OLL

Liquidation Mechanism in Collateralized Debt Positions

Liquidation Condition

A liquidation event is triggered if and only if the Health Factor falls below 1:

$\text{Health Factor} < 1$

This can be expressed mathematically as:

$\frac{\text{Liquidation Threshold} \times \text{Collateral Value}}{\text{Borrowed Amount}} < 1$

where:

• Borrowed Amount > 0

• Liquidation Threshold ∈ (0,1)

Collateral Composition

In our model, the collateral is composed of a long asset (e.g., BTC or ETH) and a put option. The collateral value is thus defined as:

$\text{Collateral Value} = P + \max(X - P, 0)$

where:

• P is the current price of the long asset

• X is the strike price of the put option

Liquidation Scenarios

We can distinguish two scenarios based on the relationship between X and P:

Scenario 1: X > P

When the strike price exceeds the current asset price:

$\text{Collateral Value} = P + (X - P) = X$

Liquidation occurs if and only if:

$X < \frac{\text{Borrowed Amount}}{\text{Liquidation Threshold}}$

Scenario 2: X ≤ P

When the strike price is at or below the current asset price:

$\text{Collateral Value} = P$

Liquidation occurs if and only if:

$P < \frac{\text{Borrowed Amount}}{\text{Liquidation Threshold}}$

Conclusion

Given that X ≤ P in Scenario 2, we can conclude that in both scenarios, liquidation occurs when:

$X < \frac{\text{Borrowed Amount}}{\text{Liquidation Threshold}}$

This unified condition provides a concise criterion for liquidation events in our collateralized debt model.