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Token Bonding Curve

// Primary Automated Market-Maker (PAMM)

Issues tokens according to an algorithmic price curve as a function of circulating supply, where token price increases as tokens are purchased on the curve and decreases as tokens are sold back to the curve.

Token bonding curves are a dynamic pricing mechanism that uses a mathematical formula to determine token prices based on the circulating supply, unlike traditional tokens with market-driven prices. As more tokens are purchased and minted, the price increases along the predefined curve. Conversely, the price decreases when tokens are sold back to the smart contract and burned. This token type creates a direct relationship between supply and price, allowing for continuous liquidity and automated price discovery without relying on traditional order books or market makers.

This mechanism should not be confused with the more general automated market makers (AMMs) concept. Whereas AMMs typically refer to an algorithmic secondary market (S-AMM) that enables trading between two or more tokens, token bonding curves refer to the case where an AMM serves as the primary token issuing mechanism (P-AMM).

Token bonding curves originated in 2017, with two key developments occurring in parallel. Bancor introduced “smart tokens” to provide automated liquidity without traditional exchanges. At the same time, Simon de la Rouviere coined the term “bonding curves” and expanded on their potential applications in curation markets.

Advantages

  • Efficient Price Discovery: Bonding curves provide a continuous and algorithmic approach to price discovery, reflecting real-time supply and demand. This reduces the risk of price manipulation and ensures token prices adjust naturally based on market activity.
  • Built-in Liquidity: The bonding curve mechanism inherently provides liquidity, allowing users to buy or sell tokens at any time directly through the smart contract. This is particularly advantageous for new projects looking to establish a liquid market without relying on external exchanges.
  • Early Adoption: Early buyers can benefit from price appreciation as more tokens are minted, encouraging early participation.
  • Continuous Revenue/Fundraising: Projects can use token bonding curves for initial and ongoing fundraising by setting a fee on buys or sells. The continuous pricing model enables a steady inflow of funds as the project grows and attracts more participants, ensuring long-term financial sustainability.

Limitations & Risks

  • Price Volatility: The price of token bonding curves can be highly volatile, especially during the early stages when the token supply is low. Large trades can exacerbate this volatility, leading to significant price swings.
  • Market Manipulation: Although bonding curves mitigate some forms of manipulation, they are still susceptible to market dynamics and speculative behavior, which can destabilize the token price.

Design Considerations

  • Curve Design: Select a mathematical function that aligns with project goals and economic incentives. Options include linear curves (steady price increase per token), exponential curves (early adopter rewards with accelerating price growth), logarithmic curves (rapid early price increases with later stabilization), and sigmoid curves (growth phases with a controlled maturity stage to prevent runaway prices).
  • Reserve Ratio: Balance liquidity and price stability by setting an appropriate reserve fraction. Consider low reserve ratios (higher price sensitivity and speculative upside) and high reserve ratios (greater price stability and deeper liquidity but lower speculative gains). Hybrid models can adjust the ratio dynamically based on supply milestones.
  • Fee Structure: Design buy/sell fees to sustain protocol funding while maintaining token attractiveness. Look into fixed transaction fees (a percentage charged on every buy/sell), dynamic fees (adjusting based on network demand or volatility), and split-fee models, where fees are partially redistributed to stakers, the treasury, or burned to manage supply.
  • Front-Running Protection: Mitigate exploitative trading behavior. Consider batch auctions, where transactions execute at uniform clearing prices within fixed intervals and slippage limits, restricting how much prices can move within a single transaction.

Resources

Examples

AaveGotchi

GHST is sold for DAI on a bonding curve gated to users who have been approved through a centralized KYC process. GHST is a currency token that users can spend on portals and wearables. Spent GHST is split between users via rarity farming, the developer team, and the community DAO, and a portion is burned, which increases the bonding curve price.

Commons Stack Augmented Bonding Curve

Integrates additional mechanisms to address some of the limitations and risks of traditional bonding curves. It includes a reserve pool to stabilize the token price and a funding pool to support community projects. It also incorporates a vesting mechanism to prevent early speculation and a governance model to ensure that the funding is allocated to initiatives that benefit the community. The curve can be polynomial or another complex function, depending on the specific implementation.

DeSo

Each profile has a personal token bonding curve (i.e., “creator coin”) tied to their reputation that any user can buy and sell. Profiles can share revenue with their token holders by selling goods and access to services that share revenue with the curve, thereby increasing the token redemption price. Creator coins are designed to be naturally scarce, typically ranging from 100 to 1,500 coins per profile. As more people buy a creator's coins, the price increases at an accelerating rate, following a quadratic bonding curve formula.