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Curve CryptoSwap Exchange: Overview

The "Automatic Market-Making with Dynamic Peg" (CryptoSwap) algorithm introduces a new approach to liquidity provision in decentralized finance. It aims to improve liquidity for assets that are not directly pegged to each other, differentiating itself from the traditional x·y = k model.

The core of this algorithm lies in its ability to concentrate liquidity around a price point determined by an internal oracle, adjusting this price in a way that balances potential losses and system profits.

Key features include the use of transformed pegged invariants, a method for quantifying profits and losses, and the CurveCrypto invariant, specifically designed for efficient execution on the EVM.

The algorithm also incorporates a dynamic fee structure that responds to changing market conditions. This approach seeks to enhance liquidity provision and optimize returns for liquidity providers within the decentralized finance ecosystem.

CryptoSwap Whitepaper

For a detailed overview of the CryptoSwap design, please read the official whitepaper.


The CryptoSwap market-making algorithm contains of three different classes of parameters:

  • Bonding Curve: A and gamma
  • Price Scaling: ma_time, allowed_extra_profit and adjustment_step
  • Fees: mid_fee, out_fee and fee_gamma


An excellent deep-dive artilce on the parameters:

Bonding Curve Parameters

Similar to many AMMs, Curve v2 employs a bonding curve to determine asset prices according to the pool's supply of each asset. To centralize liquidity around the midpoint of the bonding curve, Curve v2 adopts an invariant that falls between the StableSwap (Curve v1) approach and the constant-product method used by platforms like Uniswap and Balancer.

  • A: regulates the concentration of liquidity at the core of the bonding curve
  • gamma: regulates the overall breadth of the curve

Price Scaling

Curve v2 pools automatically adjust liquidity to optimize depth close to the prevailing market rates, reducing slippage. This is achieved by tracking a continuous EMA (exponential moving average) of the pool's latest exchange rates (referred to as an "internal oracle") and reallocating liquidity around this EMA only when it's economically beneficial for LPs.

  • ma_time: regulates the duration of the EMA price oracle
  • allowed_extra_profit: excess profit required to allow price re-pegging
  • adjustment_step: minimum size of price scale adjustments


Fees are charged based on the balance/imbalance of the pool. Fee is low when the pool is balanced and increases the more it is imbalanced.

There are three different kind of fees:

  • fee_mid: charged fee when pool is perfectly balanced (minimum possible fee).
  • out_fee: charged fee when pools is completely imbalanced (maximum possible fee).
  • fee_gamma: determines the speed at which the fee increases when the pool becomes imbalanced. A low value leads to a more rapid fee increase, while a high value causes the fee to rise more gradually.