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Multi-position liquidation price calculation

Multi-position liquidation price calculation:
​
otTMM: Sum of maintenance margin of other contracts: 

                        otTMM =∑k=1nabs(Sk∗Pk∗Mk)−abs⁡(Si∗Pi∗Mi)\text { otTMM }=\sum_{k=1}^{n} a b s\left(S_{k} * P_{k} * M_{k}\right)-\operatorname{abs}\left(S_{i} * P_{i} * M_{i}\right) otTMM =∑k=1n​abs(Sk​∗Pk​∗Mk​)−abs(Si​∗Pi​∗Mi​)


otUPNL: Total unrealized gain or loss of other contracts:

                              otUPNL =∑k=1nSk∗(Pk−Pko)−Si∗(Pi−Pio)\text { otUPNL }=\sum_{k=1}^{n} S_{k} *\left(P_{k}-P_{k}^{o}\right)-S_{i} *\left(P_{i}-P_{i}^{o}\right) otUPNL =∑k=1n​Sk​∗(Pk​−Pko​)−Si​∗(Pi​−Pio​)
​
The liquidation price of the Ith  I^{\text {th}}\;Ith
contract (PilP_i^lPil​
):
Pil=Si∗Pio−BI+ otTMM - otUPNL Si∗(1−dir⁡i∗Mi)P_{i}^{l}=\frac{S_{i} * P_{i}^{o}-\mathrm{BI}+\text { otTMM - otUPNL }}{S_{i} *\left(1-\operatorname{dir}_{i} * M_{i}\right)}Pil​=Si​∗(1−diri​∗Mi​)Si​∗Pio​−BI+ otTMM - otUPNL ​
Variables:
​BIBIBI
:  Static account equity
​Pi:P_i:Pi​:
Current oracle price of the Ith  I^{\text {th}}\;Ith
contract
​Pil:P_i^l:Pil​:
The liquidation price of the Ith  I^{\text {th}}\;Ith
contract
​Pi0P_i^0Pi0​
: The opening price of the Ith  I^{\text {th}}\;Ith
contract
​Si:S_i: Si​:
 The number of open positions of the Ith  I^{\text {th}}\;Ith
contract, positive for long positions and negative for short positions.
​diri:dir_i: diri​:
The opening direction of the Ith  I^{\text {th}}\;Ith
contract, +1 for long positions and -1 for short positions
​Mi:M_i:Mi​:
Maintenance margin rate of the Ith  I^{\text {th}}\;Ith
contract
Example:
Initial account balance BI=1000BI = 1000BI=1000
, ETH-USDC maintenance margin rateMi=3M_i = 3%Mi​=3
%, the opening price of ETH-USD Pi0=3000P_i^0 = 3000Pi0​=3000
, Current oracle price PiP_iPi​
= 2900; BTC-USDC maintenance margin rateMi=3M_i = 3%Mi​=3
%, the opening price of BTC-USDC Pn0=40000P_n^0 = 40000Pn0​=40000
, Current oracle price PnP_nPn​
= 38000. A trader buys SiS_iSi​
= 1.5 ETH-USDC, sells SnS_nSn​
= -0.1 BTC-USDC.
The liquidation price of the ETH contracts is:
otTMM = abs(−0.1∗38000∗3%)=144abs(-0.1*38000*3\%)=144abs(−0.1∗38000∗3%)=144
​
otUPNL =−0.1∗(38000−40000)=200-0.1*(38000-40000)=200−0.1∗(38000−40000)=200
​
Pil=1.5∗3000−1000+114−2001.5∗(1−3%)=2346.39P_{i}^{l}=\frac{1.5 *3000 -1000+114-200}{1.5 *(1-3\%)}=2346.39Pil​=1.5∗(1−3%)1.5∗3000−1000+114−200​=2346.39
The liquidation price of the BTC contracts is:
otTMM = abs(1.5∗2900∗3%)=130.5abs(1.5*2900*3\%)=130.5abs(1.5∗2900∗3%)=130.5
 
otUPNL =1.5∗(2900−3000)=−1501.5*(2900-3000)=-1501.5∗(2900−3000)=−150
​
Pnl=−0.1∗40000−1000+130.5+150−0.1∗(1+3%)=45820.388P_{n}^{l}=\frac{ -0.1*40000 -1000+130.5+150}{-0.1 *(1+3\%)}=45820.388Pnl​=−0.1∗(1+3%)−0.1∗40000−1000+130.5+150​=45820.388
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Last modified 1yr ago