Research Uniswap price impact

[nampc1]

We need to calculate price impact for swaps on Asset Hub to warn users

[nampc1]

https://calculator.academy/price-impact-calculator/ https://stackoverflow.com/questions/74282316/uniswap-v2-pool-priceimpact https://support.uniswap.org/hc/en-us/articles/8643794102669-Price-Impact-vs-Price-Slippage https://dailydefi.org/articles/price-impact-and-how-to-calculate/ https://stackoverflow.com/questions/74282316/uniswap-v2-pool-priceimpact https://medium.com/@arian.web3developer/everything-about-price-impact-slippage-rate-and-deadline-in-dex-swaps-explained-on-uniswap-dex-7f700ffa3948 https://blog.uniswap.org/uniswap-v3-math-primer https://blog.uniswap.org/uniswap-v3-math-primer-2 https://medium.com/luchadores-chronicles/how-to-calculate-price-impact-b4c87d8b10ed

[bluezdot]

Short note: We apply Fomular 3. Base formulation:

• x token A; y token B; k = x * y; rate = x/y. x,y,k are known
• swap m token A to n token B. m is known
• x' = x + m
• y' = k / x' (Because x' * y' must also equal to k)
• n = y - y'

Where:

• x: the amount of token A in Pool.
• x': the amount of token A in Pool after swappnig.
• y: the amount of token B in Pool.
• y': the amount of token B in Pool after swapping.
• k: Pool constant.
• m: Amount of token A used to swap.
• n: Amount of token B actual receive.
• Skip for fees and slippage impact.

---

• PI = n / y'

=> Finally formula 1: PI = ym/k

• Detail:
  • PI = n / y' = (y - y') / y' = (y - k / x') / (k / x') = (y - k / (x + m)) (x + m) / k = (y (x + m) - k) / k = y (x + m) / k - 1 = y m / k.

---

• PI = actual_rate/market_rate - 1
• m/n = actual_rate
• x/y = market_rate

=> Finally formula 2: PI = m/x

• Detail:
  • m/n = m / (y - k / x') = m / (y - k / (x + m)) = m / ((xy + my - k) / (x + m)) = m * (x + m) / my = (x + m) / y.
  • PI = ((x + m) / y) / (x / y) - 1 = (x + m) / x - 1 = m / x

---

• PI = 1 - market_rate/market_rate_after_swap
• x/y = market_rate
• x'/y' = market_rate_after_swap

=> Finally formula 3: PI = (x + m)^2 / xy

• Detail:
  • x'/y' = (x + m)/(xy / x') = (x + m) * (x + m) / xy = (x + m)^2 / xy

[Sokol142196]

Version test: https://9dcf8574.subwallet-webapp.pages.dev/ Validation passed in case:

• Show low liquidity warning with Price impact < 0.15 %

---

Re-check:

• [x] Formula of price impact
• [x] Compare with https://app.dotacp.mvpworkshop.co/swap

[Sokol142196]

Version test: https://00ebb04b.subwallet-webapp.pages.dev/

Validation passed in cases:

• Price impact < 0.15%
• Price impact >= 0.15%: Show warning