Constant-Product AMM

Install and import

bash

npm install fintech-algorithms

import { constantProductQuote } from "fintech-algorithms/digital-assets-and-on-chain-finance/amm-pricing/constant-product-amm";

Signature

constantProductQuote(reserve0, reserve1, amount0In, feeRate)

The x · y = k curve behind Uniswap v2. Price is set by the reserve ratio, so every trade moves it — and the slippage a trade suffers is a deterministic function of its size relative to the pool.

Parameters

Name	Type	Notes
`reserve0`	`number`	Reserve of the input token. min: 0
`reserve1`	`number`	Reserve of the output token. min: 0
`amount0In`	`number`	Input amount. min: 0
`feeRate`	`number`	Fee as a fraction, taken from the input before the swap. min: 0 · max: 1

Returns

{ amountOut, priceImpact, effectivePrice, spotPriceAfter, … }

Output amount with the price impact and the post-trade spot price.

Errors

When a reserve is zero, or feeRate falls outside 0…1 — throws

Complexity: time O(1), space O(1).

Worked example

executed Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

Input

reserve0

reserve1

amount0In

feeRate

0.003

Call

constantProductQuote(reserve0, reserve1, amount0In, feeRate)

Returns

object with 16 fields: model, reserve0Before, reserve1Before, amount0In, effectiveAmount0In, feeAmount0, amount1Out, reserve0After, …

{
  "model": "constant-product",
  "reserve0Before": 1000,
  "reserve1Before": 1000,
  "amount0In": 10,
  "effectiveAmount0In": 9.97,
  "feeAmount0": 0.03,
  "amount1Out": 9.871580343971,
  "reserve0After": 1010,
  "reserve1After": 990.128419656029,
  "invariantBefore": 1000000,
  "invariantAfter": 1000029.7038525896,
  "spotPriceBeforeToken1PerToken0": 1,
  "spotPriceAfterToken1PerToken0": 0.980325167976,
  "executionPriceToken1PerToken0": 0.987158034397
}

Showing 14 of 16 fields.

Other exports

This module also exports constantSumQuote, stableSwapInvariant, stableSwapQuote, weightedProductQuote, concentratedLiquidityPosition. Every module additionally exports run as an alias of its primary function, and a meta object carrying its catalog id, domain, family, shape and article URL.

Diagrams

How it works

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References

Uniswap v2 Core whitepaper — Uniswap
StableSwap whitepaper — Curve Finance / Michael Egorov
Balancer whitepaper — Balancer Labs
Uniswap v3 Core whitepaper — Uniswap
Source discipline