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Pricing Curve

A SONICSALE pool works exactly like Uniswap V2 or a Volatile AMM pool: it uses the x*y = k curve. To account for the inexistent FTM at launch, a theoretical FTM amount is added to the pool. This is the Virtual FTM amount.

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How is this accounted?

To account for this inflated FTM amount that doesn’t actually exist, the token amount is also inflated by a certain amount considering the pool’s parameters (see below); so when the target price is achieved (when max ftm is the amount in the pool), both amounts are set to the real amounts and the price is kept the same.

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Why?

Other presale apps may use bonding curves or linear price. However, this pricing method has the following benefits:

  • uses a liquidity model that everyone is familiar with: x*y = k;
  • presale and resulting final pool are closely related in the way they’re priced, since they use the same curve

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Virtual Reserve Calculations

A SonicPool takes 3 parameters:

  • Max Supply (total supply of created token)
  • Virtual FTM
  • Max FTM

The contract will then calculate the virtual amounts to be used in pricing:

At pool creation, virtual reserves are:

  • FTM reserve: Virtual FTM as set during creation.
  • Token reserve: maxSupply / (1 - (virtualFTM / maxFTM)²)

There are a few presets for these parameters, which are seen in the app’s main page.

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Example

A pool is launched with parameters:

  • Max Supply: 5,000,000
  • Virtual FTM: 1,000
  • Max FTM: 20,000

This means the presale will end once 19,000 FTM worth of Token have been bought.

Reserve formula: maxSupply / (1 - (virtualFTM / maxFTM)²)

5000000 / (1 - (1000 / 20000)²) = 5012531.32

Applying the x*y = k curve:

5012531.32 * 1000 = k

Solving for FTM reserve = 20000 (max FTM)

x * 20000 = 5012531.32 * 1000; x = 250626.57

Price at max FTM = 20,000 / 250,626.57 = 0.07979

Now, we must switch to using the correct reserves. They are:

  • 19,000 FTM (max - virtual)
  • 238,095.25 (sold tokens - max supply)

Price with correct reserves: 19,000 / 238,095.25 = 0.07979

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