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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(SkPkMk)abs(SiPiMi)\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)
  • otUPNL: Total unrealized gain or loss of other contracts:
     otUPNL =k=1nSk(PkPko)Si(PiPio)\text { otUPNL }=\sum_{k=1}^{n} S_{k} *\left(P_{k}-P_{k}^{o}\right)-S_{i} *\left(P_{i}-P_{i}^{o}\right)
The liquidation price of the
Ith  I^{\text {th}}\;
contract (
PilP_i^l
):
Pil=SiPioBI+ otTMM - otUPNL Si(1diriMi)P_{i}^{l}=\frac{S_{i} * P_{i}^{o}-\mathrm{BI}+\text { otTMM - otUPNL }}{S_{i} *\left(1-\operatorname{dir}_{i} * M_{i}\right)}

Variables:

  • BIBI
    : Static account equity
  • Pi:P_i:
    Current oracle price of the
    Ith  I^{\text {th}}\;
    contract
  • Pil:P_i^l:
    The liquidation price of the
    Ith  I^{\text {th}}\;
    contract
  • Pi0P_i^0
    : The opening price of the
    Ith  I^{\text {th}}\;
    contract
  • Si:S_i:
    The number of open positions of the
    Ith  I^{\text {th}}\;
    contract, positive for long positions and negative for short positions.
  • diri:dir_i:
    The opening direction of the
    Ith  I^{\text {th}}\;
    contract, +1 for long positions and -1 for short positions
  • Mi:M_i:
    Maintenance margin rate of the
    Ith  I^{\text {th}}\;
    contract

Example:

Initial account balance
BI=1000BI = 1000
, ETH-USDC maintenance margin rate
Mi=3M_i = 3%
%, the opening price of ETH-USD
Pi0=3000P_i^0 = 3000
, Current oracle price
PiP_i
= 2900; BTC-USDC maintenance margin rate
Mi=3M_i = 3%
%, the opening price of BTC-USDC
Pn0=40000P_n^0 = 40000
, Current oracle price
PnP_n
= 38000. A trader buys
SiS_i
= 1.5 ETH-USDC, sells
SnS_n
= -0.1 BTC-USDC.

The liquidation price of the ETH contracts is:

otTMM =
abs(0.1380003%)=144abs(-0.1*38000*3\%)=144
otUPNL =
0.1(3800040000)=200-0.1*(38000-40000)=200
Pil=1.530001000+1142001.5(13%)=2346.39P_{i}^{l}=\frac{1.5 *3000 -1000+114-200}{1.5 *(1-3\%)}=2346.39

The liquidation price of the BTC contracts is:

otTMM =
abs(1.529003%)=130.5abs(1.5*2900*3\%)=130.5
otUPNL =
1.5(29003000)=1501.5*(2900-3000)=-150
Pnl=0.1400001000+130.5+1500.1(1+3%)=45820.388P_{n}^{l}=\frac{ -0.1*40000 -1000+130.5+150}{-0.1 *(1+3\%)}=45820.388