# Equation

## Staking

$$
HOOK = CLOCK
$$

 Swaps between **HOOK** and **CLOCK** during staking and unstaking are always honored 1:1. The amount of **HOOK** deposited into the staking contract will always result in the same amount of **CLOCK**. And the amount of **CLOCK** withdrawn from the staking contract will always result in the same amount of **HOOK**.

$$
rebase = 1 - ( HOOKdeposits / CLOCK
outstanding )
$$

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

## Minting

$$
Minting Price=Market Price \* (1 - DicountRate)
$$

 Intrinsic value of **HOOK** token starts from 1 KUSDT. Minting price is determined after discount from  the market price.

$$
mintPayout = marketValue\_{asset}\ /\ mintPrice
$$

 Mint payout determines the number of **HOOK** sold to a minter. Regardless of asset type, the market value of the assets supplied by the minter is used to determine the mint payout. For example, if a user supplies 1000 KUSDT and the Mint price is 250 KUSDT, the user will be entitled 4 **HOOK**.

## HOOK Supply

$$
HOOK\_{supplyGrowth} = HOOK\_{stakers} + HOOK\_{minters} + HOOK\_{protocol}
$$

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

* **HOOK** is minted and distributed to the stakers.
* **HOOK** is minted for the bonder. This happens whenever someone mints.
* **HOOK** is minted for the protocol. This happens whenever someone mints. The protocol gets the same number of **HOOK** as the minter.

$$
HOOK\_{stakers} = HOOK\_{totalSupply} \* rewardRate
$$

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

$$
HOOK\_{minters} = mintPayout
$$

 Whenever someone purchases a bond, a set number of **HOOK** is minted. These **HOOK** will not be released to the minter all at once - they are vested to the minter linearly over time. The mint payout uses a different formula for different types of mints. Check the minting section above to see how it is calculated.

$$
HOOK\_{protocol} = HOOK\_{minters}
$$

 The protocol receives the same amount of **HOOK** as the minter. This represents the protocol profit.

## Backing per HOOK

$$
HOOK\_{backing} = treasuryBalance\_{stableLP} + treasuryBalance\_{otherLP}
$$

 Every **HOOK** in circulation is backed by the **Neverland** treasury. The assets in the treasury can be divided into three categories: LP including **HOOK** (HOOK LP), stableLP and non-stableLP.

$$
treasuryBalance\_{stable} = RFV\_{stableLP} + RFV\_{hook LP}
$$

 The stable balance in the treasury grows when users mint. RFV is calculated differently for different bond types.

$$
RFV\_{stableLP} = assetSupplied
$$

 For stableLP such as KUSDT-KDAI and KUSDT-KUSDC, the RFV simply equals to the amount of the underlying asset supplied by the minter.

$$
RFV\_{hookLP} = 2sqrt(constantProduct) \* (%\ ownership\ of\ the\ pool)
$$

 For HOOK LP such as HOOK-KUSDT, the RFV is calculated differently because the protocol needs to mark down its value. Why? The LP token pair consists of **HOOK**, and each **HOOK** in circulation will be backed by these LP tokens - there is a cyclical dependency. To safely guarantee all circulating **HOOK** are backed, the protocol marks down the value of these LP tokens, hence the name *risk-free* value (RFV).

$$
HOOK LP constantProduct = HOOKqty \* OTHERTOKENqty
$$

 constantProduct of HOOK LP is product of **HOOK** quantity and other token. In case of 10 HOOK - 1000 KUSDT LP at HOOK price $100, the constantProduct is 10,000 and 2 squareroot is 100. It means it can back total 100 HOOK for $1 where there's bankrun and people dump **HOOK**. It will be 100 HOOK - 100 KUSDT at HOOK price at $1.

$$
CV\_{otherLP} = VALUE\_{otherLP} \* 1/2
$$

 For other LPs except HOOK LP, we set the backing value for 50% of the asset value. LP token has high resistence to market volatility especially when one of the asset is stable token such as KUSDT or KDAI. In case of KETH - KUSDT, the 50% of the LP value can be kept until KETH price drops to 25% from its original value. (ex: $5,000 → $1,250)

 **Neverland** sets Corrected Value of other LPs to 50% of its current value, and mints HOOK based on it. (User gets 100% of **HOOK** tokens based on the minting price but the tokens to be released for staking reward is 50% of the asset value) Thus, it has 50% of buffer to back the intrinsic value and let the protocol acquire budget from 3% of the treasury for marketing and development for building richer **Neverland** eco-system.