Volatility-based Swap Fee

Bunni v2 implements a volatility-based dynamic swap fee mechanism that adjusts fees based on the deviation of the spot price from the Time-Weighted Average Price (TWAP). This feature is designed to optimize fee revenue and protect liquidity providers (LPs) during periods of high volatility.

Overview

The volatility-based swap fee is used in the absence of an am-AMM manager. It increases the swap fee quadratically as the pool's spot price deviates from the TWAP value, providing a simple yet effective way to adjust fees based on market conditions.

Fee Calculation

The swap fee is calculated using the following formula:

$f(p, \bar{p}) = \min(f_{min} + k \cdot (\frac{p}{\bar{p}} - 1)^2, f_{max})$

Where:

• $f(p, \bar{p})$ is the fee percentage charged for a swap
• $p$ is the spot price of the pool after the swap
• $\bar{p}$ is the TWAP of the pool
• $f_{min}$ is the minimum fee
• $f_{max}$ is the maximum fee
• $k$ is a scaling factor

All parameters ($f_{min}$, $k$, $f_{max}$) are non-negative, and $f_{min} \leq f_{max}$.

Key Features

1. Quadratic Scaling: The fee increases quadratically with the deviation from TWAP, providing a rapid response to volatility.

2. Bounded Range: The fee is bounded between $f_{min}$ and $f_{max}$, ensuring it remains within a reasonable range.

3. Directional Sensitivity: Higher fees are charged for swaps that push the spot price away from the TWAP, and lower fees for swaps that bring the price closer to TWAP.

4. Rapid Volatility Response: Large swaps that significantly deviate from TWAP immediately incur higher fees, protecting LPs during sudden price movements.

Benefits

1. Protection Against Volatility: Higher fees during volatile periods help compensate LPs for increased risk.

2. Improved Capital Efficiency: Lower fees during stable periods can attract more volume and improve capital utilization.

3. Automatic Adjustment: The fee adjusts automatically based on market conditions without requiring manual intervention.

4. Simplicity: The mechanism is straightforward to implement and understand, requiring only the current price and TWAP as inputs.

Considerations

1. TWAP Window: The effectiveness of this mechanism depends on choosing an appropriate TWAP window. A shorter window makes the fee more responsive to recent price changes, while a longer window provides more stability.

2. Parameter Tuning: The values of $f_{min}$, $f_{max}$, and $k$ need to be carefully chosen to balance fee revenue, LP protection, and competitiveness with other exchanges.

3. Market Impact: Very high fees during extreme volatility might deter some traders, potentially reducing volume during these periods.

4. Complex Market Dynamics: While this model provides a reasonable approximation of volatility, it may not capture all nuances of market behavior.

Interaction with Other Bunni v2 Features

• am-AMM: The volatility-based swap fee is used only when an am-AMM manager is not present. If an am-AMM manager is active, they have full control over fee setting.

• Autonomous Rebalancing: The volatility-based fee can help protect the pool during rebalancing operations that occur during high volatility periods.

While the volatility-based swap fee provides a solid default mechanism for fee adjustment, it's worth noting that an am-AMM manager using sophisticated off-chain models could potentially achieve even better results. The volatility-based fee serves as a robust fallback when am-AMM is not in use.