📊Bonding Curves

How Apex Burst Bonding Curves Work

Similar to the Liquidity Book feature on Trader Joe, Apex Burst’s bonding curves use bins to hold token amounts and determine prices. When AVAX is exchanged for a token, tokens are distributed from a bin until it’s empty, then the process moves to the next available bin. Token prices increase by 20% per bin, using a step-wise approach for a structured and incremental bonding curve.

This design allows Apex Burst to support multiple pricing strategies, offering flexibility for various token launches.

Curve Types Available on Apex Burst

On the Create page, Apex Burst provides several curve options:

1. Linear Pricing: Price increases linearly with supply. This curve offers predictable pricing where each additional token incrementally increases in cost.

2. Carrying Capacity Curve (Logarithmic-like): Price rises quickly initially but levels off as supply increases. Early buyers face higher price increases, but later growth stabilizes, reducing further price jumps.

3. Exponential Curve: Price increases exponentially with supply. This curve rewards early participants, but prices escalate rapidly.

4. Cubic Curve (Bell): Price increases rapidly at the start, consolidates in the middle, and rises again towards the end. This curve offers both early and late buyers opportunities, with a mid-point where prices stabilize.

Mathematical Formulas for Bonding Curves

Price Calculation for Each Bin

To calculate the price in each bin, the formula is:

$$price = basePrice \times \left(1 + \frac{i \times x}{100}\right)$$

Where i is the bin index (starting from 0), basePrice is the initial token price and x is the increment factor per bin.

Calculating the Last Non-Zero Bin Price

The price for the final bin with non-zero tokens is:

$${lastNonZeroPrice} = \text{basePrice} \times \left(1 + \frac{(n - 1) \times 20}{100}\right)$$

Where n is the total number of bins and x is the increment factor. This helps determine the final bin price at the end of the distribution.

Market Cap Calculation

The market cap, representing the token’s final value on a DEX like Trader Joe, is calculated as:

$${requiredMarketCap} = \text{totalDistribution} \times \text{lastNonZeroPrice}$$

Fraction Validation

To validate the fraction of total supply in the bins, use:

$${cumulativeValue} = \sum_{i=0}^{n-1} \text{lists}[i] \times \text{price}_i$$

Then, the fraction is calculated as:

$${fraction} = \frac{10,000 \times \text{requiredMarketCap}}{\text{cumulativeValue} + \text{requiredMarketCap}}$$

This formula ensures the allocation aligns with the desired distribution on the bonding curve and the total selected amount required for bonding.