Bonding Curve and Delta

A bonding curve is a mathematical formula that defines the relationship between the price and the supply of a given asset in a pool (or between the assets in a pool). The curve is the core functionality that adjusts the price of the assets accordingly to the supply, and present it to users who are interested to buy and / or sell against the pool.

There are 2 types of bonding curves:

1. Linear Curve

The linear curve performs an additive operation to update the price. If the pool sells an NFT by giving out an NFT and receiving tokens, the next price it quotes to sell NFTs at will increase by a flat amount (known as delta).

• As an item is bought from the pool, the price will increase by a fixed amount. The reverse happens when an item is sold into the pool.

• For example, the start price is 1.0Ξ and the delta is 0.2Ξ. After someone buys 1 NFT from the pool, the price will be 1.2Ξ. If someone sells an NFT into the pool, the price will be 0.8Ξ.

1. Exponential Curve

The exponential curve performs a multiplicative operation where the delta acts as a multiplier function. If the pool has just sold an NFT by giving out an NFT and receiving tokens, the next price it will quote to sell NFTs at will increase by a percentage amount (known as delta).

• The price of the NFT increased by a percentage each time an item is bought from the pool. The reverse happens when an item is sold into the pool.

• delta is a percentage and assumes that the starting price 100%. If input the delta as 20% it means we want the price to increase/decrease by 20% after each trade. For example, initial price is 1Ξ, after someone buys 1 NFT from the pool, the next price will increase by the delta to 1.2Ξ, conversely, if someone sells 1 NFT tot he pool, the next price will decease by a multiple of the delta to 0.8333Ξ