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Pricing Algorithm
The Automated Market Making (AMM) pricing algorithm based on the ERC404 protocol focuses on utilizing bonding curves for managing liquidity depth and volatility in the NFT market, alongside facilitating direct exchanges between ERC404 and ERC20 tokens. Here are the core components of the algorithm and its mathematical model:
Choice of Bonding Curve
A bonding curve is a mathematical model defining the relationship between the supply of tokens and their price. In the NFT market, this curve aids in automatic price adjustments, dynamically changing prices based on demand fluctuations. The most common types of bonding curves include linear, exponential, and logarithmic.
Model Selection Criteria

Linear curve: Suitable for markets with high liquidity and relatively stable price changes.

Exponential curve: Fits rapidly growing markets, where demand increases lead to accelerated price rises.

Logarithmic curve: Best for mature markets, where the impact of demand increases on price gradually diminishes.
Mathematical Model
Assuming the exponential bonding curve is chosen, its basic form can be expressed as:
P=C×Sk
Where:

p represents the price,

C is a constant,

S is the supply,

k is the curve's slope (a constant greater than 0).
The model's key is to control the pricesupply relationship by adjusting the values of C and k to meet different market demands.
Dynamic Adjustment Mechanism
To accommodate market condition changes, a dynamic adjustment mechanism is needed to update the values of C and k in realtime. This can be achieved by monitoring market liquidity and trading activity.
Adjustment Strategies:

Liquidity Indicators: Monitor transaction volume and the number of active trading addresses to assess market liquidity.

Price Volatility: Analyze the rate of price changes to determine market volatility.

Adaptive Adjustment: Automatically adjust the values of C and k based on changes in liquidity and volatility.
Exchange Mechanism
For direct exchanges between ERC404 and ERC20 tokens, the following formula can determine the equivalent value:
ERC20amount=ERC404value
Pcurrent
Where:

ERC20amount is the amount of ERC20 tokens,

ERC404value is the current value of ERC404 tokens,

Pcurrent is the current price of ERC404 tokens.

Implementing this pricing algorithm provides an efficient, transparent, and marketadaptive liquidity management and marketmaking solution for ERC404based NFT assets.