Price Tick

What is Tick?

Pangea's liquidity providers can provide liquidity to different price ranges. Because they provide liquidity to different price bands, the amount of liquidity the pool uses for swaps should be updated for each price range.

Let's look at an example below. LP X and LP Y each provided liquidity (Lx, Ly) to different price ranges. When the price of the pool changes from $P_c$ to $P_b$ by swap, Lx+Ly, the sum of the two liquidities, is used for swap in the $P_c$~$P_a$ range, and only Lx is used for the swap in the $P_a$~$P_b$ range.

In order to more efficiently adjust the liquidity size in response to price changes, Pangea's Concentrated Liquidity Pool manages liquidity by ticks. Ticks are the boundaries between discrete areas in price space. Ticks are spaced such that an increase or decrease of 1 tick represents a 0.01% (1 basis point) increase or decrease in price at any point in price space. Liquidity providers set a minimum price tick and a maximum price tick for their positions to be supplied, and provide liquidity to the interval between them.

Tick Spacing

While ticks are spaced at each 1 basis point by default, it would be inefficient to divide the price by 1 tick for the pools of Pangea. This is because each time the price changes and crosses a tick, the fees earned by liquidity providers within that interval must be settled, and the liquidity size of the new tick must be calculated. These operations can incur high gas fees when a large swap request comes in.

Therefore, when creating a pool in Pangea, tick spacing is specified according to the properties of the pool. A tick interval of 5 means the price band can be adjusted in multiples of about 0.05%, and A tick interval of 60 means the price band can be adjusted in multiples of about 0.6%.

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

Tick Structure

Designed based on Sushiswap's Trident protocol, Pangea's tick has a different structure from Uniswap V3. Uniswap V3 implements ticks in the form of an array, but Pangea's ticks are implemented in the form of a Linked List.

Tick Principles

The price ticks of the price range liquidity providers pick when providing liquidity must be multiples of the tick spacing of the pool. Lower Tick (Min Price or Price Lower) must be even multiples of the tick spacing, and Upper Tick (Max Price or Price Upper) must be odd multiples of the tick spacing.

• Lower Tick = Tick Spacing * Even Number

• Upper Tick = Tick Spacing * Odd Number

Also, since the Tick Structure of Pangea is designed as a Linked List, when supplying liquidity, it should be called with the previous tick of the Lower Tick and the previous tick of the Upper Tick. To solve this complexity, the PoolManager contract of the Pangea protocol has built-in calibration logic for Lower Tick and Upper Tick. This logic calibrates the tick information according to Pangea’s tick rules when new liquidity positions are minted.