concepts

primer

Before the math, four definitions. The rest of this page assumes all four.

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. Arbs are 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 eats per arb event. Every time an arb 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 arb 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).

why IL gets worse in tight price ranges

Concentrated designs (including wAMM) do not create a new kind of risk. They compress the same AMM rebalancing into a narrower price range, which amplifies IL when price moves far. A full-range V2 pair might see ~5.7% IL on a 2× move; a narrow DLMM position can approach full loss if price exits the price range entirely.

How the four connect, in one sentence: arbitrage is the mechanism, 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, and the rest of this page measures or mitigates these.

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 monetizes the rebalancing flow it creates

Everything below is the reasoning behind those choices. For product behavior, see dynamic fees and Wick arbitrage.

fee-volatility mismatch

LP risk changes minute-to-minute with volatility; a fixed fee does not. The result on a static-fee pool is the same 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.

A subtle point about higher fees: they don't reduce how much total value arbitrage pulls out of a pool over a trading window. They shift the split: a larger slice comes back to the LP as fee revenue, a smaller slice gets kept by the arbitrageur. That is why Wick talks about "recapture" rather than "reduction". The share-not-total result is worked through below.

For how the live algorithm responds, see dynamic fees.

fee-to-volatility ratio

Wick sizes swap fees so per-block price jitter rarely crosses the fee barrier. The knob it tunes is one number: the fee-to-volatility ratio, the ratio of the swap fee to the typical per-block price move. Everything else on this page (per-block extraction, arb frequency, 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 relative to the price jitter, arbs only fire on genuinely large moves, and almost all of what they extract comes back to LPs as fees. Below a ratio of 1:1, the fee barrier is porous and the arbitrageur keeps most of the extraction.

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

Three quantities, all in plain English:

• 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. Their ratio has no units, so it compares cleanly across chains, assets, and fee tiers.

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

Wick's venue timing

Wick runs on Lighter EVM and the Lighter orderbook because both update price on sub-second block times. That keeps the fee-to-volatility ratio in the dilute regime at normal fee tiers. 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. Per-event extraction is mostly recaptured as fees; endpoint IL, the gap defined in the primer above, is structural and out of scope for fees.

fee-arb decomposition

Wick sizes its swap fee so fees take most of what the arb would have kept on every event that touches the pool. That split is worth unpacking, because it is what every other number on this page reduces to.

Every arb 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.

At small overshoots, fees dominate; the arbitrageur's surplus is negligible compared to the fee charge. Only when the overshoot gets large relative to the fee does the quadratic term start to matter.

In the dilute regime (the ratio regime defined above), arbs fire at small overshoots because the fee barrier is wide relative to per-block moves. That pushes essentially all of the per-event LVR back to LPs as fees. At a ratio of about 10:1, fee capture is >95%. At a ratio of 1:1, it collapses toward 50%. Below 1:1, the arbitrageur's share dominates and fees recover very little.

fees redistribute, they don't reduce

Wick's fee algorithm is framed as recapture, not reduction, and this section is why. Aggregate the per-event split across a trading period and something important falls 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. The sum is pinned. The naive claim that "higher fees reduce LP losses" is wrong on its face: higher fees reduce the arbitrageur's share of a fixed quantity. What LPs lose via the price channel (over a long window, total LVR tracks how much the LP underperformed a hold portfolio, the endpoint gap from the primer) is unchanged by fee choice. The useful design question is never "how much does the fee lower LVR?" It is "how much of that extraction comes back to LPs as fees?"

liquidity asymmetry

The CEX vs DEX depth gap is why Wick internalizes arbitrage instead of simply widening fees. The arb is going to happen; the question is who eats the move and who books the profit, and the math is unforgiving for the shallower venue.

In cross-venue arbitrage, what the arbitrageur gains equals what both venues lose combined. Moving liquidity between venues changes who pays, not the total.

The pool with less liquidity eats more of the move. At a CEX / DEX liquidity ratio of 100:1 (a conservative estimate for major markets), the DEX bears 99.1% of the total extraction and the CEX bears 0.9%. As the CEX side grows, the DEX eats even more of the pain.

This is the structural reason DEX LPs need protection. Absent any internalization, CEX-driven arbitrage is a direct subsidy from DEX LPs to CEX market makers; the deeper venue takes almost none of the pain and books almost all of the realized basis. Internalizing the arb flips that flow: Wick captures the same spread the external bot would have taken, and routes it back to the protocol rather than to an outside venue.

path costs vs endpoint costs

The primer defined IL as an endpoint gap. This section is why path costs and endpoint costs respond differently to fees, and why Wick's dynamic fees and internalized arb attack one but not the other.

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. Those two layers behave completely differently, and conflating them is where most AMM fee discussions go wrong.

• Capturable layer (the path cost) — the per-step cost of the pool's price moving through its own concave value surface. Fees and internalized arb recapture this layer. Dynamic fees + backrun internalization address it directly.
• Structural layer (the endpoint cost) — the accumulated exposure gap between the LP position and a flat hold portfolio. 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.

In plain English: the path cost is how you got there: the cost paid at every arb event along the path. 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.

Slice the price move into many small steps. The per-step path cost is small and shrinks as steps get finer; anything that reacts per swap (fees, internalized arb) can recapture it. The endpoint cost adds up linearly with each step, so IL stays finite no matter how finely you slice the path. 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 design implication is clean: maximize capture of the path cost (dynamic fees, backrun internalization, tight ranges), minimize exposure duration to the endpoint cost (narrow positions, frequent rebalancing, directional hedging at the portfolio level).

an LP is continuously writing a straddle

A two-sided LP position behaves like a perpetually open short straddle: it collects premium (swap fees), loses on volatility (rebalancing cost), and can never be closed. 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.

protocol-owned ALM

Wick runs an in-house protocol-owned ALM because the same protocol that supplies tight liquidity on the main pool is the one best placed to monetize the rebalancing flow that tight liquidity creates. Concretely: keep liquidity near the current price to improve execution for traders, and route the rebalancing flow through the dynamic fees + in-protocol arbitrage instead of leaking it to outside bots.

why tight ALM normally fails

Tight ALM gives traders excellent execution, but it also has to be repriced constantly as the market moves. In a standard vault, the LP keeps swap fees while arbitrageurs take the rest of the repricing spread, which is why tight ALM often loses money even when fees look strong.

value extracted = fees kept + value lost to arbitrage

Tight liquidity is productive because it concentrates depth where trading happens, but that same concentration also makes the position more sensitive to constant repricing. In many tight ALM setups, fees are not enough to offset IL and constant repricing losses. The position can generate strong fees and still lose more than it earns because arbitrage keeps extracting value every time price moves.

Arbitrage is what keeps the position aligned with the market, but it is also what extracts value from the LP. That is why many tight ALMs fail: they earn fees, but lose more to arbitrage and IL than they make back.

Wick's structural advantage

Wick is not just another LP. It operates the venue, the dynamic fees system, and the internal arbitrage layer.

position result = fees + value kept by protocol - IL

Wick changes that failure mode. Dynamic fees protect more of the fees during volatile repricing, and Wick's internal backrun captures part of the value that standard ALMs leak. Instead of relying on fees alone, Wick's ALM is designed to keep both fees and part of the arbitrage profit inside the system.

That is the structural advantage of running an in-house ALM alongside in-protocol arbitrage. The same protocol that provides the tight liquidity is also the protocol best positioned to monetize the rebalancing flow it creates.

If fees plus internalized arbitrage exceed IL, the position compounds. If not, it decays. Tight ALM maximizes both fee income and capturable path-cost recovery, but cannot hedge the directional endpoint loss, which is why directional exposure is managed above the position level.

the recapture loop

1. The ALM keeps deep liquidity near price, improving execution for traders.
2. Price moves create rebalancing flow that would normally leak value.
3. Dynamic fees reclaim more of the fees when repricing risk rises.
4. Wick internalizes the remaining arbitrage profit, keeping more value inside the system.
5. That value can be recycled back into the strategy instead of being fully externalized.

why this is structurally different

Wick can recover the capturable part of the repricing cost, but not IL. A two-sided position still loses value when price trends hard in one direction. IL is the irreducible cost of providing two-side liquidity, not external leakage.

Standard ALMs lose both layers. Wick recovers the capturable layer; the structural residual is the minimum cost possible.

scaling properties

There is still a tradeoff. A tighter range makes the strategy more productive when markets are active, but it also increases how often the position needs to be repriced. Tighter positioning increases both fee generation and arbitrage pressure. The strategy only works if Wick captures enough of that arbitrage to outweigh the additional IL.

Wick's edge is not that this tradeoff disappears. It is that Wick can optimize it from both sides at once:

• charge adaptive fees when repricing risk rises
• internalize arbitrage when value would otherwise leak

In that regime, tighter liquidity does not just magnify loss events. It also magnifies the amount of rebalancing flow that Wick can recycle back into the strategy.

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, the fee vs arb decomposition, and the liquidity-asymmetry result) 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.