Price Stability

How arbitrage keeps BD-Stable's price-stable

BD-Stables can always be minted and redeemed from the system for the value of its peg. This allows arbitragers to balance the demand and supply of BD-Stables in the open market. If the market price of a particular BD-Stable is above the price of its peg, then there is an arbitrage opportunity to mint this BD-Stable tokens by placing the value of the peg into the system per BD-Stable and selling the minted BD-Stable for over the peg price in the open market. At all times, in order to mint BD-Stables, a user must place the peg worth of value into the system. The difference is simply what proportion of collateral and BDX makes up that value.

When BD-Stable is in the 100% collateral phase, 100% of the value that is put into the system to mint it is collateral. As the protocol moves into the fractional phase, part of the value that enters into the system during minting becomes BDX (which is then burned from circulation). For example, in a 98% collateral ratio, every BD-Stable minted requires 98% of the value of its peg in collateral and burning 2% of its peg value in BDX. In a 97% collateral ratio, every BD-Stable minted requires 97% of the value of its peg in collateral and burning 3% of its peg value in BDX, and so on. If the market price of BD-Stable is below the price range of its peg, then there is an arbitrage opportunity to redeem BD-Stable tokens by purchasing them cheaply on the open market and redeeming BD-Stable for the worth of its peg's value from the system. At all times, a user is able to redeem BD-Stable for its peg's worth of value from the system. The difference is simply what proportion of the collateral and BDX is returned to the redeemer. When BD-Stable is in the 100% collateral phase, 100% of the value returned from redeeming BD-Stable is collateral. As the protocol moves into the fractional phase, part of the value that leaves the system during redemption becomes BDX (which is minted to give to the redeeming user). For example, in a 98% collateral ratio, every BD-Stable can be redeemed for 98% of collateral and 2% of minted BDX. In a 97% collateral ratio, every BD-Stable can be redeemed for 97% of collateral and 3% of minted BDX. The BD-Stables redemption process is seamless, easy to understand, and economically sound. During the 100% phase, it is trivially simple.

The logic above derives from the original FRAX protocol. Blindex introduces 2 new elements to the protocol: Effective Collateral Ratio and Effective BDX Coverage Ratio which modify the protocol when a shortage of collateral or BDX occurs. The goal of these changes is to provide more just collateral and BDX distribution in a situation when many users simultaneously decide to redeem or buyback.

Collateral Ratio

The protocol adjusts the collateral ratio during times of BD-Stables expansion and retraction. During times of expansion, the protocol decollateralizes (lowers the ratio) the system so that less collateral and more BDX must be deposited to mint BD-Stables. This lowers the amount of collateral backing all BD-Stables. During times of retraction, the protocol recollateralizes (increases the ratio). This increases the ratio of collateral in the system as a proportion of BD-Stables supply, increasing market confidence in BD-Stables as its backing increases. At genesis, the protocol adjusts the collateral ratio once every hour by a step of .25%. When a particular BD-Stable is above its peg, the function lowers the collateral ratio by one step per hour and when the price of BD-Stable is below its peg, the function increases the collateral ratio by one step per hour. This means that if BD-Stable price is over its peg for the majority of the time through some time frame, then the net movement of the collateral ratio is decreasing. If BD-Stable price is under its peg for the majority of the time, then the collateral ratio is increasing toward 100% on average. In a future protocol update, the price feeds for collateral can be deprecated and the minting process can be moved to an auction-based system to limit reliance on price data and further decentralize the protocol. In such an update, the protocol would run with no price data required for any asset including BD-Stables and BDX. Minting and redemptions would happen through open auction blocks where bidders post the highest/lowest ratio of collateral plus BDX they are willing to mint/redeem BD-Stables for. This auction arrangement would lead to collateral price discovery from within the system itself and not require any price information via oracles. Another possible design instead of auctions could be using PID-controllers to provide arbitrage opportunities for minting and redeeming BD-Stables similar to how a Uniswap trading pair incentivizes pool assets to keep a constant ratio that converges to their open market target price.

Effective Collateral Ratio

Effective Collateral Ratio was introduced to equalize users chances to withdraw collateral ratio. The formula for Effective Collateral Ratio is:

efCr=Cv/BDsefC_r = C_v / BD_s

where

CvC_v is collateral value in all collateral pools for a given BD-Stable expressed in underlying fiat currency

BDsBD_s is total supply of this BD-Stable​

Effective Collateral Ratio (efCR) replaces Collateral Ratio (CR) in Buyback and Redemption process when efCR < CR.

In result user will get less collateral (and more BDX) then CR suggests. This approach prevents users leaving the protocol early from getting unfair advantage over those to leave later and could otherwise be left with no collateral.

Effective BDX Coverage Ratio

BDX is a deflationary token - there will only be 21M BDX tokens minted. In the original FRAX protocol, the amount of FXS rewarded to the user was (1-CR). This won't work with BDX due to its deflationary nature.

In Blindex, every BD-Stable is supplied with a number of BDX tokens (decided by governance). These tokens are released to users in redemption and recollateralization processes.

At any moment we can calculate the total value of BDX need to support BD-Stable collateralization:

BDXn=(BDs(1min(CR,efCR)))/BDXpBDX_n = (BD_s *(1- min(CR, efCR)))/BDX_p

where

BDXnBDX_n is BDX value needed to support BD-Stable collateralization

BDsBD_s is total supply of this BD-Stable​

CRCR is collateral ratio

efCRefCR​ is effective collateral ratio

BDXpBDX_p​ is BDX/BD-Stable price

If we need more BDX then is assigned to a particular BD-Stable, Effective BDX Coverage Ratio is equal to:

efBDXCr=min(1,BDXs/BDXn)efBDXC_r = min(1, BDX_s/BDX_n)

where

BDXsBDX_s is BDX supply which belongs the this BD-Stable

BDXnBDX_n is BDX value needed to support BD-Stable collateralization

When there is excessive amount of BDX assigned to the BD-Stable, the Effective BDX Coverage Ratio = 100%.

In result user will get less BDX. This approach prevents users leaving the protocol early from getting unfair advantage over those to leave later and could otherwise be left with no BDX.

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