Concentrated Liquidity Tick-Walking Simulator
Simulate granular non-linear tick crossing, liquidity utilization (L = Δy / Δ√P), and fee tier slippage on concentrated AMMs.
Simulation Parameters
CLMM Mathematical Invariant
Unlike constant-product AMMs (x · y = k), concentrated liquidity allocates capital strictly within discrete price intervals [P_a, P_b]. When a trade consumes all real reserves in the active tick interval, the router advances to the next initialized tick (i_next), compounding slippage non-linearly.
Traversed Tick Crossing Ladder
Individual price steps executed by the smart contract router to fulfill $100,000 volume.
| Step | Tick Index | Price Interval | Available Depth | Volume Filled | Marginal Price | Marginal Impact |
|---|---|---|---|---|---|---|
| #1 | #78770 | $2,620.00 - $2,630.00 | $4,200,000 | $100,000 | $2,625.00 | +0.01% |
Mastering Concentrated Liquidity: The Microstructure Revolution of Decentralized Exchanges
The transition from automated market makers governed by constant-product curves (e.g., Uniswap V2's $x \cdot y = k$) to Concentrated Liquidity Market Makers (CLMMs, exemplified by Uniswap V3, Curve Finance, and Raydium CLMM on Solana) represents the most consequential structural milestone in decentralized finance. By allowing liquidity providers (LPs) to allocate capital strictly within discrete price intervals rather than across an infinite price spectrum ($0, \infty$), concentrated AMMs dramatically compress bid-ask spreads and allow billions of dollars in volume to clear with fractional capital requirements.
However, this exponential leap in capital efficiency introduces complex execution microstructure. Unlike continuous orderbooks where limit orders sit on explicit price rungs, or constant-product pools where slippage scales predictably with trade size, concentrated liquidity pools execute trades across contiguous piecewise-linear price steps known as ticks. When an incoming market order exceeds the reserves available within the current tick range, the smart contract router transitions across initialized tick boundaries, compounding slippage non-linearly.
Virtual Reserves & The CLMM Invariant
In a concentrated pool, the relationship between price ($P$), liquidity ($L$), and token balances is defined by virtual reserves:
Here, $L$ represents the liquidity density of the active tick. Within any single tick interval $[P_a, P_b]$, the pool acts exactly like a traditional constant-product AMM with real reserves augmented by virtual offsets. As price approaches $P_b$, the pool converts all real base tokens into quote tokens.
Discrete Tick Spacings & Router Traversal
Ticks are indexed as integer exponents of 1.0001 ($P(i) = 1.0001^i$). Because updating every single tick on-chain would incur excessive gas overhead, pools enforce a tick spacing parameter tailored to pool volatility.
For example, a 0.05% fee pool uses a tick spacing of 10 ticks (approximately 0.1% price delta per bin), while a 0.30% fee pool enforces a tick spacing of 60 ticks. When large orders deplete the active bin, the router crosses multiple spacing boundaries, creating discrete execution steps as captured in our simulator ladder.
Capital Efficiency vs. Uniswap V2 Benchmark
The capital efficiency multiplier of concentrated liquidity is expressed as:
For stablecoin pairs trading within tight bands (e.g., $0.9995 to $1.0005), concentrated capital achieves up to 4,000x greater depth than a constant-product pool with the same TVL. For volatile pairs like ETH/USDC operating within a $\pm 10\%$ band, efficiency ranges between 20x and 80x.
Protocol Comparison: Uniswap V3, Curve & Raydium
While Uniswap V3 popularized tick-based CLMM on EVM networks, Raydium ported this architecture to Solana, leveraging sub-second block times and low transaction fees to enable high-frequency tick updates. Curve Finance implements concentrated crypto pools via its automated internal peg-shifting algorithm, dynamically re-centering liquidity around an exponential moving average price.
Frequently Asked Questions: Concentrated Liquidity Simulation
Detailed technical answers regarding algorithmic trade routing, tick calculations, and fee tiers.
How does trade size affect the number of ticks crossed?
As trade volume expands, it absorbs the token inventory within the active tick. If the net swap amount exceeds the available depth, the execution price jumps to the next initialized tick boundary. Larger trades traverse multiple bins, each with its own marginal price, compounding total price impact.
Why are fee tiers critical for concentrated liquidity pools?
Fee tiers (0.01%, 0.05%, 0.30%, 1.00%) compensate liquidity providers for volatility and impermanent loss risk. Stable pairs thrive on 0.01% with tight tick spacing (1), while volatile pairs require 0.30% with wider spacing (60) to protect LPs against high-frequency arbitrageurs.
What is the difference between price impact and LP fee slippage?
LP fees are deducted upfront from the swap input (e.g., 0.05% of trade size goes to liquidity providers). Price impact, conversely, is the execution price deviation caused by walking through the orderbook or CLMM tick ladder. Total slippage is the sum of fee deduction and price impact.
How does Coinorama simulate multi-chain CLMM liquidity?
Coinorama pulls live tick bitmaps and liquidity descriptors directly from verified smart contracts on Ethereum, Arbitrum, Base, and Solana, reconstructing exact depth ladders for top trading pairs.