Discrete Bonding Curves

Bonding curves have been instrumental in shaping token economies for several years. They have played a critical role in the success of Automated Market Makers (AMMs) and have transformed token liquidity, fundraising, and data curation, among other areas.

A continuous bonding curve example

This article discusses the Discrete Bonding Curve (DBC), a particular type of bonding curve that combines the best features of bonding curves and discrete AMMs (dAMMs) to enhance primary market efficiency.

What is a Discrete Bonding Curve?

A DBC is a bonding curve that behaves like a step function, unlike traditional bonding curves where the price changes continuously with the token supply. In DBC, the price changes at specific intervals of token supply.

Token distribution and sales in a DBC. Protocol captures all trading fees and offers zero slippage at constant-price levels.

A DBC could consist of buy and sell curves (or a single buy function with tax), both behaving like step functions. The difference between the buy and sell curves could diminish as more token supply is minted, making the bonding curve an efficient discrete liquidity AMM (dAMM) with minimal slippage at a sufficiently large token supply. Users purchase tokens at the buy curve price and sell them at the sell curve price.

The buy and sell curves start from the origin, moving upwards in a step-like manner. However, the sell curve is always below the buy curve, meaning the sell price is consistently lower than the buy price for the same token supply.

Each “step” represents a specific interval of token supply where the price remains constant. This resembles the “price bins” in dAMMs like Trader Joe and Maverick Protocol. Assuming small price jumps in percentages (e.g., 0.05%), a DBC becomes highly capital efficient and earns all trading fees in this primary market.

In each trade, the protocol earns the spread (i.e., tax) between the buy and the sell prices and creates another revenue stream. This is akin to fees obtained from protocol-owned liquidity (POL). This additional revenue could be gamified and given back to the protocol contributors via a staking scheme or a protocol-specific Contribution Scoring Framework.

Advantages of DBC

The DBC model offers several advantages over traditional bonding curves:

1. Controlled Price Volatility: The step function nature of the bonding curve controls price volatility. The price remains constant over a range of token supply, providing stability.
2. Reduced Slippage: As the token supply increases, the difference between the buy and sell curves decreases, reducing slippage.
3. Increased Primary Market Efficiency: Constant price regions help DBC offer a much-increased market efficiency, potentially reducing the need for a secondary market.
4. Token Launch with Elastic Supply: DBCs can be used for token launches with an elastic supply, adjusting the supply based on demand.
5. Protocol-owned Liquidity: The protocol earns trading fees, which can be shared with the community via staking. This creates a self-sustaining liquidity model.
6. No Impermanent Loss: In a DBC, the protocol itself acts as the sole liquidity provider, minting and burning tokens as needed. Since there are no external liquidity providers supplying two different assets, there’s no risk of impermanent loss in the traditional sense.
7. DBC as a dAMM: The constant-price regions in a DBC act like bins with a fixed liquidity amount. The bin steps in a dAMM are the differences between these constant-price regions. The trading fee in a dAMM is the difference between the buy and sell curve in a DBC, which is solely captured by the protocol. This eliminates the need for liquidity providers in the primary token market.

While DBCs need careful preparation and extensive testing before deployment, they combine the best features of bonding curves and discrete liquidity AMMs in a single product, offering a vast design space for diverse token economies.

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Disclaimer: This article is for informational purposes only and should not be considered financial or investment advice. Always do your own research and consult with a professional before making any financial decisions.