Weighted-Product AMM

Install and import#

npm install fintech-algorithms

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

Signature#

weightedProductQuote(balanceIn, balanceOut, weightIn, weightOut, amountIn, feeRate)

Balancer's generalisation of constant product to arbitrary weights, so a pool can hold 80/20 rather than 50/50. The weights set both the target allocation and the slippage profile.

Parameters#

Returns#

{ amountOut, priceImpact, spotPrice, … }

Output amount with the weighted spot price.

Errors#

• When a weight is zero, or a balance is not positive — 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#

800

200

0.8

0.2

40

0.003

Call#

weightedProductQuote(balanceIn, balanceOut, weightIn, weightOut, amountIn, feeRate)

Returns#

object with 18 fields: model, balanceInBefore, balanceOutBefore, weightIn, weightOut, amountIn, effectiveAmountIn, feeAmountIn, …

{
  "model": "weighted-product",
  "balanceInBefore": 800,
  "balanceOutBefore": 200,
  "weightIn": 0.8,
  "weightOut": 0.2,
  "amountIn": 40,
  "effectiveAmountIn": 39.88,
  "feeAmountIn": 0.12,
  "amountOut": 35.365448312358,
  "balanceInAfter": 840,
  "balanceOutAfter": 164.634551687642,
  "invariantBefore": 606.286626604159,
  "invariantAfterFeeRetained": 606.355925414232,
  "spotPriceBeforeOutputPerInput": 1
}

Showing 14 of 18 fields.

Other exports#

This module also exports constantProductQuote, constantSumQuote, stableSwapInvariant, stableSwapQuote, 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#

Calculation flow#

flowchart LR
    A["Normalize balances, amount, and token order"] --> B["Select Weighted-Product AMM contract"]
    B --> C["Apply declared fee convention"]
    C --> D["Solve invariant or piecewise position"]
    D --> E{"Valid state?"}
    E -- "No" --> F["Reject: exhaustion, bounds, or convergence"]
    E -- "Yes" --> G["Update actual balances"]
    G --> H["Compute spot, execution, and diagnostics"]
    H --> I["Report exclusions and state label"]

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

The rest of the AMM Pricing family#

• Constant-Product AMMThe x · y = k curve behind Uniswap v2.
• Constant-Sum AMMThe x + y = k curve: zero slippage, and the pool can be fully drained of one asset.
• StableSwap InvariantCurve's invariant: nearly constant-sum near the peg, constant-product away from it.
• Concentrated-Liquidity PositionUniswap v3 positions: liquidity supplied only within a price range.