StableSwap Invariant

Install and import#

npm install fintech-algorithms

import { stableSwapQuote } from "fintech-algorithms/digital-assets-and-on-chain-finance/amm-pricing/stableswap-invariant";

Signature#

stableSwapQuote(balances, amountIn, amplification, feeRate, inputIndex, outputIndex)

Curve's invariant: nearly constant-sum near the peg, constant-product away from it. The amplification coefficient sets where that transition happens, and it is what lets a stablecoin pool quote size with almost no slippage until it suddenly cannot.

Parameters#

Returns#

{ amountOut, invariant, priceImpact, iterations, converged, … }

Output with the invariant D and whether the Newton solve converged — an unconverged quote must not be traded on.

Errors#

• When the indices are equal or out of range, or the solve fails to converge — throws

Complexity: time O(assets × iterations), space O(assets).

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#

[1000, 1000]

10

100

0.0004

Call#

stableSwapQuote(balances, amountIn, amplification, feeRate, inputIndex, outputIndex)

Returns#

object with 18 fields: model, balancesBefore, balancesAfter, inputIndex, outputIndex, amountIn, grossAmountOut, feeAmountOut, …

{
  "model": "stableswap",
  "balancesBefore": [1000, 1000],
  "balancesAfter": [1010, 990.004497337927],
  "inputIndex": 0,
  "outputIndex": 1,
  "amountIn": 10,
  "grossAmountOut": 9.999502463058,
  "feeAmountOut": 0.003999800985,
  "amountOut": 9.995502662073,
  "executionPriceOutputPerInput": 0.999550266207,
  "priceImpactFromPegFraction": 0.000049753694,
  "DBefore": 2000,
  "DAfterFeeRetained": 2000.004000000989,
  "DIterations": 1
}

Showing 14 of 18 fields.

Other exports#

This module also exports constantProductQuote, constantSumQuote, stableSwapInvariant, 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#

Calculation flow#

flowchart LR
    A["Normalize balances, amount, and token order"] --> B["Select StableSwap Invariant 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.
• Weighted-Product AMMBalancer's generalisation of constant product to arbitrary weights, so a pool can hold 80/20 rather than 50/50.
• Concentrated-Liquidity PositionUniswap v3 positions: liquidity supplied only within a price range.