Rebase Protocol

The Idea Behind It

As a fundamental economic principle, when supply shrinks, the price rises; when it expands, the price falls. Rebase Protocol uses that simple principle to stabilize the price. It adjusts the supply to ensure that the demand always matches the supply. Under this protocol, the balance of users is elastic; it shrinks when the price is under its target and expands when the price is above its target. These changes are applied slightly, smoothly, and gently to avoid user confusion.

This method of stabilizing the price is similar to the one that Amplfoth uses.

More In Depth

How is it implemented?

For each user, a number named "share" is stored on the blockchain. The user's share indicates how much of PARSE's total supply is owned by that user. There is a conversion coefficient that indicates each share is equal to how much PARSE.

$$\mathrm{conversion~coefficient} = \frac{\mathrm{total~nummber~of~shares}}{\mathrm{total~PARSE~supply}}$$

Rebase Protocol changes the total PARSE supply by altering the conversion coefficient.

How is it calculated?

The function $f$calculates the rebase percentage, a number between $u$ and $l$. The rebase percentage determines how much the total supply should change; if it is greater than one, the total supply expands, and if it is smaller than one, the total supply shrinks. The rebase percentage equal to one means no changes to the total supply. The function $f$ is an S-shaped curve with two asymptotes (upper and lower bounds) named $u$ and $l$. There is another hyperparameter called $g$, the growth rate which determines the curve's steepness. The function $f$ is defined as below: ($p$ is the price)

$$f(p)=l+\frac{u-l}{1-\frac{u}{l}\cdot 2^{-g\cdot p}}$$

Using the S-shaped curve makes the behavior of Rebase Ptorocol smooth, bounded, and resistant to the noisy oracle price. For more details, see here and here.

Scheduling

Same as the Tax Protocol schedule.

Tax vs. Rebase

There are three thresholds:

• rebase upper threshold

• tax threshold (or $\theta$)
• rebase upper threshold

As soon as the price varies between the tax threshold and rebase upper threshold, nothing happens. When the price goes beyond the rebase upper threshold, the total supply extends. When the price goes below the tax threshold but not lower than the rebase lower threshold, the contract imposes some degree of tax on all transactions. For prices lower than the rebase lower threshold, the tax rate is set to zero, and the Rebase protocol shrinks the total supply.

tax and rebase thresholds