Surge Fee

Surge fees preserve LP value when positions are undergoing autonomous liquidity updates, protecting liquidity providers (LPs) from sandwiching attacks. Together with dynamic fees and the am-AMM, surge fees form Warren's MEV-aware architecture, and they are crucial for maintaining the security and profitability of Warren pools, especially those that frequently update their liquidity distribution.

The Problem: Sandwiching Attacks

When a pool's liquidity is autonomously updated (a "surge" occurs), whether due to LDF updates, rehypothecation yields, or autonomous rebalances, it can create a sandwiching opportunity. An attacker could potentially sandwich the update with two swaps and make a profit at the expense of the LPs.

The Solution: Surge Fee

Warren addresses this issue by implementing a dynamic fee mechanism called surge fees. Essentially, Warren starts a Dutch auction every time a pool surges, where the swap fee is initially set to a high value and gradually decreases over time back to normal.

How Surge Fee Works

The surge fee is calculated using the following formula:

$f_{surge} = f_{sMax} \cdot 2^{-\frac{t - \min(t_{surge}, t_{swap} + \tau_{auto})}{\tau}}$

Where:

• $f_{surge}$ is the current surge fee
• $f_{sMax}$ is the maximum surge fee
• $t$ is the current timestamp
• $t_{surge}$ is the timestamp of the most recent surge
• $t_{swap}$ is the timestamp of the most recent swap
• $\tau_{auto}$ is the surge autostart time
• $\tau$ is the surge half-life

The actual swap fee is then computed as:

$f = \max(f_{surge}, f_0)$

Where $f_0$ is the regular swap fee.

Key Components of Surge Fee

1. Dutch Auction: The fee starts high and decreases exponentially, allowing the market to determine the fair price for the MEV opportunity.

2. Autostart Mechanism: The $\min(t_{surge}, t_{swap} + \tau_{auto})$ term ensures that the surge fee automatically begins decreasing after $\tau_{auto}$ seconds since the last swap, preventing the pool from halting swaps indefinitely.

3. Exponential Decay: The use of exponential decay (with half-life $\tau$) allows for a rapid initial decrease in fee, followed by a more gradual approach to the normal fee level.

Benefits of Surge Fee

1. MEV Protection: By capturing the majority of the potential MEV, surge fees preserve LP value against losses due to sandwiching attacks.

2. Efficiency: The Dutch auction mechanism allows the market to efficiently price the MEV opportunity.

3. Flexibility: Pool creators can adjust parameters like $f_{sMax}$, $\tau_{auto}$, and $\tau$ to suit their specific needs and risk tolerance.

4. Continuous Operation: The autostart mechanism ensures that the pool continues to function even if no swaps occur immediately after a surge.

Interaction with am-AMM

In pools where an am-AMM manager is present, the manager has the option to enable or disable surge fees. This is because the am-AMM mechanism itself can help recapture MEV, potentially making surge fees unnecessary in some cases.

By implementing surge fees, Warren provides a robust defense against MEV extraction during liquidity updates, ensuring that LPs can confidently use advanced features like shapeshifting and autonomous rebalancing without fear of exploitation.