Liquidation

Liquidation Condition

Once this condition is triggered, the position is ready to be liquidated.

$$\text{Liquidation} \iff \begin{cases} \text{collateral\_size}+\text{PNL}_{\text{long}}-\text{close\_fee}\;\le\;\dfrac{\text{size}}{\text{max\_lev}}, & \text{Expiry Long},\\ \text{collateral\_size}+\text{PNL}_{\text{short}}-\text{close\_fee}\;\le\;\dfrac{\text{size}}{\text{max\_lev}}, & \text{Expiry Short}. \end{cases}$$

Where:

$$\mathrm{PNL}= \begin{cases} \dfrac{\text{size}}{F(S_0,r,T_0)}\Bigl(F(S_1,r,T_1)-F(S_0,r,T_0)\Bigr), & \text{Expiry Long},\\ \dfrac{\text{size}}{F(S_0,r,T_0)}\Bigl(F(S_0,r,T_0)-F(S_1,r,T_1)\Bigr), & \text{Expiry Short}. \end{cases}$$

• S_1 is the current oracle price
• S_0 is the oracle price at entry
• T_1 is the current time
• T_0 is the time at entry

Liquidation Price

$$P_{\text{liq}}= \begin{cases} \text{price}\,e^{r(t_0-t_1)}-\dfrac{\left|\text{collateral\_size}-\text{close\_fee}-\dfrac{\text{size}}{\text{max\_lev}}\right|\;\text{price}\,e^{r(t_0-t_1)}}{\text{size}}, & \text{Expiry Long},\\ \text{price}\,e^{r(t_0-t_1)}+\dfrac{\left|\text{collateral\_size}-\text{close\_fee}-\dfrac{\text{size}}{\text{max\_lev}}\right|\;\text{price}\,e^{r(t_0-t_1)}}{\text{size}}, & \text{Expiry Short}. \end{cases}$$

Where:

• price is the oracle price
• t_0 is the time position was opened
• t_1 is the current time
• r is the interest rate

$$r= \begin{cases} r_{\text{TOKEN-fixed}}, & \text{Expiry Long},\\ -r_{\text{USDC-fixed}}, & \text{Expiry Short}. \end{cases}$$