Equations

GRP Staking

$$deposit = withdrawal$$

Swaps between GRP and the reciept tokens during staking and unstaking are always honored 1:1. The amount of GRP deposited into the staking contract will always result in the same amount of the receipt tokens. And the amount of receipt tokens withdrawn from the staking contract will always result in the same amount of GRP.

$$rebase = 1 - (G RPDeposits / Reciept Outstanding)$$

The treasury deposits GRP into the distributor. The distributor then deposits GRP into the staking contract, creating an imbalance between GRP and receipt token. receipt token is rebased to correct this imbalance between GRP deposited and receipt outstanding. The rebase brings the receipt outstanding back up to parity so that 1 receipt token equals 1 staked GRP.

GRP Minting

Minting happens by allowing users to purchase a bond. This bond price is the Mint price.

$$bond Price = 1 + Premium$$

GRP has an intrinsic value of 1 MIM, which is roughly equivalent to $1. In order to make a profit from minting, Gryphon Dao 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 GRP is minted from the profit and subsequently distributed among all stakers.

$$debt Ratio = bondsOutstanding/GRP supply$$

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

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

Bond payout determines the number of GRP 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 MIM and the mint price is 250 MIM, the user will be entitled 4 GRP.

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

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 GRP-AVAX LP token which is valued at 1000 MIM at the time of bonding, and the bond price is 250 MIM, the user will be entitled 4 GRP.

GRP Supply

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

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

• GRP is minted and distributed to the stakers.

• GRP is minted for the bonder. This happens whenever someone purchases a bond.

• GRP is minted for the DAO. This happens whenever someone purchases a bond. The DAO gets the same number of GRP as the bonder.

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

At the end of each epoch, the treasury mints GRP at a set reward rate. These GRP will be distributed to all the stakers in the protocol.

$$GRP_{bonders} = bondPayout$$

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

$$GRP_{DAO} = GRP_{bonders}$$

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

Backing per GRP

$$GRP_{backing} = treasuryBalance_{stablecoin} + treasuryBalance_{otherAssets}$$

Every GRP in circulation is backed by the Gryphon Dao treasury. The assets in the treasury can be divided into two categories: stablecoin and non-stablecoin.

$$treasuryBalance_{stablecoin} = BackingPerGRP_{reserveBond} + BackingPerGRP_{lpBond}$$

The stablecoin balance in the treasury grows when bonds are sold. Backing per GRP is calculated differently for different mints types.

$$BackingPerGRP_{reserveBond} = assetSupplied$$

For reserve mints such as MIM minting, the Backing per GRP simply equals to the amount of the underlying asset supplied by the minter.

$$BackingPerGRP_{lpBond} = 2sqrt(constantProduct) * (\%\ ownership\ of\ the\ pool)$$

For LP Mints such as GRP-AVAX Minting, the RBacking Per GRP is calculated differently because the protocol needs to mark down its value. Why? The LP token pair consists of GRP, and each GRP in circulation will be backed by these LP tokens - there is a cyclical dependency. To safely guarantee all circulating GRP are backed, the protocol marks down the value of these LP tokens.