# Liquidity

The liquidity of the Athena protocol is measured by the availability of assets in cover pools for key protocol operations such as providing insurance coverage and paying out claims. It is a critical metric, as insufficient liquidity could impair the protocol's ability to offer adequate coverage or settle valid claims. At any given time, the liquidity of the protocol can be assessed through the utilization ratio (i.e., the share of the pool that is currently committed to active cover policies versus the total assets in each cover pool).

## Dynamic Premium Pricing in Athena

Athena's premium pricing algorithm is calibrated to manage liquidity risk and optimize utilization of cover pools. The cover premiums are derived from the Utilization Rate (U) of each pool.

U is an indicator of the availability of capital within the pool. The premium pricing model manages liquidity risk in the protocol through user incentives to support liquidity:

When capital is abundant: lower premiums to encourage cover purchases.

When capital is scarce: higher premiums to encourage additional liquidity provision.

### Premium Pricing Model

Liquidity risk materializes when utilization is high, becoming more problematic as U approaches 100%. To address this constraint, the premium pricing curve is split into two parts around an optimal utilization rate (U_optimal). Before U_optimal, the slope is gentle; after it, the slope rises sharply.

The premium rate (P_r) follows the model:

For U ā¤ U_optimal: $P_r = r_0 + \frac{U}{U_{optimal}} \cdot r_{slope1}$

For U > U_optimal: $P_r = r_0 + r_{slope1} + \frac{U - U_{optimal}}{1 - U_{optimal}} \cdot r_{slope2}$

Where:

r_0 is the base premium rate

r_slope1 is the premium slope below optimal utilization

r_slope2 is the premium slope above optimal utilization

This model ensures:

When U ā¤ uOptimal, premiums increase slowly with utilization

When U > uOptimal, premiums increase sharply to discourage over-utilization and incentivize liquidity provision

### Model Parameters

The premium pricing model incorporates various factors to ensure accurate risk assessment and fair pricing for DeFi protocol coverage. Protocol risk profile plays a crucial role, with higher-risk protocols typically requiring higher premiums to account for increased potential for exploits or failures.

Market conditions are also factored in, as Athena's premiums must align with current risk perceptions and comparable cover products in the DeFi insurance market. For multi-protocol positions, a leverage factor is applied in the risk fee calculation to account for the increased risk associated with covering multiple protocols simultaneously.

The model is calibrated differently for various types of DeFi protocols. Protection pools for riskier protocols, such as newer or more complex DeFi applications, are set with a low Optimal Utilization Ratio to ensure fairer pricing evolution. Established protocols with strong security track records may have a higher Optimal Utilization Ratio. Well-audited, battle-tested protocols are calibrated to lower rates to encourage coverage purchases while maintaining appropriate risk management.

Ultimately, the premium rate is dynamically determined by the interplay between cover demand from buyers and liquidity supply from providers, reflecting real-time market conditions and risk assessments within the Athena protocol.

### Liquidity Provider Rewards

The premiums paid by cover buyers are distributed as rewards to liquidity providers who have supplied assets to the protocol, excluding a share sent to the protocol treasury defined by the reserve factor.

The Liquidity Provider APY (LP_Y) is calculated as the sum of the yields from each pool the position provided liquidity to, plus the strategy's base APR:

$LP_Y = \sum_{i=1}^{n} (U_i \cdot P_{r_i}) + S_y$

Where:

n is the number of pools the position provided liquidity to

U_i is the utilization ratio of pool i

P_r_i is the premium rate of pool i

S_y is the strategy's base yield from the underlying LP tokens

This model ensures that liquidity providers are rewarded both for the risk they're underwriting across multiple pools and for the base yield of their supplied assets. The summation allows for a comprehensive reward calculation that accounts for varying utilization and premium rates across different pools within a single position.

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