Liquidations

Interest Rates

RISK FRAMEWORK

GOVERNANCE

Borrowing Strategies

Market Interest Model Configuration

Interest Rate Model Parameters for launched markets

The Silo protocol can manage interest rates differently for every token asset. In other words, the interest model is a a plugin that works on top of every market, enabling the protocol to use different configurations to control the utilization of assets in their respective markets.

A simple example of custom configurations can be exemplified in interest rates increasing faster for volatile assets than that of stable ones.

Silos are deployed on the blockchain through on-chain votes. Take for example SIP-11. The vote proposes the deployment of CRV Silo with custom settings, including how the borrowing rate of CRV is managed (interest model configuration).

Let's take a look at CRV interest model configuration:

"uopt": "800000000000000000",

"ucrit": "900000000000000000",

"ulow": "500000000000000000",

"ki": "367011",

"kcrit": "951293759513",

"klow": "95129375951",

"klin": "1585489599",

"beta": "277777777777778",

"ri": 0,

There are three key levels of utilization for the interest rate model:

*uopt*(optimal utilization) = 80% for every asset;*ucrit*(critical utilization) = 90% for every asset;*ulow*(low utilization) = 60% for high-capitalization assets and 50% for low-capitalization assets, like CRV.

To understand the coefficients *ki*, *kcrit*, *klin*, and *klow*, it is best to convert them to annual interest rate via multiplying by 365*24*3600 (number of seconds in a year). Dividing by 10^18 to account for 18 decimal places, we obtain the following values:

ki = 0.000011574058896;

kcrit = 30;

klow = 3;

klin = 0.05

- “ki”: If utilization is near the optimal value
*ulow*and*ucrit)*, the interest rate is proportional to the integral of the difference between the current utilization and*uopt*. Such integrator works all the time, growing or falling depending on whether utilization is above or below the optimal level (*uopt*). The integrator's rate of change is governed by the coefficient*ki*= 0.000011574058896 = 1/(24*3600). The meaning is: if utilization deviates by X percentage points from*uopt*, then the integrator term will change by 1*X percentage points per day (24*3600 seconds). - “kcrit”: If utilization is close to 100% (i.e. above
*ucrit*), the APY is jacked up by the additional term which is proportional to the difference between the current utilization and*ucrit*. At the first moment of exceeding the critical level of utilization (*ucrit*), the proportionality factor equals*kcrit*. For CRV*kcrit*= 30, so if utilization is X percentage points over*ucrit*, then the nominal value of the proportional term is 30*X percentage points. The value 30 for CRV was chosen based on the parameter values of the AAVE model to get approximately the same interest rate at the first moment at 100% utilization. - “klow”: If utilization is lower than
*ulow*, another additional term appears in the model, which is used to reduce the APY sharply. This term is proportional to the difference between the current utilization and*ulow*. For CRV the proportionality factor is*klow*= 3, which means: if utilization is X percentage points under*ulow*, then the proportional term equals -3*X percentage points. For example, at 0% utilization, the proportional term equals –150 percentage points*.*The value 150% is approximately equal to the maximal historical interest rate on AAVE. - “klin”: Borrowing APY can never drop below the lower bound which is proportional to the current utilization. This bound is defined by the proportionality factor
*klin*. In the case of CRV,*klin*= 0.05, meaning: if utilization is X%, then the lower bound on the borrowing APY is 0.05*X%. The value*klin*is chosen to have at our optimal utilization level the minimal possible interest rate equals 1/2 of the interest rate set by AAVE’s formula on their optimal utilization level. - “beta”: While
*kcrit*determines the proportional term only at the first moment of exceeding*ucrit*, the complete formula for the proportionality factor is*kcrit*(1+Tcrit)*. The "time multiplier"*Tcrit*adds 1 every hour that utilization spends above*ucrit*. This is seen from the value of*beta*which equals 1/3600 (3600 seconds make up one hour). So, the value of proportionality factor after 1 hour over the critical level becomes 60, after 2 hours it's 90, etc. As utilization leaves the critical zone,*Tcrit*starts dropping at the same rate governed by*beta*. - “Tcrit” = 0: The initial value for
*Tcrit*is zero. - “ri” = 0: The integrator described earlier is initialized to zero.

All parameters for the 10 assets that will be available in the first stage of the protocol are compiled in the following table. For convenience, the table shows the values of parameters ci, ccrit, clow, clin, cbeta. Formulas relating these values with ki, kcrit, klow, klin, beta are presented below.

80%

90%

60%

20%

80%

35%

2%

100%

80%

90%

60%

20%

70%

60%

2%

100%

80%

90%

60%

20%

300%

100%

1%

100%

80%

90%

50%

20%

300%

150%

4%

100%

80%

90%

50%

20%

300%

150%

4%

100%

80%

90%

50%

20%

300%

100%

4%

100%

80%

90%

50%

20%

300%

100%

1%

100%

80%

90%

50%

20%

300%

100%

1%

100%

80%

90%

60%

20%

300%

10%

4%

100%

80%

90%

60%

20%

100%

10%

1%

100%

80%

90%

60%

20%

300%

100%

1%

100%

80%

90%

50%

20%

300%

100%

1%

100%

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Reading the interest model configuration for an asset

Existing interest model configurations