Bonding Curve

The logic underpinning the curve and real world examples

Introduction

This is an implementation of a bonding curve mechanism for buying and selling Moonshot tokens based on virtual collateral and token reserves, also known as a Constant Product curve. The curve has an quadratic shape so that the price rises slowly at the start and fast towards the end. Once ~80% of the 1B token supply is sold on the curve, the market cap reaches ~431 SOL and all remaining tokens & collateral migrate to either Meteora or Raydium (as set by the creator at launch). Approximately ~88 SOL of collateral is collected on the curve.

The curve described here applies to all coins launched after 12 August, '24. Coins launched prior use a linear curve that collects ~250 SOL in collateral before migration.

Definitions

Curve

vTOKEN * vSOL = k

Where,

vTOKEN = virtual reserve of the token
vSOL = virtual reserve of the collateral (SOL)
k = constant that determines the shape of the curve

Setting initial values

We set the value of the coefficient k based on the initial price of the token

k = vTOKEN * vSOL = iVTOKEN * iVSOL - (1)

Where, iVTOKEN is initial amount of vTOKEN = 1,073,000,000

Initial price is set at 27.95 lamports or 0.00000002795 SOL

So initial price = iVSOL/iVTOKEN = 27.95 lamports

Initial virtual and collateral reserves are set as follows :

iVTOKEN = 1,073,000,000
iVSOL = 30

Values

Total supply of tokens (T) = 1,000,000,000
Minimum price is set to 27.95 lamports or 27.95e^-9 SOL
Mcap = price * 1,000,000,000
Allocation at Migration (A) = ~80% of total supply
- The minimal token amount is 799820983207404442 (tokens have 9 decimals). That's the exact point trading stops and the migration begins. Its close to 80% of token allocation but not exact since the smart contract derives this number from the the MarketCapThreshold
- MarketCapThreshold is set to 345 SOL (A * price). The equates to a fully diluted market cap of ~431 SOL
- If a buyer places a larger trade right before the ~80% threshold, a max allocation of 82% can be sold on the curve
- Curve progress % = allocation * min token amount
Fee to be deducted at the time of migration (F) = 6 SOL for Raydium or 3 SOL for Meteora
- Raydium: 1 SOL is paid to Raydium and 3 SOL is paid to openbook
- Meteora: 1 SOL for creating various token accounts for Launch. Lock. Earn
- 2 SOL migration fees paid to Moonshot

Calculation on tokens to Migrate (M) :

For calculating M, we will calculate, at the time of migration (when supply reaches the allocation A),

SOL collected as collateral
Reduce the fee to be charged from the collateral SOL
Calculate the price at the time of migration (allocation reached)
Determine the no of tokens (to be migrated) based on the collateral collected and price at allocation

M = (collateral collected - migration fees) / price of token

Collateral Collected= current_virtual_collateral_reserves - initial_collateral_reserves
Migration fees = Fee charged for creating a pool on Raydium/Meteora + Moonshot migration Fee = 6SOL
Price of token = current_virtual_collateral_reserve / current_virtual_token_reserve