Setup
A portfolio using Cross Margin mode with positions in m m m { D 1 , . . . , D m } \small\{D_1,...,D_m\} { D 1 , ... , D m }
For each synthetic asset { D 1 , . . . , D m } \small\{D_1,...,D_m\} { D 1 , ... , D m }
Open position of size n P n_P n P
A set of open buy orders with total size of n B ≥ 0 \small n_B\ge0 n B ≥ 0
A set of open sell orders with total size of n S ≥ 0 \small n_S\ge0 n S ≥ 0
Open sizes
Position Size long = max ( n P , 0 ) \small\text{Position Size}_\text{long}=\max(n_P,~0) Position Size long = max ( n P , 0 ) Long position.Position Size short = max ( − n P , 0 ) \small\text{Position Size}_\text{short}=\max(-n_P, ~0) Position Size short = max ( − n P , 0 ) Short position.Buy open size : Open Size buy = max ( n B + n P , 0 ) \small\text{Open Size}_\text{buy}=\max(n_B+n_P,~0) Open Size buy = max ( n B + n P , 0 )
Sell open size : Open Size sell = max ( n S − n P , 0 ) \small\text{Open Size}_\text{sell}=\max(n_S-n_P,~0) Open Size sell = max ( n S − n P , 0 )
Margin Fractions The initial margin fractions (IMF) are increasing functions of the notional (i.e. the maximum allowed leverage decreases with higher notional).
For perpetual positions IMF buy \text{IMF}_\text{buy} IMF buy IMF sell \text{IMF}_\text{sell} IMF sell
IMF buy/sell ( D j ) = max ( Base IMF , IMF Factor ∗ max ( Open Size buy/sell ( D j ) ∗ Mark Price ( D j ) − IMF Shift , 0 ) ) \begin{aligned}
& \text{IMF}_\text{buy/sell}(D_j)= \\
& \\
& \small\max\Biggl(~\small\text{Base IMF}~,~\small\text{IMF Factor}~*~\sqrt{\max\bigl(\small\text{Open Size}_\text{buy/sell}(D_j)*\small\text{Mark Price}(D_j)-\small\text{IMF~Shift},0\bigr)}~\Biggr)
\end{aligned} IMF buy/sell ( D j ) = max ( Base IMF , IMF Factor ∗ max ( Open Size buy/sell ( D j ) ∗ Mark Price ( D j ) − IMF Shift , 0 ) )
i.e. the Initial Margin Fraction (which is the inverse if the Maximum Allowed Initial Leverage) increases as a square root of USD Notional for large notionals.
Position IMF is similar to the IMF but excludes open orders :
Position IMF ( D j ) = max ( Base IMF , IMF Factor ∗ max ( Position Size ( D j ) ∗ Mark Price ( D j ) − IMF Shift , 0 ) ) \begin{aligned}
& \text{Position IMF}(D_j)= \\
& \max\Biggl(~\small\text{Base IMF}~,~\small\text{IMF Factor}*\sqrt{\max\bigl(\small\text{Position Size}(D_j)*\small\text{Mark Price}(D_j)-\small\text{IMF~Shift},0\bigr)}~\Biggr)
\end{aligned} Position IMF ( D j ) = max ( Base IMF , IMF Factor ∗ max ( Position Size ( D j ) ∗ Mark Price ( D j ) − IMF Shift , 0 ) ) The Maintenance Margin Fraction MMF \text{MMF} MMF
MMF ( D j ) = MMF Factor ∗ Position IMF ( D j ) \small\text{MMF}(D_j)=\text{MMF Factor}*\text{Position IMF}(D_j) MMF ( D j ) = MMF Factor ∗ Position IMF ( D j ) The plots below show the example of margin fractions for ETH-USD-PERP :
ETH-USD-PERP Margin Fractions (%) as functions of USD Notional ETH-USD-PERP Maximum Leverage as a function of USD Notional The margin fractions can be translated into the margin requirements below. Since the margin fractions increase for large notionals, the margin requirements increase non-linearly for those notionals :
ETH-USD-PERP Margin Requirements (USD) as a function of USD Notional Fee Provision Given the conservative fee rate :
Fee Rate = max ( Account Maker Fee Rate , Account Taker Fee Rate ) \small\text{Fee Rate}=\max\Big(\text{Account Maker Fee Rate},~\text{Account Taker Fee Rate}\Big) Fee Rate = max ( Account Maker Fee Rate , Account Taker Fee Rate ) For a given synthetic asset D j D_j D j
Fee Provision ( D j ) = Fee Rate ( n B + n S + ∣ n P ∣ ) ∗ Mark Price ( D j ) \text{Fee Provision}(D_j)=\text{Fee Rate}\Big(n_B+n_S+|n_P|\Big)*\text{Mark Price}(D_j) Fee Provision ( D j ) = Fee Rate ( n B + n S + ∣ n P ∣ ) ∗ Mark Price ( D j ) For MMR and Position IMR , open orders are not included in fee provision calculation :
Position Fee Provision ( D j ) = Fee Rate ∗ ∣ n P ∣ ∗ Mark Price ( D j ) \text{Position Fee Provision}(D_j)=\text{Fee Rate}*|n_P|*\text{Mark Price}(D_j) Position Fee Provision ( D j ) = Fee Rate ∗ ∣ n P ∣ ∗ Mark Price ( D j ) Open Loss
The Open Loss is an additional margin requirement for orders which are more aggressive than the Mark Price . It offsets the difference between the order limit price and the Mark Price.
Open Loss = { max ( Limit Price − Mark Price , 0 ) for a Buy Order max ( Mark Price − Limit Price , 0 ) for a Sell Order \text{Open Loss} = \begin{cases} \max\big( \text{Limit Price}-\text{Mark Price} ,~0\big) \text{ for a Buy Order}\\ \max\big( \text{Mark Price}-\text{Limit Price} ,~0\big) \text{ for a Sell Order} \end{cases} Open Loss = { max ( Limit Price − Mark Price , 0 ) for a Buy Order max ( Mark Price − Limit Price , 0 ) for a Sell Order Note that the “limit” price of a Market Order is defined by the instrument’s Price Band .
Margin Requirements Position Margin Requirement
Initial margin requirement (IMR )
For all derivatives positions IMR buy \text{IMR}_\text{buy} IMR buy IMR sell \text{IMR}_\text{sell} IMR sell
IMR buy/sell ( D j ) = IMF buy/sell ( D j ) ∗ Open Size buy/sell ( D j ) ∗ Mark Price ( D j ) \small\text{IMR}_\text{buy/sell}(D_j)=\text{IMF}_\text{buy/sell}(D_j)*\text{Open Size}_\text{buy/sell}(D_j)*\text{Mark Price}(D_j) IMR buy/sell ( D j ) = IMF buy/sell ( D j ) ∗ Open Size buy/sell ( D j ) ∗ Mark Price ( D j ) IMR ( D j ) = IMR ( D j ) = max ( IMR buy ( D j ) , IMR sell ( D j ) ) + Fee Provision ( D j ) + Open Loss ( D j ) \small\text{IMR}(D_j)=\text{IMR}(D_j)=\max\Big(\text{IMR}_\text{buy}(D_j),~\text{IMR}_\text{sell}(D_j)\Big)+\text{Fee Provision}(D_j)+\text{Open Loss}(D_j) IMR ( D j ) = IMR ( D j ) = max ( IMR buy ( D j ) , IMR sell ( D j ) ) + Fee Provision ( D j ) + Open Loss ( D j ) Position Initial margin requirement (Position IMR )
Position IMR ( D j ) = Position IMF ( D j ) ∗ ∣ n P ∣ ∗ Mark Price ( D j ) + Position Fee Provision ( D j ) \small\text{Position IMR}(D_j)=\text{Position IMF}(D_j)*|n_P|*\text{Mark Price}(D_j)+\text{Position Fee Provision}(D_j) Position IMR ( D j ) = Position IMF ( D j ) ∗ ∣ n P ∣ ∗ Mark Price ( D j ) + Position Fee Provision ( D j ) Maintenance margin requirement (MMR )
MMR ( D j ) = MMF ( D j ) ∗ ∣ n P ∣ ∗ Mark Price ( D j ) + Position Fee Provision ( D j ) + Open Loss ( D j ) \small\text{MMR}(D_j)=\text{MMF}(D_j)*|n_P|*\text{Mark Price}(D_j)+\text{Position Fee Provision}(D_j)+\text{Open Loss}(D_j) MMR ( D j ) = MMF ( D j ) ∗ ∣ n P ∣ ∗ Mark Price ( D j ) + Position Fee Provision ( D j ) + Open Loss ( D j ) Account Margin Requirement
The account requirements are then calculated as the simple sum of individual synthetic asset balance requirements:
Account IMR = ∑ j = 1 m IMR ( D j ) \small\text{Account IMR}=\sum\limits_{j=1}^m \text{IMR}(D_j) Account IMR = j = 1 ∑ m IMR ( D j ) Account MMR = ∑ j = 1 m MMR ( D j ) \small\text{Account MMR}=\sum\limits_{j=1}^m \text{MMR}(D_j) Account MMR = j = 1 ∑ m MMR ( D j )
Leverage
Account Leverage
Account Leverage = ∑ j = 1 m [ Open Size buy/sell ( D j ) ∗ Mark Price ( D j ) ] Account Value \text{Account Leverage}=\frac{\sum\limits_{j=1}^m [\text{Open Size}_\text{buy/sell}(D_j)*\text{Mark Price}(D_j)]}{\text{Account Value}} Account Leverage = Account Value j = 1 ∑ m [ Open Size buy/sell ( D j ) ∗ Mark Price ( D j )] Max Leverage
Max Leverage = ∑ j = 1 m [ Open Size buy/sell ( D j ) ∗ Mark Price ( D j ) ] Account IMR \text{Max Leverage}=\frac{\sum\limits_{j=1}^m [\text{Open Size}_\text{buy/sell}(D_j)*\text{Mark Price}(D_j)]}{\text{Account IMR}} Max Leverage = Account IMR j = 1 ∑ m [ Open Size buy/sell ( D j ) ∗ Mark Price ( D j )] 
