Equations

It's not as tough as it looks, give it a try and understand how we operate.

Staking // Rebasing

$$deposit = withdrawal$$

Swaps between LUX and LUM during deposits and withdrawals are always honored 1:1. The amount of LUX deposited will always result in the same amount of LUM. The amount of LUM withdrawn from the staking contract will always result in the same amount of LUX.

$$rebase = 1 - ( LUX_D / LUM _O)$$

The treasury deposits LUX into the distributor. The distributor then deposits LUX into the staking contract, creating an imbalance between LUX and LUM.

LUM is rebased to correct this imbalance between LUX deposited (d) and LUM outstanding (o). The rebase brings LUM outstanding back up to parity so that 1 LUM equals 1 staked LUX.

Circulating Supply

Circulating Supply is equal to total LUX minted, minus the total balance of Luxor stored as collateral for SOR (s), our stable coin.

$$circulating = total - backing_s$$

Minting and Bond Price

Minting enables users to purchase bonds. This bond price is the mint price.

$$bond Price = 1 + Premium$$

LUX has an intrinsic value of 1 USD (not to be confused by backing as defined below), which is roughly equivalent to $1. In order to make a profit from minting, Luxor charges a premium for each minting action.

$$Premium = debt Ratio * BCV$$

The premium is derived from the debt ratio of the system and a scaling variable called BCV.

BCV allows us to control the rate at which bond prices increase.

The premium determines profit due to the protocol and in turn, stakers. This is because new LUX is minted from the profit and subsequently distributed among all stakers.

$$debt Ratio = bondsOutstanding/LUXSupply$$

The debt ratio is the total of all LUX promised to bonders divided by the total supply of LUX. This allows us to measure the debt of the system.

$$bondPayout_{reserveBond} = marketValue_{asset}\ /\ bondPrice$$

Bond payout determines the number of LUX sold to a minter.

For reserve mints, the market value of the assets supplied by the minter is used to determine the bond payout.

For example, if a user supplies 1000 DAI and the mint price is 250 DAI, the user will be entitled 4 LUX.

$$bondPayout_{lpBond} = marketValue_{lpToken}\ /\ bondPrice$$

For liquidity mints, the market value of the LP tokens supplied by the minter is used to determine the bond payout. For example, if a user supplies 0.001 LUX-FTM LP token which is valued at 1000 DAI at the time of bonding, and the bond price is 250 DAI, the user will be entitled 4 LUX.

Luxor Supply

$$LUX_{supplyGrowth} = LUX_{stakers} + LUX_{bonders} + LUX_ {DAO}$$

LUX supply does not have a hard cap. Its supply increases when:

• LUX is minted and distributed to LUM holders (those staking LUX).

• LUX is minted for the bonder. This happens whenever a bond is purchased.

• LUX is minted for the DAO.

  • This happens whenever someone purchases a bond with a tax fee.

$$LUX_{stakers} = LUX_{totalSupply} * rewardRate$$

At the end of each epoch, the treasury mints LUX at a set reward rate. These LUX will be distributed to those staking in the protocol.

$$LUX_{bonders} = bondPayout$$

Whenever someone purchases a bond, a set number of LUX is minted.

These LUX will not be released to the minter all at once - they are vested to the bonder linearly over time.

The bond payout uses a different formula for different types of bonds.

Check the Minting section above to see how it is calculated.

$$LUX_{DAO} = LUX_{bonders}$$

The DAO receives the same amount of LUX as the minter. This represents the DAO profit.

Backing Price (Price Floor)

$$Price Floor = Reserves / Supply_c$$

Treasury assets may be divided into two categories: reserves and liquidity.

Unlike other reserve currencies, Luxor DAO guarantees a defendable price floor, which is determined by the equation above, where the floor equals the value of the protocol's reserves divided by the circulating (c) supply.

The intuition here is for each dollar value in our reserves, we are able to cover the circulating supply at a floating price floor.

Reserves are stated in the Dashboard and equal to the following:

$$Reserves = DAI_b + (FTM_b * FTM_p)$$

Where b is the balance held in the Treasury and p is the asset price.