Dynamic Fee

Bean's DLMM introduces a Dynamic Fee system — a smart, self-adjusting mechanism that tunes trading fees in real-time, based on volatility, price movement, and deposit behavior. The goal is simple: reward LPs fairly during volatile periods, keep costs low for traders during calm times, and make the protocol sustainable long-term.

Core Objectives

Stakeholder	Goals
Liquidity Providers (LPs)	✅ Volatility-adjusted returns ✅ Minimum guaranteed base fees ✅ Protection against toxic/imbalanced flow
Traders	✅ Lower fees during stable periods ✅ Predictable and transparent pricing ✅ Fair cost during volatility
Protocol	✅ Consistent revenue share ✅ Adaptive market efficiency ✅ Built-in risk controls

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1. Fee Architecture

Bean calculates the total trading fee as:

$$TotalFee = Base Fee + Variable Fee$$

Base Fee : The fixed minimum charged regardless of volatility

Variable Fee: Increases as price volatility rises

All calculations utilize 9-decimal precision (1,000,000,000 = 100%)

System safeguards:

• Max Total Fee: 10%

• Max Protocol Share: 25% of total fees

Base Fee:

Provides a fixed floor to reward LPs even in calm markets.

$$Base Fee = Base Factor * Bin Step * 10$$

• Base Factor: Set during pool creation (e.g., 100)

• Bin Step: The price gap between adjacent bins (e.g., 5)

• 10: Fixed scaling Constant

Think of this as your guaranteed minimum paycheck.

Variable Fee:

Encourages LPs to stay in volatile markets by rewarding them with higher fees.

$$Variable Fee = (Volatility Accumulator × Bin Step)² × Variable Fee Control ÷ 100$$

• Volatility Accumulator: Measures recent price fluctuations

• Variable Fee Control: Adjusts sensitivity (e.g., 2500 = 0.25x)

The more the price jumps around, the more LPs earn.

Worked Example:

Given:

• Base Factor = 100

• Bin Step = 5

• Volatility Accumulator = 50,000

• Control = 2,500

Results:

Base Fee = 100 × 5 × 10 = 5,000 (0.0005%)
Variable Fee = (50,000 × 5)² × 2,500 ÷ 100 = 1,562,500,000,000 (0.156%)
Total Fee = 0.1565%

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2. Volatility Management System

To avoid manipulation and overreaction to short-term noise, Ferra introduces a decay-based tracking system.

Accumulator Formula:

$$Volatility Accumulator = Volatility Reference + (Current Bin ID − Reference Bin ID) × 10,000$$

Tracks how far price has moved from its last "anchor" bin.

Time-Weighted Decay Logic:

Time Passed Since Last Update (Δt)	Behavior
Δt < t_f (Filter)	No update — blocks spam/MEV
t_f ≤ Δt < t_d (Decay)	Volatility decays by reduction factor
Δt ≥ t_d (Reset)	Full reset of volatility tracker

Think of it like a memory that forgets old volatility if things calm down.

Worked Example:

T=0: 8-bin move → Accumulator = 80,000
T=45s: 3-bin move → Accumulator = 70,000 (decay applies)
T=350s: 1-bin move → Reset to 10,000

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3. Specialized Fee Types

Composition Fee:

Prevents LP manipulation from imbalanced deposits (e.g., only one token).

$$Composition Fee = Excess Amount × Total Fee × (Total Fee + 1)$$

• Triggered when a deposit skews the ideal token ratio.

• Applies only in active bins.

Flash Loan Fee:

Charged on flash loans independently of volatility.

$$Flash Loan Fee = Loan Amount × Flash Loan Rate ÷ 1,000,000,000$$

• Max Fee: 10%

• Flat Rate: Does not vary with volatility

Worked Example:

Given:

• Excess deposit: 300 USDC

• Total fee: 1%

Results:

Composition Fee = 300 × 0.01 × 1.01 = 3.02 USD

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4. Fee Distribution Logic

Fees are distributed proportionally based on LP contribution per bin.

Bin-Level Fee Growth:

$$Fee Growth Per Unit = Accumulated Fees ÷ Total Bin Liquidity$$

LP Earnings Formula:

$$LP Fees = LP Liquidity × (Current Fee Growth - Last Claimed Growth)$$

Ensures long-term LPs earn more if they stay in active bins.

Worked Example:

Given:

• Total Fee: 100 USDC

• Protocol Share: 20%

Results:

Protocol = 100 × 20% = 20 USDC  
LPs = 80 USDC

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5. Configuration Parameters

Type	Parameters
Static (Set on Pool Init)	Base Factor, Variable Fee Control, Protocol Share, Max Volatility, t_f, t_d, Reduction Factor
Dynamic (Updated with Trades)	Volatility Accumulator, Reference Bin, Last Update Timestamp