Multi-positions bankruptcy price calculation

bankruptcy Price:

The bankruptcy price of the $I^{\text {th}}\;$contract$(P_i^C)$:

$$P_{i}^{c}=\frac{P_{i}-\left[B I+\sum_{k=1}^{n} S_{k} *\left(P_{k}-P_{k}^{o}\right)\right] * \frac{\operatorname{dir}_{i} * M_{i} * P_{i}}{\sum_{k=1}^{n} \operatorname{dir}_{k} * S_{k^{*} M_{k} * P_{k}}}}{1-\operatorname{dir}_{i} * \text { FeeRate }}$$

Variables:

• $BI$: Static account equity

• $P_i:$Current oracle price of the $I^{\text {th}}\;$contract

• $P_i^C:$The bankruptcy price of the $I^{\text {th}}\;$contract

• $P_i^0$: The opening price of the $I^{\text {th}}\;$contract

• $S_i:$The number of open positions of the $I^{\text {th}}\;$contract, positive for long positions and negative for short positions.

• $dir_i:$The opening direction of the $I^{\text {th}}\;$contract, +1 for long positions and -1 for short positions

• $M_i:$Maintenance margin rate of the $I^{\text {th}}\;$contract

Example:

Initial account balance $BI = 1000$USDC, Trading Fee = 0.3%

Contract Type	Open Positions	Opening Price	Current Price	Maintenance Margin	PNL
ETH	4	1100	1000	200(5%)	-400
BTC	2	2200	2000	400(10%)	-400
AVA	-3	2100	2000	300(5%)	300

ETH bankruptcy Price:

$$\frac{1000-[1000+(-400-400+300) ] * \frac{0.05 * 1000}{200+400+300 }}{1-0.003}=975.15$$

BTC bankruptcy Price:

$$\frac{2000-[1000+(-400-400+300) ] * \frac{0.1 * 2000}{200+400+300 }}{1-0.003}=1894.57$$

AVA bankruptcy Price:

$$\frac{2000-[1000+(-400-400+300) ] * \frac{-1*0.05 *2000}{200+400+300 }}{1+0.003}=2049.40$$

ETH PNL: $(975.15-1100)*4-975.15*4*0.003=-511.1018$

BTC PNL: $(1894.57-2200)*2-1894.57*2*0.003=-622.23$

AVA PNL: $(2049.40-2100)*-3-2049.40*3*0.003=133.354$