$NUMA Token

An rETH-backed utility token

The numa protocol introduces a unique method to facilitate and incentivize the issuance of synthetic assets. The protocol issued assets in aggregate are always over-collateralized by a centralized vault of rETH (Rocket Pool ETH), as described in The Vault. This over-collateralization can vary from 101% to infinity, based on collective user demand for collateral or synthetics.

As the net market value of the synthetics and the centralized vault are non-correlated, and the collateral backing ratio is dynamic—the protocol requires inherent elasticity to absorb the varying demand and currency fluctuations. The endogenous $NUMA token is designed explicitly to provide this utility to the protocol by being both reflexive in price and elastic in supply.

This is achieved by the vault internally pricing the $NUMA token such that its market capitalization (nominal price * supply) is always equivalent to the over-collateralization of synthetic issuance within the numa protocol. From this price, new $NUMA tokens can be minted by proportionally depositing more collateral + buy_fee into the system, or $NUMA can be burned in exchange for withdrawing a proportional amount of collateral from the system with a sell_fee.

The nominal_price of $NUMA tokens as determined by the Vault is calcuated as (rETH_$value-numoney_$value)/(numaTokensCirculating).

It can be deduced from the formula that $NUMA price will increase when ETH outperforms the net value of issued nuMoney, and will decrease when the issued nuMoney outperforms ETH.

The resulting nominal_price is then adapted to a buy_price and sell_price as adjusted by the buy_fee and sell_fee, respectively. A portion of each of the buy and sell fees are retained in the Vault, such that the collateral backing ratio of the protocol increases with every buy and sell. This increasing backing ratio is in turn reflected in the $NUMA nominal price. The rest of the fees are sent to another contract to be used for nuMoney 'Yield and LP Rewards'.

The process for minting $NUMA by depositing rETH into the vault is shown below:

Deposit rETH in to Vault to mint $NUMA

The $NUMA token is also made liquid via exchanges, and therefore users may also choose to purchase $NUMA on the open market. Arbitrage is possible between the vault and any market liquidity, and thus it can be assumed that the market price is bound by the vault pricing, including the buy/sell fees.

The market price of $NUMA is tracked via a 15minute and 30minute time-weighted average prices (TWAP) operating on the main protocol-owned-liquidity (POL) pool. This TWAP market price is then used by the protocol to allow $NUMA to be burned or minted for an equivalent value of synthetics.

Users burn $NUMA tokens in order to mint nuMoney, such as $nuUSD or $nuBTC. The value is transferred 1:1 or dollar-for-dollar from the $NUMA market price. For example, if a user wants to mint $500 worth of $nuUSD, they will burn $500 worth of $NUMA token, plus a small fee (0.15%).

Both $NUMA and nuMoney are elastic in supply, which allows for the relative supply of tokens in circulation to increase or decrease, based on the burn and mint mechanism. To exit $NUMA positions, users can either sell their tokens into an LP, or they can burn their tokens for $NUMA and subsequently remove rETH from the vault.

It should be clear that demand for minting nuMoney synthetics necessarily requires users to first obtain the protocol's utility token, $NUMA. To obtain $NUMA, users can purchase tokens via an exchange or mint new tokens by depositing additional rETH collateral into the main vault.

The supply and price of $NUMA will automatically adjust with demand for the $NUMA token and nuMoney respectively, such that the market cap of $NUMA represents the present value of the over-collateralization in the protocol.