Formulas and Definitions
Margin and Balance Formulas
Futures Margin Ratio
Current margin ratio = total_collateral_value / sum(abs(position_notional_i))
Total Collateral
Total collateral of the user (doesn’t account for any pending orders, includes unsettled PnL) = total_balance + upnl + pending_short_USDC
Free Collateral
Available collateral/balance to trade (accounts for any pending orders, includes unsettled PnL) = collateral + upnl - total_initial_margin_with_orders - pending_short_USDC
Portfolio Value
Total potfolio value including position notionals = USDC Balance + (non USDC assets) * mid_price + unsettled pnl
Withdrawable Balance
Collateral available to withdraw (excludes unsettled PnL) = total_balance - total_initial_margin_with_orders - positive_upnl
Ex. 1 user’s total_balance
= 100 USDC, unsettled PnL = -40 USDC, => total_collateral is then 60 USDC. User has a position which takes up 20 USDC maintenance margin, then free_collateral
or withdrawable_balance
= 60 - 20 = 40 USDC
Ex. 2 user’s total_balance
= 100 USDC, unsettled PnL = 40 USDC, => total_collateral is then 100 USDC. User has a position which takes up 20 USDC maintenance margin, then free_collateral
= 100 - 20 = 80 USDC and withdrawable_balance
= 80 - 40 = 40 USDC
Withdrawable balance/collateral does not equal to total or free collateral.
Initial Margin Ratio
IMR i = Max(1 / Max Account Leverage, Base IMR i, IMR Factor i * Abs(Position Notional i)^(4/5))
initial_margin_i = abs (position_notional_i * IMR_i)
weighted_initial_margin_ratio_i = abs (position_notional_i / total_notional ) * IMR_i
initial_margin_ratio = sum (weighted_initial_margin_ratio_i)
Maintenance Margin Ratio
MMR i = Max(Base MMR i, (Base MMR i / Base IMR i) * IMR Factor i * Abs(Position Notional i)^(4/5))
maintenance_margin_i= abs (position_notional_i * MMR_i)
weighted_maintenance_margin_ratio_i = abs (position_notional_i / total_notional ) * MMR_i
maintenance_margin_ratio = sum (weighted_maintenance_margin_ratio_i)
Positions PnL
Unrealized PnL = position_qty * (mark_price - avg_open)
Liquidation Price
Qi = position_qty
liquidation_price = max[( Mark Price + ( total_collateral_value - total_notional * MMR ) / ( |Qi| * MMRi - Qi )), 0]
Notional = position_notional_i = abs(mark_price_i * position_qty_i)
Fut Notional or Total Notional = sum (abs (position_notional_i))
Unsettled PnL is retrieved from the API and cannot be calculated
Order placement formulas
Max Order Quantity
newOrderSize => (total_collateral_value - others_IM) * min(1/Base_IMR_i,maxLeverage_account) / markPrice maxLeverage_account
IMR i = Max(1 / Max Account Leverage, Base_IMR_i, IMR Factor i * Abs(Position Notional i)^(4/5))
MMR i = Max(Base MMR i, (Base MMR i / Base IMR i) * IMR Factor i * Abs(Position Notional i)^(4/5))
aftertrade_IMR.i → Max(1 / Max Account Leverage, Base_IMR_i, IMR Factor i * Abs(After Trade Position Notional i)^(4/5))
If total_collateral_value < total_initial_margin_with_orders
if (side == buy && position_qty >=0 ) or (side == sell && position_qty < 0)
return 0
else
if side == buy
return max( abs(position_qty) - pending_long_qty, 0 )
else
return max( position_qty + pending_short_qty, 0 )
else
newOrderSize = (total_collateral_value - others_IM) * min(1/Base_IMR_i,maxLeverage_account) / markPrice
calculate afterTradeIM
newTotalIM = othersIM + afterTradeIM
if side = buy
others = -holding - pendingLongQty
else
others = holding + pendingShortQty
if totalCollatValue >= newTotalIM
return max(0, newOrderSize * 99.5% + others)
else
newOrderSize_iter = ITERATE()
return max(0, newOrderSize_iter * 99.5% + others)
with :
total_collateral_value = total_balance + upnl + pending_short_USDC
total_initial_margin_with_orders = sum (position_notional_with_orders_i * IMR_i (with_orders))
position_qty_with_orders_i = max[abs(position_qty + sum_position_qty_buy_orders),abs(pos_qty + sum_position_qty_sell_orders)]
position_notional_with_orders_i = abs(mark_price_i * position_qty_with_orders_i)
others_IM = sum[i#j)(initial_margin_with_orders_i) (where j represents the pair i on which the order is being placed)
Liquidation Price
Qi = position_qty + order_qty
liquidation_price = max( Mark Price + ( total_collateral_value - total_notional_with_order * MMR_with_order ) / ( |Qi| * MMR_with_order_i - Qi )), 0)