Price and Ticks

Tracking Price

Fusion AMM pools track prices using the square-root price method, which enhances precision and optimizes on-chain efficiency.

For a pool containing two tokens, say A and B, the square-root price is calculated as the square root of the exchange rate, representing the amount of tokens B needed to obtain one unit of token A. This approach ensures accurate price tracking within the decentralized system.

The square-root price is constrained within the range of [$2^{-64}$, $2^{64}$], accommodating a wide spectrum of possible exchange rates between the tokens.

Tick

Users can deposit liquidity on a custom price range in a Whirlpool. The smallest unit of price measurement (tick) is 1bps. Whirlpool represents the price range as a sequence of ticks and stores accounting information in each initialized tick that hosts liquidity.

Sqrt-price maps to a tick with the formula below. Each tick represents 1 basis point of change from the neighboring tick.

$$\sqrt{p}(i) = \sqrt{1.0001}^i$$

Given the supported price-range of [$2^{-64}$, $2^{64}$], the tick range for a Whirlpool is [−443636,443636][−443636,443636].

The Whirlpool account tracks both the current sqrt-price and the current tick-index.

Tick Spacing Mechanics

Due to compute cost and rent constraints, it is often not economical for a Whirlpool to allow users to deposit liquidity into every single tick. Whirlpools requires pool owners to define an additional "Tick-Spacing" parameter. This allows them to define the space between "initializable ticks", where liquidity information can be stored.

A tick-spacing of 5 means that liquidity can be deposited into tick-index that are a multiple of 5. (ex. [...-10, -5, 0, 5, 10...]).

As a general rule, the smaller the expected volatility of a pool is, the smaller tick-spacing should be. To help you decide on the best tick-spacing for your whirlpool, consider the following attributes.

1. Granularity of user definable price ranges​

The smaller your tick-spacing, the more granular the price users can deposit their liquidity in. For more stable pools, a more granular tick-spacing would let users define a tighter range to maximize their leverage.

Tick Spacing = 1

Price	Initializable Tick Index
$1.0001^{-2}$ = $\frac{1}{1.00020001}$	-2
$1.0001^{-1}$ = $\frac{1}{1.0001}$	-1
$1.0001^{0}$ = 1	0
$1.0001^{1}$ = 1.0001	1
$1.0001^{2}$ = 1.00020001	2

Tick Spacing = 100

Price	Initializable Tick Index
$1.0001^{-200}$ = $\frac{1}{\approx1.0202003198939341}$	-200
$1.0001^{-100}$ = $\frac{1}{\approx1.0100496620928766}$	-100
1.0001^0 = 1	0
1.0001^100 = $\approx1.0100496620928766$	100
1.0001^200 = $\approx1.0202003198939341$	200

2. Maximum price movement per swap​

The size of the tick-spacing defines the maximum price movement a single swap can move the price by for a Whirlpool.

Whirlpool's swap operates by iterating through each ticks with initialized liquidity. The larger the gap between initialized ticks are, the more it can theoretically traverse the price range.

A low tick-spacing pool undergoing a massive price movement may require multiple swap instructions to complete the price movement. Therefore, more volatile pairs that often has large price swings should look at higher tick-spacing to mitigate this pain point for their pool users.

3. Account rent cost for users​

On-chain storage requires account space, and the more data a program needs to store, the higher the rent required. With larger tick-spacing, fewer ticks are needed to manage liquidity across a set price range, reducing the storage cost for users.