concepts

primer

Four definitions the fee-and-arb sections below assume.

An LP (liquidity provider) deposits two tokens into a pool. Traders swap against the pool, and the LP earns a cut of every swap as a fee. In return, the LP's holdings rebalance automatically: when price rises, the pool sells the appreciating token; when price falls, the pool buys it. The LP doesn't pick the trades; the pool's pricing curve does.

Arbitrage is what keeps the pool's price roughly in line with the rest of the market. When the pool is even slightly out of line with a faster venue (a CEX, another DEX), a bot buys on the cheaper side and sells on the pricier side until the prices converge. The pool's price tracks the outside world because of arbitrage, not despite it. Arbitrage is the mechanism that updates the pool's price.

Impermanent loss (IL) is the gap between what the LP holds at the end and what they would have held by simply sitting on the two tokens in a wallet. It is an endpoint metric: it only depends on the starting price and the ending price, not on the price changes in between. If price moves and comes back, IL is small. If price drifts in one direction, IL is permanent. Under the hood, that gap is a directional mismatch: as price rises the pool sells the appreciating token; as price falls it buys the depreciating one, so the LP is always on the wrong side of the move relative to a hold portfolio.

LVR (loss-versus-rebalancing) is the cost an LP pays on each arbitrage trade. Every time arbitrage updates the pool's price, the LP has effectively sold at a slightly stale price to the bot. LVR measures how much worse the pool did versus a hypothetical LP who could rebalance instantly at the outside price for free. It is a path metric: it accumulates over every arbitrage event along the path, whether or not price ends up anywhere in particular.

The chart above shows both: the red marks along the LP line are LVR (the cost at every arb along the way), and the red bracket at the right is IL (the gap between where the hold portfolio and the LP position land at the end).

How the four definitions connect: arbitrage is the mechanism that reprices the pool. LVR is the per-event path cost it inflicts on the LP. IL is the end-state gap you actually see on your position when you close it. The sections below measure and mitigate the path cost.

Three design choices flow from that picture, and Wick ships all three:

• a dynamic fees algorithm that keeps fees large enough to dominate per-block price movement
• a permissioned arbitrage layer that captures the residual spread at 0% internal fee
• an in-house ALM that recaptures the rebalancing flow it creates

For product behavior, see dynamic fees and Wick arbitrage.

pricing risk with dynamic fees

LP risk changes minute-to-minute with volatility; a fixed fee does not. On a static-fee pool the result is a fee-volatility mismatch in both directions: overcharging traders when markets are calm, undercharging for risk when markets move. Wick's algorithm tracks volatility live and closes that gap continuously.

Wick closes that gap four ways: it sizes fees against one ratio, splits the fee into a reactive and a predictive layer, calibrates it to the bin grid, and runs on fast block times. The rest of this section covers each one.

fee-to-volatility ratio

Wick's fee algorithm targets one number: the fee-to-volatility ratio, the swap fee compared to the typical per-block price move. Everything else on this page (how often arbs hit the pool and how much LPs keep) follows from it.

A ratio of 10:1 means the swap fee is roughly 10x larger than the typical per-block price move. Once the fee is that big, arbitrage only happens on genuinely large moves, and almost all of what the arb pays comes back to LPs as fees. Below a ratio of 1:1, fees are too low to block arbitrage and the arbitrageur keeps most of the value.

fee-to-volatility ratio = fee / (volatility × √block time)

The three inputs:

• fee — the swap fee rate charged on the pool (e.g. 0.30% = 0.0030).
• volatility — annualized price volatility of the asset (e.g. 0.50 for 50% per year).
• block time — the time between price updates, measured as a fraction of a year.

The numerator is what the pool charges per swap. The denominator is the size of the typical per-block price move, i.e., how far the pool is expected to drift before the next arb opportunity appears. The ratio has no units, so you can compare it across chains, assets, and fee tiers.

The design goal is simple: keep the ratio in the dilute regime. The live dynamic fee algorithm achieves this by raising the fee during high-volatility periods so the ratio stays above 10:1 even when per-block volatility spikes.

two fee layers

On wAMM, every swap charges:

totalFee = baseFee + variableFee

The reactive layer is automatic and driven by the pool's own activity: the variable fee rises when swaps cross bins. Wick adds a predictive layer on top: the predictive fee model adjusts fee parameters from external CEX and DEX feeds before toxic flow is likely to hit the pool. Both stack; neither replaces the other.

If BTC moves hard on a CEX but nobody trades the Wick pool yet, the variable fee does not change until swaps move bins. Predictive fees monetize that lag. Reactive fees still matter during bursts: rapid bin crossings and fee memory after volatile stretches.

bin step and fee calibration

bin step is fixed at pool creation. It sets the width of each bin on the price grid and scales both parts of the trader fee: the static floor (baseFactor × binStep) and the variable fee (which grows with the square of volatilityAccumulator × binStep). A wider bin step raises the static floor and makes each bin crossing move the fee further, so it doubles as a volatility-sensitivity knob. A good starting point is a bin step of roughly 2× the base fee rate, a guideline from DLMM arb research, not a hard rule.

venue timing

Wick runs on Lighter EVM and the Lighter orderbook because both update price on sub-second block times. Block time sits in the denominator of the ratio (volatility × √block time), so a shorter block shrinks the typical per-block move and pushes the ratio higher, deeper into the dilute regime, at the same fee tier. Fast venues do the work a higher fee would otherwise have to. The chart below shows the ratio at 1, 5, 30, and 100 bp for each surface, using typical BTC volatility (50% annualized; toggle to stress-test).

At 30 bp both surfaces sit firmly in the dilute regime; even at 5 bp Lighter EVM stays dilute. That is why Wick's fee algorithm can target high ratios without choking volume: the venue timing does most of the work. Most of what each arb event takes is recaptured as fees; endpoint IL, the gap defined in the primer, is structural and fees can't change it.

fee-arb decomposition

Wick sizes its swap fee so fees take most of what the arbitrageur would have kept on every event that touches the pool. Here is how that split works; every other number on this page comes back to it.

Every arbitrage event splits into exactly two pieces:

LVR per event = Fee + Arb

Measuring the price overshoot as the log of (new price / old price):

• Fee grows linearly with the overshoot, collected by the pool and returned to LPs.
• Arb grows with the square of the overshoot, kept by the arbitrageur.

When the overshoot is small, the fee is almost the whole payment and the arb's profit is crumbs. Only when the overshoot gets large relative to the fee does the arb's square-law share start to matter.

discrete bins and arb economics

When fixed per-trade gas is in play, discrete bins bundle repricing into fewer, larger arbitrage events than a continuous curve. That means more of the value each event moves can return to LPs as fees rather than arbitrageur profit. Wick's internal 0% path is a separate channel, but the bundling effect is one reason external arbitrageurs face different economics on wAMM than on tick-based pools.

In the dilute regime (the ratio regime defined above), arbs fire while the overshoot is still small, because the fee barrier is wide relative to per-block moves. So nearly all of each event's LVR comes back to LPs as fees. At a ratio of about 10:1, fee capture is >95%. At a ratio of 1:1, capture falls to roughly 65%. Below 1:1, the arbitrageur's share dominates and fees recover very little.

recapture, not reduction

Wick's fee algorithm is framed as recapture, not reduction. Add the per-event split up over a trading period and one thing stands out:

1. Total LVR over a window is determined by volatility and time, not by the fee level.
2. Raising the fee doesn't shrink the total. It only shifts how much comes back to LPs as fees versus what the arbitrageur keeps.

Fee revenue per block grows with volatility; arbitrageur profit per block shrinks as the fee-to-volatility ratio grows. Volatility sets the total; the fee only decides how it is split between LPs and the arbitrageur. "Higher fees reduce LP losses" gets it wrong: higher fees don't shrink the total, they shrink the arbitrageur's share of it.

On average, total LVR and endpoint IL end up around the same size, but on any single path they can look completely different. The useful design question is never "how much does the fee lower LVR?" It is "how much of it comes back to LPs as fees?"

path costs vs endpoint costs

The primer defined IL as an endpoint gap. Path costs and endpoint costs respond differently to fees: Wick's dynamic fees and internalized arb attack the path cost; the endpoint cost is IL itself, and Wick does not claim to solve it. Conflating the two is where most AMM fee discussions go wrong.

• Capturable layer (the path cost) — the small cost the LP eats each time an arb reprices the pool. Dynamic fees and internal arbitrage recapture this layer directly.
• Structural layer (the endpoint cost) — the gap that builds up between the LP position and just holding the tokens. As price rises, the LP has systematically sold the appreciating asset; as price falls, the LP has bought the depreciating one. No fee rate, auction design, or execution rule eliminates this.

Put simply: the path cost is how you got there, the cost paid at every arbitrage event along the way. The endpoint cost is where you ended up, the gap between what you hold now and what you would have held had you never LP'd.

Break the price move into many small steps. Each step's path cost is tiny, and anything that reacts per swap (fees, internalized arb) can recapture it. The endpoint gap doesn't care how many steps you take; it only depends on where price ends up. Fees react per swap; IL is where you land when you close the position. That is why no fee auction or execution tweak can eliminate endpoint IL: those tools attack the path cost and leave the endpoint gap untouched.

The takeaway: capture as much of the path cost as possible (dynamic fees, internal arbitrage, tight ranges), and keep exposure to the endpoint cost short (narrow positions, frequent rebalancing, directional hedging at the portfolio level).

An LP is a perpetually open short on volatility. While liquidity is deployed, a two-sided position collects premium (swap fees) and loses when price moves (the path-layer rebalancing cost). Options traders call this payoff a short straddle, charted below. Static fees are equivalent to a market maker quoting the same spread in calm and crisis: the premium never adjusts to the risk, even when vol spikes.

Wick's dynamic fees add a premium that scales with vol, so the position is paid more in the conditions that hurt it most. Dynamic fees do not eliminate volatility risk; they compensate for it, which is the exact decision Wick's fee algorithm encodes.

wAMM options

The path/endpoint split above maps directly onto wAMM options, which program payoffs through bin layout and hooks. Like IL, the payoff is defined by where price ends relative to a strike; like LVR, each arb-driven bin cross along the path can incur repricing cost (and the position may still earn swap fees). Hook settlement sets the endpoint payoff versus the strike. In the diagram below, red ticks mark path cost at each repricing step and the end bracket is payoff set by where spot finishes relative to the strike. Use the controls to compare paths that share the same endpoint (Zigzag vs Direct) or finish above the strike.

references

• Milionis et al. (2024) — Automated Market Making and Loss-Versus-Rebalancing. arXiv:2208.06046
• Alexander, Lambert, Fritz (2025) — IL and LVR II. arXiv:2502.04097
• Nezlobin & Tassy (2025) — LVR under Deterministic Block-Times. arXiv:2505.05113

The quantitative framework that anchors this page (the fee-to-volatility ratio, the dilute / transitional / saturated regime classification, and the fee vs arb decomposition) is grounded in research by Spherical Cow Labs. Wick's fee algorithm and in-protocol arbitrage are developed in ongoing collaboration with the Spherical Cow Labs team.