Stability Mechanism
How does USDs keep the peg?

## 1. USDs is always valued at $1 by the protocol USDs protocol guarantees that USDs can be minted or redeemed for$1 at all times. Even when sufficient collateral is not available, USDs redeemers would get $1 worth of collateral in the form of SPA minted by the protocol. Whenever the price of USDs goes above or below$1, arbitrageurs can profit off the USDs price by utilizing the mint/redeem function and help in bringing the price back to the peg.
1. 1.
If USDs trades above $1, arbitrageurs can mint USDs for$1 of eligible collateral and SPA, then sell to profit on the peg difference (this inflates USDs supply, pushing price towards the peg).
2. 2.
If USDs trades below $1, arbitrageurs can burn USDs for$1 of SPA or eligible collateral, then sell to profit the peg difference (this deflates USDs supply, pushing the price towards peg).
In a nutshell, mint cheap and sell for profit, or buy cheap and redeem for profit. For more information on how mint and redeem functions work check outMinting and Redeeming

## 2. Dynamic Transition between Algorithmic and Collateralized Stabilisation

Sperax protocol has a fully on chain mechanism that determines the fraction of the money supply that is algorithmically determined versus collateralized. The fraction of USDs that should be collateralized by crypto-assets (χtarget) is a function of time and price of USDs.
1. 1.
As USDs matures as an asset over time, the protocol will gradually rely less on collateral and more on algorithm.
2. 2.
If the price of USDs is below the peg, the reliance on external collateral will increase. If the price of USDs is above the peg, the protocol will rely increasingly more on algorithmic stabilization (further increasing SPA deflation).
χtarget calculation
χtarget should be close to the aggregate collateral ratio (or CR = Total Value Locked/USDs Circulating Supply). However, due to the volatile nature of crypto-assets, the value of locked collateral might change and the above relationship might not hold exactly. So χredeem is designed to be lower than χmint when CR falls below χtarget.This ensures that the protocol will always be solvent even if sufficient collateral is not locked.
χmint and χredeem calculation

## 3. Dynamic Swap Fees

The protocol collects swap fees whenever USDs is minted or redeemed. The fee is dynamic and can be between 0.1% to 1.5% of the transaction value based on price and inflow/outflow volume of USDs. This discourages rapid changes in the USDs supply, acting as an added security layer.
1. 1.
When USDs price falls, dynamic minting fee will help deflate USDs supply and move price back to the peg - When 1 hour average USDs price falls below $0.99, the fee increases quadratically based on the size of deviation and deters excess USDs minting. • $Mint Fee = 0.1$ % when 1 hour average USDs price, P >$0.99
• $Mint Fee = 0.1+ [50*(.99-P)]^2$
% when P<=\$0.99
2. 2.
Dynamic redeeming fee will prevent a bank-run situation that depletes the amount of collateral locked in the protocol - When 12 hour average outflow to inflow of USDs exceeds 1.2 then the fee increases exponentially and deters excess USDs redemption.
• $Redeem Fee = 0.1$
% when 12 hour average outflow to inflow of USDs, R <1.2
• $Redeem Fee = 20^{R-1.2}$
% when R>=1.2

## 4. Auto-yield for USDs holders

As more people use USDs, the yield rate will serve as a second-layer protection from a high selling pressure, further empowering a mass adoption in various use cases including payment, derivatives, and portfolio construction. For more information on how auto-yield works check outAuto Yield