Redemption Rate Bounds

The redemption rate is currently bounded in the RAI protocol. These bounds set the per-second minimum and maximum values that the redemption rate can have.

Current Mainnet Values

The mainnet redemption rate bounds can be found in the Oracle Relayer, as the redemptionRateLowerBound and redemptionRateUpperBound.

Parameter Value
redemptionRateLowerBound 999999934241503702775225172
redemptionRateUpperBound 1000000065758500621404894451

Conversion to Annual Rates

The above values are RAYs in the system, which means they represent numbers with 27 decimal places.

To convert to annual rates, they must first be converted to per-second ones. Annual rates can be calculated by exponentiating per-second rates to the number of seconds in a year.

annual lower bound = (redemptionRateLowerBound/1e27)^(86400*365)

Redemption Rate Bounds as Annual Rates

Parameter Annual Value
redemptionRateLowerBound (999999934241503702775225172/1e27)^(86400*365) ~= 0.1257
redemptionRateUpperrBound (1000000065758500621404894451/1e27)^(86400*365) ~= 7.9547

These convert to approximately -88% APY and 695% APY.

Under What Conditions Will the Bounds Be Hit?

The system uses the RAI/USD market price TWAP to determine the latest redemption rate.

Using the mainnet controller settings, we can determine what RAI/USD TWAP values will cause the lower and upper redemption rate bounds to be hit.

Mainnet Controller Parameters

Parameter Value Description
Kp 7.5e-8 Proportionate Constant
Ki 2.4E-14 Integral Constant
alpha 0.9999997112 Integral leak decay

Scenario #1 P-only Deviation

To calculate what market price deviation would cause the proportionate part of the redemption rate to hit the lower bound, we can use the proportionate part of the PI calculation.

1 - Kp*(redemptionPrice - marketPrice) = redemptionRateLowerBound

Solve for lower bound using mainnet Kp:

1 - 7.5e-8*(redemptionPrice - marketPrice) = 0.999999934241503702775225172

1-0.999999934241503702775225172 = 7.5e-8*(redemptionPrice - marketPrice)

(1-0.999999934241503702775225172)/(7.5e-8) = redemptionPrice - marketPrice ~= 0.877

Similarly, for the redemptionRateUpperBound:

(1-1.000000065758500621404894451)/7.5e-8 = redemptionPrice - marketPrice ~= -0.877

If the market TWAP of RAI/USD achieves a ± 0.88 deviation, the redemption rate will hit it’s upper/lower bound.

Scenario #2 Sustained Deviations

Using mainnet Kp, Ki and alpha parameters, we have calculated what types of sustained deviations will cause the redemption rate to hit upper or lower bounds.

Deviation, $ Length of deviation
± 0.5 45 days
± 0.6 22 days
± 0.7 11 days
± 0.8 4 days