calculate the inverse of the previous section. That is, given a volume bought from/sold to the AMM, at what price should the trade be executed. This could be calculated naively by summing across all the smallest increment volume differences, however this would be computationally inefficient and can be optimised by instead considering the full trade size.

To calculate this, the interface will need the starting price $p_s$, ending price $p_e$, upper price of the current range $p_u$ (upper price if P < 0 else base price), lower price of the current range $p_l$ (base price if P < 0 else lower price), the volume to trade $\Delta x$ and the L value for the current range. At P = 0 use the values for the range which the volume change will cause the position to move into.

First, the steps for calculating a fair price should be followed in order to obtain the implied price. Next the virtual x and y balances must be found:

1. If P > 0:
   1. The virtual x of the position can be calculated as $x_v = P + \frac{L}{\sqrt{p_b}}$, where $L$ is the value for the lower range, $P$ is the market position and $p_b$ is the base price.
   2. The virtual y can be calculated as $y_v = L * \sqrt{p_f}$ where $p_f$ is the fair price calculated above.
2. If P < 0:
   1. The virtual x of the position can be calculated as $x_v = P + P_{v_u} + \frac{L}{\sqrt{p_u}}$ where $p_u$ is the upper price and $P_{v_u}$ is the theoretical volume at the upper bound.
   2. The virtual y can be calculated as $y_v = L * \sqrt{p_f}$ where $p_f$ is the fair price calculated above.

Once obtained, the price can be obtained from the fundamental requirement of the product $y \cdot x$ remaining constant. This gives the relationship

$$ y_v \cdot x_v = (y_v + \Delta y) \cdot (x_v - \Delta x) , $$

From which $\Delta y$ must be calculated

$$ \Delta y = \frac{y_v \cdot x_v}{x_v - \Delta x} - y_v , $$

Thus giving a final execution price to return of $\frac{\Delta y}{\Delta x}$.

Volume between two prices

For the second interface one needs to calculate the volume which would be posted to the book between two price levels. In order to calculate this for an AMM one is ultimately asking the question "what volume of swap would cause the fair price to move from price A to price B?"

To calculate this, the interface will need the starting price $p_s$, ending price $p_e$, upper price of the current range $p_u$ (upper price if P < 0 else base price) and the L value for the current range. At P = 0 use the values for the range which the volume change will cause the position to move into.

First, calculate the implied position at starting price and ending price and return the difference.

For a given price $p$ calculate implied position $P_i$ with

$$ P_i = L \cdot \frac{\sqrt{p_u} - \sqrt{p}}{\sqrt{p} \cdotp \sqrt{p_u}} , $$

Then simply return the absolute difference between these two prices.

Determining Liquidity Contribution

The provided liquidity from an AMM commitment must be determined for two reasons. Firstly to decide instantaneous distribution of liquidity fees between the various liquidity types and secondly to calculate a virtual liquidity commitment amount for assigning AMM users with an ELS value. This will be used for determining the distribution of ELS-eligible fees on a market along with voting weight in market change proposals.

As an AMM does not directly place orders on the book this calculation first needs to infer what the orders would be at each level within the eligible price bounds (those required by SLA parameters on the given market). From here any given AMM curve should implement functionality to take two prices and return the volume it would place to trade fully across that range. Calling this function across the price range out to lower and upper SLA bounds retrieves the full order book shape for each AMM.

Once these are retrieved, the price / volume points should be combined with a precomputed array of the probability of trading at each price level to calculate the liquidity supplied on each side of the orderbook as defined in probability of trading. Once this is calculated, use this value as the instantaneous liquidity score for fee distribution as defined in setting fees and rewards.

As the computation of this virtual order shape may be heavy when run across a large number of passive AMMs the number of AMMs updated per block should be throttled to a fixed maximum number, updating on a rolling frequency, or when updated/first created. Additionally, a network parameter of market.liquidity.maxAmmCalculationLevels should be used to determine the maximum number of levels to be used between the upper and lower SLA bounds. If this number is exceeded the space between upper and lower should be linearly interpolated to produce at most this many sampling points and an estimate using those price levels be used instead.

A given AMM's average liquidity score across the epoch should also be tracked, giving a time-weighted average at the end of each epoch (including 0 values for any time when the AMM either did not exist or was not providing liquidity on one side of the book). From this, a virtual stake amount can be calculated by dividing through by the market.liquidity.stakeToCcyVolume value and the AMM key's ELS updated as normal.

Setting Fees

The proposed_fee provided as part of the AMM construction contributes to the fee determination logic on the market, if a setup where LPs decide on the market fee is in use. In the case where it is the AMM's current assigned ELS, or the running average liquidity provided so far if the commitment was made in the current epoch, is used for weighting the AMM's vote for the fee.

Market Settlement

At market settlement, an AMM's position will be settled alongside all others as if they are a standard party. Once settlement is complete, any remaining funds in the AMM's account will be transferred back to the creator's general account and the AMM can be removed.

Acceptance Criteria

• When market.amm.minCommitmentQuantum is 1, mid price of the market 100, a user with 1000 USDT is able to create a vAMM with commitment 1000, base price 100, upper price 150, lower price 85 and leverage ratio at each bound 0.25. (0090-VAMM-001)

• When market.amm.minCommitmentQuantum is 1, mid price of the market 100, a user with 1000 USDT is able to create a vAMM with commitment 1000, base price 100, no upper price, lower price 85 and leverage ratio at lower bound 0.25. (0090-VAMM-002)

• When market.amm.minCommitmentQuantum is 1, mid price of the market 100, a user with 1000 USDT is able to create a vAMM with commitment 1000, base price 100, upper price 150, no lower price and leverage ratio at upper bound 0.25. (0090-VAMM-003)

• When market.amm.minCommitmentQuantum is 1, mid price of the market 100, a user with 100 USDT is unable to create a vAMM with commitment 1000, and any other combination of settings. (0090-VAMM-004)

• When market.amm.minCommitmentQuantum is 1000, mid price of the market 100, a user with 1000 USDT is able to create a vAMM with commitment 100, and any other combination of settings. (0090-VAMM-005)

• When market.amm.minCommitmentQuantum is 1000, mid price of the market 100, and a user with 1000 USDT creates a vAMM with commitment 1000, base price 100, upper price 150, lower price 85 and leverage ratio at each bound 0.25:

  • If other traders trade to move the market mid price to 140 the vAMM has a short position. (0090-VAMM-006)
  • If other traders trade to move the market mid price to 90 the vAMM has a long position (0090-VAMM-007)
  • If other traders trade to move the market mid price to 150 the vAMM will post no further sell orders above this price, and the vAMM's position notional value will be equal to 4x its total account balance. (0090-VAMM-008)
  • If other traders trade to move the market mid price to 85 the vAMM will post no further buy orders below this price, and the vAMM's position notional value will be equal to 4x its total account balance.(0090-VAMM-009)
  • If other traders trade to move the market mid price to 110 and then trade to move the mid price back to 100 the vAMM will have a position of 0. (0090-VAMM-010)
  • If other traders trade to move the market mid price to 90 and then trade to move the mid price back to 100 the vAMM will have a position of 0. (0090-VAMM-011)
  • If other traders trade to move the market mid price to 90 and then in one trade move the mid price to 110 then trade to move the mid price back to 100 the vAMM will have a position of 0. (0090-VAMM-012)
  • If other traders trade to move the market mid price to 90 and then move the mid price back to 100 in several trades of varying size, the vAMM will have a position of 0. (0090-VAMM-013)
  • If other traders trade to move the market mid price to 90 and then in one trade move the mid price to 110 then trade to move the mid price to 120 the vAMM will have a larger (more negative) but comparable position to if they had been moved straight from 100 to 120. (0090-VAMM-014)

• A vAMM which has been created and is active contributes with it's proposed fee level to the active fee setting mechanism. (0090-VAMM-015)

• At the end of an epoch, the vAMM's virtual ELS should be equal to the ELS of a regular LP with the same committed volume on the book who joined at the end of the same epoch as the vAMM did (i.e. if a vAMM has an average volume on each side of the book each epoch of 10k USDT, their ELS should be equal to that of a regular LP who has a commitment which requires supplying 10k USDT who joined at the same time as them). (0090-VAMM-016)

  • A vAMM's virtual ELS should grow at the same rate as a full LP's ELS who joined at the end of the epoch in which the vAMM joined (0090-VAMM-017)

• A vAMM can vote in market update proposals with the additional weight of their ELS (i.e. not just from governance token holdings). (0090-VAMM-018)

• If a vAMM is cancelled with Abandon Position then it is closed immediately. All funds which were in the general account of the vAMM are returned to the user who created the vAMM and the remaining position and margin funds are moved to the network to close out as it would a regular defaulted position. (0090-VAMM-019)

• If a vAMM is cancelled and set in Reduce-Only mode when it is currently long, then: (0090-VAMM-020)

  • It creates no further buy orders even if the current price is above the configured lower price.
  • When one of it's sell orders is executed it still does not produce buy orders, and correctly quotes sell orders from a higher price.
  • When the position reaches 0 the vAMM is closed and all funds are released to the user after the next mark to market.

• If a vAMM is cancelled and set in Reduce-Only mode when it is currently short, then: (0090-VAMM-021)

  • It creates no further sell orders even if the current price is below the configured upper price.
  • When one of it's buy orders is executed it still does not produce sell orders, and correctly quotes buy orders from a lower price.
  • When the position reaches 0 the vAMM is closed and all funds are released to the user after the next mark to market.

• If a vAMM is cancelled and set in Reduce-Only mode when it currently has no position then all funds are released after the next mark to market. (0090-VAMM-022)

• If a vAMM is cancelled and set into Reduce-Only mode, then an amend is sent by the user who created it, the vAMM is amended according to those instructions and is moved out of Reduce-Only mode back into normal operation. (0090-VAMM-023)

• When market.amm.minCommitmentQuantum is 1000, mid price of the market 100, and a user with 1000 USDT creates a vAMM with commitment 1000, base price 100, upper price 150, lower price 85 and leverage ratio at each bound 0.25:

  • If other traders trade to move the market mid price to 140 the vAMM has a short position. (0090-VAMM-024)
  • If the vAMM is then amended such that it has a new base price of 140 it should attempt to place a trade to rebalance it's position to 0 at a mid price of 140.
    • If that trade can execute with the slippage as configured in the request then the transaction is accepted. (0090-VAMM-025)
    • If the trade cannot execute with the slippage as configured in the request then the transaction is rejected and no changes to the vAMM are made. (0090-VAMM-026)

• When a user with 1000 USDT creates a vAMM with commitment 1000, base price 100, upper price 150, lower price 85 and leverage ratio at each bound 0.25, if other traders trade to move the market mid price to 140 quotes with a mid price of 140 (volume quotes above 140 should be sells, volume quotes below 140 should be buys). (0090-VAMM-027)

• When a user with 1000 USDT creates a vAMM with commitment 1000, base price 100, upper price 150, lower price 85 and leverage ratio at each bound 0.25, the volume quoted to move from price 100 to price 110 in one step is the same as the sum of the volumes to move in 10 steps of 1 e.g. 100 -> 101, 101 -> 102 etc. (0090-VAMM-028)

• When a user with 1000 USDT creates a vAMM with commitment 1000, base price 100, upper price 150, lower price 85 and leverage ratio at each bound 0.25, the volume quoted to move from price 100 to price 90 in one step is the same as the sum of the volumes to move in 10 steps of 1 e.g. 100 -> 99, 99 -> 98 etc. (0090-VAMM-029)

• When a user with 1000 USDT creates a vAMM with commitment 1000, base price 100, upper price 150, lower price 85 and leverage ratio at each bound 0.25:

  1. Take quoted volumes to move to 110 and 90
  2. Execute a trade of the quoted size to move the fair price to 110
  3. Take a quote to move to price 90
  4. Ensure this is equal to the sum of the quotes from step 1 (with the volume from 100 to 110 negated) (0090-VAMM-030)

• When an AMM is active on a market at time of settlement with a position in a well collateralised state, the market can settle successfully and then all funds on the AMM key are transferred back to the main party's account (0090-VAMM-031)

• When an AMM is active on a market at time of settlement but the settlement price means that the party is closed out no funds are transferred back to the main party's account (0090-VAMM-032)

• An AMM with base price 1000, upper price 1100, lower price 900 and current position 0:

  • Quotes a volume of 8.216 units to buy to move fair price to 900
  • Quotes a price of 948.683 to buy 8.216 units
  • Quotes a volume of 7.814 units to sell to move fair price to 1100
  • Quotes a price of 1048.809 to sell 7.814 units

• An AMM with base price 1000, upper price 1100, lower price 900 and current position short 7.814:

  • Quotes a volume of 0 units to buy above 1100
  • Quotes a volume of 7.814 units to buy to move fair price to 1000
  • Quotes a price of 1048.809 to buy 7.814 units
  • Quotes a price of 997.488 to sell 16.030 units
  • Does not quote a price to sell 17 units

• With an existing book consisting solely of one vAMM (at any fair price) a new vAMM entering the market at a differing base price to the existing vAMM's current price, but where upper and lower bounds of each are far beyond the base/fair prices, triggers a trade between the two vAMMs, after which they both have the same fair price and the book is not crossed. (0090-VAMM-033)

• With an existing book consisting solely of one vAMM (at any fair price) a new vAMM entering the market at a differing base price to the existing vAMM's current price, with upper and lower bounds set such that the entire structure is separate to the existing vAMM (e.g. the incoming vAMM's lower price is greater than the existing vAMM's upper price), a trade occurs between the two AMMs leaving at least one of them at the extreme edge of their quoting range. (0090-VAMM-034)

• With two vAMMs existing on the market, and no other orders, both of which have the same fair price, another counterparty placing a large buy order for a given volume, followed by a large sell order for the same volume, results in the vAMMs both taking a position and then returning to 0 position, with a balance increase equal to the maker fees received plus those for the incoming trader crossing the spread. (0090-VAMM-035)