LP Collateral Configuration

Choice of Collateral Factor and Liquidation Threshold

As the LP composition could quickly turn into 100% of either asset of the LP asset pair, an effective and safe choice is to use the minimum collateral factors and liquidation thresholds of the two assets as the collateral factor and liquidation threshold for the LP token. E.g. for an ETH/USDT LP, its collateral factor is $\min(CF_{ETH}, CF_{USDT})$, and its liquidation threshold is $\min(Liq\_thld_{ETH},Liq\_thld_{USDT})$.

Adjusting CF to avoid instant liquidation

As the minimum collateral factor and minimum liquidation threshold can come from different assets, it is possible that borrowing of maximum collateral factor could result in liquidation with very little fluctuation in collateral or even instant liquidation. Therefore, the collateral factor is subject to a cap implied by the liquidation threshold. Specifically:

$$\begin{cases} CF_{LP}=\min\left(CF_{ETH}, CF_{USDT},CF_{\max}\right)\\ CF_{\max}=\min(Liq\_thld_{ETH},Liq\_thld_{USDT})*(1-fluctuation\_margin) \end{cases}$$

where $fluctuation\_margin$ denotes the safety margin that as long as collateral value depreciates less than such level no liquidation will be triggered. E.g. For ETH, its CF is 50% and liquidation threshold is 75%. The implied fluctuation margin is $1-\frac{50\%}{75\%}=33.33\%$. A bigger fluctuation margin provides a better user experience that the loan can tolerate bigger fluctuation in collateral value without triggering liquidation.

Why not average or weighted average collateral factors and liquidation threshold?

This is to avoid exploitation from the scenario that the depositor, rather than depositing asset X which has a very low collateral factor and liquidation threshold, adds asset X into an X/USDT LP position with LP range far out-of-money and deposits such LP token to the platform which has higher collateral factor and liquidation threshold. Effectively the depositor still provides the same amount of X tokens without providing any USDT. However, his collateral factor and liquidation threshold are higher than those of X token as they are averaged with the collateral factor and liquidation threshold of USDT, which are rather high.

Untitled

Why not dynamic weighted average, i.e. averaging the collateral factors and liquidation thresholds of the two assets in the LP position based on their live weights in the LP?

This is to avoid liquidation of a loan as the composition of the collateralized LP position shifts without much change in the value. In the plot below on a hypothetical LP position on X token and USDT with LP range being (-1%, 1%) of the current price level, as the price of X token moves down 1%, the LP shifts from being 50/50 composed by X token and USDT into 100% composed by X token. Depending on how different the liquidation thresholds are between X token and USDT, this could result in a significant drop in the liquidation threshold of the LP under a dynamic weighted average model, which can trigger the liquidation of the loan even if the value of LP position only decreased ~1%.

In an example where an X/USDT LP position provides liquidity within the (99%, 101%) price range of the current price. When the price of X token drops from 101% to 99%, although the LP position only devalues ~1%, the composition of the LP position shifts from 100% in USDT to 100% in X token. Under a dynamic weighted average calculation for the liquidation threshold, the LP token's liquidation threshold will shift from that of USDT to that of X token, which can trigger the liquidation of the loan. This could result in poor user experience, not to mention dynamically calculating liquidation threshold based on live LP position composition is expensive and could be vulnerable to attack.