Liquidations: Debt write-off

Debt Write-off & Streaming Collateral

Omnipair’s liquidation mechanism fundamentally differs from traditional DeFi lending protocols. Instead of relying on auctions or forced asset sales, Omnipair combines immediate debt write-off with a gradual collateral streaming mechanism, enhancing system stability and protecting liquidity providers (LPs).

Problem: Traditional Liquidation Risks

In traditional lending protocols (e.g., Aave, Compound), liquidation occurs via third-party liquidators. Liquidators repay borrower debts in exchange for discounted collateral. This causes several critical issues:

• Instant liquidation: Sudden collateral sales create market impacts, price slippage, and cascading liquidations.

• Reliance on liquidators: External liquidators may fail or delay during market volatility or network congestion.

• Oracle dependency: Real-time price oracle reliance introduces manipulation risks.

These risks are particularly pronounced in volatile, highly leveraged, or long-tail asset markets.

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Omnipair’s Solution: Debt Write-off & Streaming Collateral

Omnipair solves these issues through an internal, oracle-free liquidation process:

Step 1: Debt Write-off

When a borrower crosses the liquidation threshold (collateral value < debt value based on EMA pricing), their debt is immediately removed from the debt accounting pool. This requires no external liquidator.

Step 2: Streaming Collateral

Collateral isn't sold instantly. Instead, it's gradually streamed back into the pool reserves. This "slow-drip" replenishes reserves smoothly, avoiding sudden market impacts.

Collateral is incrementally returned to pool reserves over a defined timeframe, restoring pool solvency in a controlled manner.

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Technical Explanation

Notations:

• Let:

  • $C_0$: Collateral amount in Token0

  • $D_1$: Debt amount in Token1

  • $\text{EMA}_{1 \rightarrow 0}$: Exponential Moving Average price of Token1 denominated in Token0

  • $CF$: Collateral Factor (e.g., 85%)

Liquidation Condition:

A borrower becomes insolvent if:

$$D_1 \cdot \text{EMA}_{1 \rightarrow 0} > C_0 \cdot CF$$

Debt Write-off Mechanism:

Upon insolvency detection:

• Borrower's debt ($D_1$) is immediately subtracted from the pool’s total debt:

  $$D_{\text{total}}' = D_{\text{total}} - D_x$$
• Borrower's collateral ($C_0$) ownership is transferred internally to the pool.

Collateral Streaming Mechanics:

Collateral is gradually released back into pool reserves over time, using an exponential decay function. Define:

• $t$: Current time

• $t_0$: Insolvency event timestamp

• $\alpha$: Streaming rate constant (determines speed of collateral release)

Collateral released at time $t$ after insolvency event:

$$C_{\text{released}}(t) = C_0 \cdot \left(1 - e^{-\alpha (t - t_0)}\right)$$

Collateral remaining (yet to be released) at time $t$:

$$C_{\text{remaining}}(t) = C_0 \cdot e^{-\alpha (t - t_0)}$$

This to ensure a smooth, predictable collateral returns, preventing market shocks.

Solvency Restoration:

Pool reserves are replenished continuously over time, progressively restoring solvency:

$$R_{\text{new}}(t) = R_{\text{old}} + C_{\text{released}}(t)$$

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Practical Example:

Suppose:

• Collateral Factor: $CF = 85\%$

• Initial collateral: $C_0 = 100$ Token X

• Debt: $D_1 = 90$ Token1

• Initially, EMA: $\text{EMA}_{1 \rightarrow 0} = 1.0$

Initially solvent condition:

$$90 \times 1.0 = 90 \leq 100 \times 0.85 = 85 \quad\text{(initially insolvent scenario is false, so actually solvent initially)}$$

If EMA price suddenly drops to $0.7$:

$$90 \times 0.7 = 63 > 100 \times 0.85 = 85 \quad\text{(now insolvent)}$$

This triggers liquidation:

• Debt ($90$ Token Y) immediately written off.

• Collateral ($100$ Token X) streams back to reserves gradually with streaming rate $\alpha = 0.1 \text{ day}^{-1}$.

Collateral returned after 1 day:

$$C_{\text{released}}(1) = 100 \cdot (1 - e^{-0.1 \cdot 1}) \approx 9.5 \text{ Token0}$$

Collateral returned after 7 days:

$$C_{\text{released}}(7) = 100 \cdot (1 - e^{-0.1 \cdot 7}) \approx 50.3 \text{ Token0}$$

This gradual restoration prevents sharp impacts on liquidity reserves.

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Advantages of Omnipair’s Approach:

• No oracle risk: EMA-based solvency checks remove real-time oracle dependencies.

• Market stability: Smooth recovery prevents sudden price impacts or liquidation cascades.

• LP Protection: Predictable collateral replenishment secures LP capital even during volatility.

• Autonomous system: Eliminates external liquidators, ensuring protocol robustness.

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Summary:

Omnipair's Debt Write-off & Streaming Collateral mechanism redefines liquidation as a stable, internalized, and predictable process, effectively managing and mitigating risks typically associated with traditional DeFi liquidations.