$PIPPIN Calculate the liquidation price of the mysterious small K-line? Okay, let's first organize the known conditions and then calculate step by step.
1.
What would be the liquidation price of the mysterious small K-line shorting PIPPIN?
- Opening price P_{\text{open}} = 0.2913794
- Current price P_{\text{now}} = 0.5484117
- Current floating loss = 3,733,826 USD
- Account remaining margin = 14,330,607 USD
- Question about liquidation price (i.e., the price at which the short position is liquidated)
Here, 'remaining margin' should refer to the current net value (i.e., initial margin + balance after floating profit and loss), but the initial margin needs to be known to calculate the leverage and liquidation conditions.
However, the problem does not directly provide the position value or leverage ratio, but gives the floating loss, allowing us to backtrack the position size.
2. Calculate the position value (short)
When shorting, if the price rises, it results in a loss.
Floating loss formula (shorting):
\text{Floating Loss} = \text{Position Size} \times (P_{\text{now}} - P_{\text{open}})
Here the price unit is 'USD/token', and Position Size is 'number of tokens'.
Substitute:
3,733,826 = N \times (0.5484117 - 0.2913794)
3,733,826 = N \times 0.2570323
N = \frac{3,733,826}{0.2570323} \approx 14,526,683.6 \ \text{(Number of tokens)}
3. Calculate the initial margin and leverage
When opening a short position, the position's USD value is:
V_{\text{open}} = N \times P_{\text{open}}
V_{\text{open}} \approx 14,526,683.6 \times 0.2913794
V_{\text{open}} \approx 4,231,631 \ \text{USD}
In other words, Xiao Li borrowed tokens worth about 4,230,000 USD to sell, receiving 4,230,000 USD cash (+ initial margin) as collateral.
Initial margin (the collateral funds invested when opening a position) = ?
Current account remaining margin (net value) = 14,330,607 USD.
Current floating loss of 3,733,826 USD, so:
The initial margin (denoted as M_0) satisfies:
M_0 - 3,733,826 = 14,330,607 \quad \text{?}
No, calculating this way gives M_0 = 18,064,433 USD, which is much larger than the position value, indicating very low leverage. Check the logic:
When shorting, the total assets in the account = initial margin + cash obtained from shorting (already included in the margin account).
A more standard formula:
Short:
Initial state: Collateral M_0 USD, borrowed tokens worth V_{\text{open}} sold, received V_{\text{open}} USD income, so the total amount in the margin account = M_0 + V_{\text{open}} USD.
When the price becomes P, the floating profit and loss = N \times (P_{\text{open}} - P) (if P is higher, profit and loss is negative).
But the floating loss of 3,733,826 is a positive number (the price has risen), so it is indeed a loss, that is:
\text{Floating Loss} = N \times (P_{\text{now}} - P_{\text{open}}) = 3,733,826
We have calculated N.
Net value (margin balance) = initial total funds - current losses (or = current margin account total - current market value of borrowed tokens).
The current market value of borrowed tokens = N \times P_{\text{now}}
Total amount in the margin account = M_0 + V_{\text{open}} (this is initial, but does profit and loss affect in real-time? Actually, it's simpler to use another method)
4. Directly calculate the liquidation price through the maintenance margin rate
General exchange short liquidation conditions:
\text{Margin Balance} = \text{Net Value} = (M_0 + V_{\text{open}}) - N \times P
When net value ≤ maintenance margin requirement (e.g., ≤ market value of borrowed assets × maintenance margin rate m), liquidation occurs.
But here m is not given. Common m for cryptocurrency leverage varies between 0.5% to 5%, but the problem may assume that liquidation occurs when 'margin balance = 0' (i.e., full margin mode, where margin balance = 0 indicates liquidation).
Full margin mode liquidation condition: margin balance = 0.
That is:
M_0 + V_{\text{open}} - N \times P_{\text{liquidation}} = 0
But M_0 is unknown, we can use current data to find M_0:
Current net value = M_0 + V_{\text{open}} - N \times P_{\text{now}} = 14,330,607
Substituting N \times P_{\text{now}} \approx 14,526,683.6 \times 0.5484117 \approx 7,965,457
So:
M_0 + V_{\text{open}} - 7,965,457 = 14,330,607
M_0 + V_{\text{open}} = 22,296,064
And V_{\text{open}} \approx 4,231,631, so:
M_0 \approx 22,296,064 - 4,231,631 \approx 18,064,433
Consistent with the previous statement. Indeed, the initial margin is 18,064,000 USD, the position value is 4,230,000 USD, and the leverage is very low (about 1.23 times).
5. Calculate the liquidation price (margin balance = 0)
Liquidation conditions:
M_0 + V_{\text{open}} - N \times P_{\text{liq}} = 0
22,296,064 - 14,526,683.6 \times P_{\text{liq}} = 0
P_{\text{liq}} = \frac{22,296,064}{14,526,683.6} \approx 1.5348 \ \text{USD}
6. Check the reasonableness
Current price 0.548, liquidation price 1.535, the price needs to rise about 180% to liquidate because the initial margin is large, and leverage is low.
Final answer:
\boxed{1.5348}
(Unit: USD/token)