# # Derivative Market Concepts

## # Definitions

In a derivative market using linear contracts (as opposed to inverse contracts), a contract with ticker AAA/BBB offers exposure to the underlying AAA using the quote currency BBB for margin and settlement. For each contract, the quotation unit is the BBB price of one unit of AAA, e.g. the USDT price of one unit of ETH.

Notional - the notional value of a position is: notional = quantity * price.

Refunds - In our clearing system, a refund refers to the action of incrementing the available balance of an account. This liberation of funds occurs as the result of an encumbrance being lifted from the account (e.g. cancelling a limit order, reducing an order's payable fee to a maker fee, using less margin to fund a market order, etc.).

## # Perpetual Market Trading Lifecycle

### # Perpetual Market Creation

A market is first created either by the instant launch functionality through MsgInstantPerpetualMarketLaunch or MsgInstantExpiryFuturesMarketLaunch which creates a market by paying an extra fee which doesn't require governance to approve it. Or it is created in the normal way through governance through MsgPerpetualMarketLaunchProposal or MsgExpiryFuturesMarketLaunchProposal.

### # Balance Management

#### # Depositing Funds into Exchange

A trader can deposit funds, e.g., USDT, into the exchange by sending a MsgDeposit which transfers coins from the Cosmos-SDK bank module to the trader's subaccount deposits on the exchange module.

Depositing a given Amount of coin will increment both the trader's subaccount deposit AvailableBalance and TotalBalance by Amount.

#### # Withdrawing Funds from Exchange

A trader can withdraw funds from the exchange by sending a MsgWithdraw which transfers coins from the trader's subaccount on the exchange module.

Withdrawal Requirement: Withdrawing a given Amount of coin will decrement both the trader's subaccount deposit AvailableBalance and TotalBalance by Amount. Note: Amount must be less than or equal to AvailableBalance.

#### # Transferring Funds between Subaccounts

A trader can transfer funds between his own subaccounts sending a MsgSubaccountTransfer which transfer coins from one of the trader's subaccount deposits to another subaccount also owned by the trader.

Subaccount transfers have the same Withdrawal Requirement as normal withdrawals.

#### # Transferring Funds to another Exchange Account

A trader can transfer funds to an external account by sending a MsgExternalTransfer which transfers funds from the trader's subaccount to another third-party account.

External Funds transfers have the same Withdrawal Requirement as normal withdrawals.

### # Order Management

#### # Placing Limit Orders

A trader can post a limit buy or sell order by sending a MsgCreateDerivativeLimitOrder. Upon submission, the order can be:

1. Immediately (fully or partially) matched against other opposing resting orders on the orderbook in the Endblocker batch auction, thus establishing a position for the user.

Note that it is possible for an order to be partially matched and for the remaining unmatched portion to be added to the orderbook.

#### # Placing Market Orders

A trader can post a market buy or sell order by sending a MsgCreateDerivativeMarketOrder. Upon submission, the market order will be executed against other opposing resting orders on the orderbook in the Endblocker batch auction, thus establishing a position for the user.

#### # Cancelling Limit Orders

User cancels a limit buy or sell order by sending a MsgCancelDerivativeOrder which removes the user's limit order from the orderbook.

### # Increasing Position Margin

A user can increase the margin of a position by sending a MsgIncreasePositionMargin.

### # Liquidating Insolvent Positions

A third party can liquidate any user's position if the position's maintenance margin ratio is breached by sending a MsgLiquidatePosition.

Initial Margin Requirement

This is the requirement for the ratio of margin to the order's notional as well as the mark price when creating a new position. The idea behind the additional mark price requirement is to minimize the liquidation risk when traded prices and mark prices temporally diverge too far from each other. Given the initial margin ratio, an order must fulfill two requirements:

• The margin must fulfill: Margin ≥ InitialMarginRatio * Price * Quantity, e.g., in a market with maximally 20x leverage, the initial margin ratio would be 0.05. Any new position will have a margin which is at least 0.05 of its notional.

• The margin must fulfill the mark price requirement:

• Margin >= Quantity * (InitialMarginRatio * MarkPrice - PNL)

PNL is the expected profit and loss of the position if it was closed at the current MarkPrice. Solved for MarkPrice this results in:

• For Buys: $\mathrm{MarkPrice}$$\mathrm{\frac{Margin - Price * Quantity}{(InitialMarginRatio - 1) * Quantity}}$
• For Sells: $\mathrm{MarkPrice}$$\mathrm{\frac{Margin + Price * Quantity}{(InitialMarginRatio + 1) * Quantity}}$

Maintenance Margin Requirement

Throughout the lifecycle of an active position, if the following margin requirement is not met, the position is subject to liquidation. (Note: for simplicity of notation but without loss of generality, we assume the position considered does not have any funding).

• For Longs: Margin >= Quantity * MaintenanceMarginRatio * MarkPrice - (MarkPrice - EntryPrice)
• For Shorts: Margin >= Quantity * MaintenanceMarginRatio * MarkPrice - (EntryPrice - MarkPrice)

Liquidation Payouts

When your position falls below the maintenance margin ratio, the position can be liquidated by anyone. What happens on-chain is that automatically a reduce-only market order of the same size as the position is created. The market order will have a worst price defined as Infinity or 0, implying it will be matched at whatever prices are available in the order book.

The payout from executing the reduce-only market order will not go towards the position owner. Instead, a part of the remaining funds are transferred to the liquidator bot and the other part is transferred to the insurance fund. The split is defined in the exchange params by LiquidatorRewardShareRate. If the payout in the position was negative, i.e., the position's negative PNL was greater than its margin, then the insurance fund will cover the missing funds.

Also note that liquidations are executed immediately in a block before any other order matching occurs.

### # Funding Payments

Funding exists only for perpetual markets as a mechanism to align trading prices with the mark price. It refers to the periodic payments exchanged between the traders that are long or short of a contract at the end of every funding epoch, e.g. every hour. When the funding rate is positive, longs pay shorts. When it is negative, shorts pay longs.

• Position Size = Position Quantity * MarkPrice
• Funding Payment = Position Size * Hourly Funding Rate (HFR)
• HFR = Cap((TWAP((SyntheticVWAPExecutionPrice - MarkPrice)/MarkPrice) + DailyInterestRate) * 1/24)
• SyntheticVWAPExecutionPrice = (Price_A*Volume_A +Price_B*Volume_B +Price_C*Volume_C)/(Volume_A + Volume_B + Volume_C)
• A is the market buy batch execution
• B is the market sell batch execution
• C is the limit matching batch execution

Funding payments are applied to the whole market by modifying the CumulativeFunding value. Each position stores the current CumulativeFunding as CumulativeFundingEntry. Subsequent funding payments are only applied upon position changes and can be calculated as:

• FundingPayment
• For Longs: FundingPayment ← PositionQuantity * (CumulativeFunding - CumulativeFundingEntry)
• For Shorts: FundingPayment ← PositionQuantity * (CumulativeFundingEntry - CumulativeFunding)
• Margin' ← Margin + FundingPayment
• CumulativeFundingEntry' ← CumulativeFunding

## # Perpetual Market Trading Specification

### # Positions

A trader's position records the conditions under which the trader has entered into the derivative contract and is defined as follows

• Position Definition:
• Quantity
• EntryPrice
• Margin
• HoldQuantity
• CumulativeFundingEntry

As an example, consider the following position in the ETH/USDT market:

• Quantity = -2
• EntryPrice = 2200
• Margin = 800
• HoldQuantity = 1
• CumulativeFundingEntry = 4838123

This position represents short exposure for 2 contracts of the ETH/USDT market collateralized with 800 USDT, with an entry price of 2200. The HoldQuantity represents the quantity of the position that the trader has opposing orders for. CumulativeFundingEntry represents the cumulative funding value that the position was last updated at.

Position Netting:

When a new vanilla order is matched for a subaccount with an existing position, the new position will be the result from netting the existing position with the new vanilla order. A matched vanilla order produces a position delta defined by FillQuantity, FillMargin and ClearingPrice.

• Applying Position Delta to a position in the same direction:
• Entry Price' ← (Quantity \* EntryPrice + FillQuantity \* ClearingPrice) / (Quantity + FillQuantity)
• Quantity' ← Quantity + FillQuantity
• Margin' ← Margin + FillMargin
• Apply Position Delta to a position in the opposing direction:
• Entry Price - no change
• Quantity' ← Quantity - FillQuantity
• Margin' ← Margin \* (Quantity - FillQuantity) / Quantity

A limit buy order seeks to purchase a specified Quantity of a derivative contract at a specified Price by providing a specified amount of margin as collateral.

### # Limit Sell Order

A limit sell order seeks to sell a specified Quantity of a derivative contract at a specified Price by providing a specified amount of margin as collateral.

A matched position will have subtracted fees which depend on whether the limit order becomes executed as a maker order or a taker order.

A market buy order seeks to purchase a specified Quantity of a derivative contract at a specified worst price using the subaccount's available balance as margin collateral.

Handler and EndBlocker Execution of the market order are conceptually identical to the Limit Buy Order (Immediately Matched case), since the trader passes the margin which implicitly sets a maximum price limit due to the initial min margin requirements.

### # Market Sell Order

A market sell order seeks to sell a specified Quantity of a derivative contract at a specified worst price using the subaccount's available balance as margin collateral.

Handler and EndBlocker Execution of the market order are conceptually identical to the Limit Sell Order (Immediately Matched case), since the trader passes the margin which implicitly sets a minimum price limit due to the initial min margin requirements.

### # Limit Buy Reduce-Only Order

A limit buy reduce-only order seeks to reduce existing long exposure by a specified Quantity ETH (base currency). The payout for closing a position will have subtracted fees.

### # Limit Sell Reduce-Only Order

A limit sell reduce-only order seeks to reduce existing short exposure by a specified Quantity ETH (base currency). The payout for closing a position will have subtracted fees.