Coverage Ratio

Coverage ratio r defines the system's equilibrium states.

CoverageRatio=AssetLiabilityCoverage Ratio = \dfrac{Asset}{Liability}

Liquidity provided to the protocol would become liability. A higher coverage ratio indicates a lower default risk. The coverage ratio is an important parameter to our protocol since it needs to be maintained above certain level to avoid default.

If coverage ratio < 1, the token is under-covered. And if coverage ratio > 1, it is over-covered.

In Hummus Exchange, when a swap happens, liquidity (in the system pool) for the swap-from token increases, while liquidity (in the system pool) for the swap-to token decreases

Hummus Exchange encourages convergence towards equilibrium and penalizes the divergence from equilibrium. Therefore, we have established price slippage as a function of coverage ratio.

Slippage Function

The slippage g(r) is designed to penalize actions that deviate coverage ratios of two pools and incentivize actions that converge two coverage ratios.

k and n are fixed parameters to be specified. Our research found that k = 0.00002 and n = 7 could be a competent choice of parameters.

For example, if the coverage ratio is 80%, the marginal slippage is -0.08%. When a swap happens, 0.08% of the swap-to token goes to the pool.

Incentives for Convergence of Coverage Ratio

Hummus Exchange encourages convergence of coverage ratio towards 1. When a user swaps from a pool where the coverage ratio is 80%, he brings the coverage ratio of the from-token to a more healthy position. Hence he is able to receive 0.08% incentives.

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