Twyne LTV vs. Underlying LTV
On Twyne, a borrower can choose to leverage idle borrowing power from other lenders to access a liquidation LTV λ_liq_twyne of their choosing, which is higher than the LLTV supported by the underlying lending market λ_liq_ext.
For the purpose of Twyne V1, the assets provided by CLPs are identical in type to those provided by the borrower as collateral, ensuring that only one type of λ_liq_ext needs to be tracked.
Key Variables
When determining the borrower’s Loan-to-Value (LTV) ratio on Twyne, three variables are considered:
- The borrower’s collateral (C)
- The borrower’s outstanding borrow (B)
- Outstanding CLP collateral being reserved (CLP)
Twyne LTV Formula
From the borrower’s collateral and borrow assets:
λ_twyne = B / C
This Twyne LTV (λ_twyne) differs from the external LTV (λ_ext) attributed by the underlying lending market:
λ_ext = B / (C + CLP)
At any given moment:
λ_twyne > λ_ext
How Twyne Works
Twyne allows the borrower to tap into underlying lending market liquidity as if they had λ_ext, even when λ_twyne may already be liquidatable on that lending market. Twyne is responsible for imposing overcollateralization on the borrower’s true position and ensuring it is triggered before the underlying market flags it for liquidation.
Portfolio Safety Conditions
This responsibility is formalized through two key conditions:
- λ_twyne ≤ λ_liq_twyne → Liquidations are not triggered on Twyne unless the borrower’s LTV exceeds their liquidation LTV.
- λ_ext ≤ (1 − β_safe) · λ_liq_ext ≡ ˜λ_liq_ext → The underlying LTV must, at all times, retain a safety buffer β_safe with respect to the external liquidation threshold.
We redefine the right-hand side as ˜λ_liq_ext to simplify notation.
Equality Condition
Equality in both safety conditions occurs only when the borrower is liable for liquidation on Twyne:
λ_ext = λ_liq_twyne / (1 + CLP / C) = ˜λ_liq_ext
Required CLP Assets
This expresses the CLP assets that must be reserved by the borrower at any moment to ensure the desired liquidation LTV:
CLP = (λ_liq_twyne / ˜λ_liq_ext − 1) · C
Twyne’s smart contracts verify this condition whenever an interaction affects a user’s portfolio. If the necessary CLP are not available to be reserved by the borrower, then:
- Their total deposited collateral C, or
- Desired liquidation loan-to-value λ_liq_twyne
must be capped to match the available CLP funds.