How does an expansion work?

If an expansion is required (i.e. if the TWAP > Target price of FLOAT) and we need to issue new FLOAT to stabilise the price closer to its target, the following procedure takes place:

• We run what is called a Dutch Auction. This is where the protocol, as a seller, offers to mint FLOAT to sell to arbitragers starting at the market price (or rather, the TWAP).

• We sell this FLOAT at decreasing price increments, every block of the auction, between the TWAP and the Target Price until either all the FLOAT offered is bought (i.e. there was a significant arbitrage opportunity available), or there is no more demand remaining to buy FLOAT (the arbitrage opportunity has been exhausted). In either case, sufficient amounts of FLOAT should have been minted to move the market price back to target.

• In general, the price range at which newly minted FLOAT is sold for is:

$$TWAP > Range \ of \ prices \ new \ FLOAT \ is \ offered \ for \ > Target \ Price$$

To buy the FLOAT available, arbitragers must pay in a blend of ETH and BANK. In general, if the Basket Factor were at target (100%), we would take the Target Price as ETH (since ideally, for every FLOAT we want to have an equivalent value of ETH in the Basket) and the difference between the TWAP and current auction price (which is below TWAP but above Target price) as BANK (since this is the profit of the expansion).

$$Price \ paid \ by \ arbitragers = Target \ Price \ component \ + \ profit \ component$$

However, it is likely that the Basket Factor will not always be at 100%. Therefore, we can use the expansion to rebalance the Basket Factor faster to its target amount when it is below 100%. In general, we do this by accepting some ETH as part of the profit component that goes to building up the Basket Factor.

The BANK collected is permanently burned and thus reducing the BANK supply. This means that there should be a positive correlation between the increase of demand for Float and the price of Bank.

In general, the amount of ETH/BANK arbitragers pay is this:

Situation	Basket Factor	Surplus/deficit Basket Factor	Target Price component split	Profit Component split
Basket Surplus	110%	10%	100% ETH 0% BANK	100% in BANK
Basket Deficit	90%	-10%	100% ETH 0% BANK	10% ETH, 90% BANK

‌The ETH generated from the sale is sent straight to the Basket.

The BANK collected is burned thus reducing the BANK supply. (meaning this will increase the price of BANK, ceteris paribus)

For every expansion, the protocol will take a small fee in terms of BANK to go into a community governed treasury to pay for future development and associated costs.