# Parameters

There is an explanation of the following parameters in [Model Parameters](https://docs.exact.ly/resources/math-paper#model-parameters).

## A. Reserve Factor

$$
\begin{align\*} \eta = 5% \end{align\*}
$$

$$\eta$$ the fraction of the total Variable Rate Pool deposits established as Liquidity Reserves can't be borrowed and will only be available for withdrawals.

## B. Treasury Fee

The treasury fee refers to the percentage of interest rate charges paid by borrowers that the protocol retains for its treasury.

* **Treasury Fee on OP Mainnet**

$$
\begin{align\*} \lambda\_r = 20% \end{align\*}
$$

OP Mainnet Treasury multisig address: <https://optimistic.etherscan.io/address/0x23fd464e0b0ee21cedeb929b19cabf9bd5215019>

* **Treasury Fee on Ethereum Mainnet**

$$
\begin{align\*} \lambda\_r = 0% \end{align\*}
$$

## C. Optimism Mainnet Interest Rate Curves

* **USDC**

| Parameter         | Value       |
| ----------------- | ----------- |
| $$A$$=            | 4.7074e-03  |
| $$B$$=            | 3.8577e-02  |
| $$U\_{max}$$=     | 1.200000000 |
| $$U\_{liq}0$$=    | 0.880000000 |
| $$k\_{sigmoid}$$= | 2.500000000 |
| $$α$$=            | 1.250000000 |

* **USDC.e**

| Parameter         | Value       |
| ----------------- | ----------- |
| $$A$$=            | 4.7074e-03  |
| $$B$$=            | 3.8577e-02  |
| $$U\_{max}$$=     | 1.200000000 |
| $$U\_{liq}0$$=    | 0.880000000 |
| $$k\_{sigmoid}$$= | 2.500000000 |
| $$α$$=            | 1.250000000 |

* **WETH**

| Parameter         | Value       |
| ----------------- | ----------- |
| $$A$$=            | 1.0164e-03  |
| $$B$$=            | 1.8718e-02  |
| $$U\_{max}$$=     | 1.300000000 |
| $$U\_{liq}0$$=    | 0.880000000 |
| $$k\_{sigmoid}$$= | 2.500000000 |
| $$α$$=            | 1.100000000 |

* wstETH

| Parameter         | Value       |
| ----------------- | ----------- |
| $$A$$=            | 1.0164e-03  |
| $$B$$=            | 1.8718e-02  |
| $$U\_{max}$$=     | 1.300000000 |
| $$U\_{liq}0$$=    | 0.880000000 |
| $$k\_{sigmoid}$$= | 2.500000000 |
| $$α$$=            | 1.100000000 |

* **OP**

| Parameter         | Value       |
| ----------------- | ----------- |
| $$A$$=            | 3.3634e-02  |
| $$B$$=            | -1.5528e-02 |
| $$U\_{max}$$=     | 1.200000000 |
| $$U\_{liq}0$$=    | 0.600000000 |
| $$k\_{sigmoid}$$= | 2.500000000 |
| $$α$$=            | 1.100000000 |

* **WBTC**

| Parameter         | Value       |
| ----------------- | ----------- |
| $$A$$=            | 8.5903e-02  |
| $$B$$=            | 7.1813e-02  |
| $$U\_{max}$$=     | 1.050000000 |
| $$U\_{liq}0$$=    | 0.500000000 |
| $$k\_{sigmoid}$$= | 2.500000000 |
| $$α$$=            | 2.000000000 |

## D. Base Interest Rate Curves

* **USDC**

| Parameter         | Value       |
| ----------------- | ----------- |
| $$A$$=            | 5.0000e-02  |
| $$B$$=            | 1.1000e-01  |
| $$U\_{max}$$=     | 1.300000000 |
| $$U\_{liq}0$$=    | 0.880000000 |
| $$k\_{sigmoid}$$= | 2.500000000 |
| $$α$$=            | 1.300000000 |

* **WETH**

| Parameter         | Value       |
| ----------------- | ----------- |
| $$A$$=            | 1.9500e-02  |
| $$B$$=            | 4.0000e-02  |
| $$U\_{max}$$=     | 1.300000000 |
| $$U\_{liq}0$$=    | 0.880000000 |
| $$k\_{sigmoid}$$= | 2.500000000 |
| $$α$$=            | 1.100000000 |

* wstETH

| Parameter         | Value       |
| ----------------- | ----------- |
| $$A$$=            | 1.9500e-02  |
| $$B$$=            | 4.0000e-02  |
| $$U\_{max}$$=     | 1.300000000 |
| $$U\_{liq}0$$=    | 0.880000000 |
| $$k\_{sigmoid}$$= | 2.500000000 |
| $$α$$=            | 1.100000000 |

* **cbBTC**

| Parameter         | Value       |
| ----------------- | ----------- |
| $$A$$=            | 1.0000e-02  |
| $$B$$=            | 1.5000e-01  |
| $$U\_{max}$$=     | 1.050000000 |
| $$U\_{liq}0$$=    | 0.500000000 |
| $$k\_{sigmoid}$$= | 2.500000000 |
| $$α$$=            | 2.000000000 |

* **cbXRP**

| Parameter         | Value       |
| ----------------- | ----------- |
| $$A$$=            | 1.5000e-02  |
| $$B$$=            | 2.0000e-01  |
| $$U\_{max}$$=     | 1.400000000 |
| $$U\_{liq}0$$=    | 0.500000000 |
| $$k\_{sigmoid}$$= | 2.500000000 |
| $$α$$=            | 1.250000000 |

## E. Ethereum Mainnet Interest Rate Curves

* WETH

| Parameter     | VRP Value   | FRP Value   |
| ------------- | ----------- | ----------- |
| $$A$$ =       | 1.9362e-2   | 3.8126e-1   |
| $$B$$ =       | -1.787e-3   | -3.6375e-1  |
| $$U\_{max}$$= | 1.003870947 | 1.000010695 |

* DAI

| Parameter     | VRP Value   | FRP Value   |
| ------------- | ----------- | ----------- |
| $$A$$ =       | 1.7852e-2   | 3.9281e-1   |
| $$B$$ =       | -2.789e-3   | -3.7781e-1  |
| $$U\_{max}$$= | 1.003568501 | 1.000014451 |

* USDC

| Parameter     | VRP Value   | FRP Value   |
| ------------- | ----------- | ----------- |
| $$A$$ =       | 1.4844e-2   | 3.9281e-1   |
| $$B$$ =       | 1.9964e-4   | -3.7781e-1  |
| $$U\_{max}$$= | 1.002968978 | 1.000014451 |

* WBTC

| Parameter     | VRP Value   | FRP Value   |
| ------------- | ----------- | ----------- |
| $$A$$ =       | 2.7194e-2   | 4.6586e-1   |
| $$B$$ =       | 3.0160e-2   | -4.1345e-1  |
| $$U\_{max}$$= | 1.007776377 | 1.050553997 |

* wstETH

| Parameter     | VRP Value   | FRP Value   |
| ------------- | ----------- | ----------- |
| $$A$$ =       | 1.9362e-2   | 3.8126e-1   |
| $$B$$ =       | -1.787e-3   | -3.6375e-1  |
| $$U\_{max}$$= | 1.003870947 | 1.000010695 |

* OP

| Parameter     | VRP Value   | FRP Value   |
| ------------- | ----------- | ----------- |
| $$A$$ =       | 2.8487e-2   | 3.5815e-1   |
| $$B$$ =       | -5.8259e-3  | -3.3564e-1  |
| $$U\_{max}$$= | 1.005690787 | 1.000005527 |

These parameters are utilized to calculate [the effective borrow interest rate](https://docs.exact.ly/getting-started/math-paper#4.1.2-the-effective-interest-rate-for-a-particular-loan).

## F. Risk Factors

* OP Mainnet

| Asset  | Value |
| ------ | ----- |
| WETH   | 0.86  |
| USDC   | 0.91  |
| USDC.e | 0.91  |
| WBTC   | 0.78  |
| wstETH | 0.82  |
| OP     | 0.58  |

* Base

| Asset  | Value |
| ------ | ----- |
| WETH   | 0.86  |
| USDC   | 0.91  |
| cbBTC  | 0.85  |
| wstETH | 0.82  |
| cbXRP  | 0.60  |

* Ethereum Mainnet

| Asset  | Value |
| ------ | ----- |
| WETH   | 0.86  |
| DAI    | 0.90  |
| USDC   | 0.91  |
| WBTC   | 0.85  |
| wstETH | 0.82  |

We associate a [Risk-Adjust Factor](https://docs.exact.ly/getting-started/math-paper#6.-liquidations) to each asset to assess each collateral asset's borrow and lending power.

To assess the Risk-Adjust Factor for each asset in the protocol, you can query the `markets()` function of the [Auditor](https://docs.exact.ly/guides/protocol/auditor) contract. This can be done using [Etherscan](https://etherscan.io/), a blockchain explorer.

Follow the steps below to check the Risk-Adjust Factor for a specific asset:

1. Go to the Auditor contract on Etherscan by navigating to the following URL: <https://etherscan.io/address/0x310A2694521f75C7B2b64b5937C16CE65C3EFE01#readProxyContract#F17> (for other networks, go to [smart-contract-addresses](https://docs.exact.ly/guides/smart-contract-addresses "mention") and click on the address of the desired Auditor contract)
2. To query the `markets` In that contract, you will need the market contract address for the specific asset. For example, you can use the following address to check the Risk-Adjust Factor for USDC: `0x660e2fC185a9fFE722aF253329CEaAD4C9F6F928`. All addresses for each network (Mainnet, Optimism, et al.) are available in [smart-contract-addresses](https://docs.exact.ly/guides/smart-contract-addresses "mention").
3. Click the "Query" button to call the function. The result will display various information about the market, including the Risk-Adjust Factor.
4. The Risk-Adjust Factor will be returned as `adjustFactor`. In this case, `910000000000000000` equals 0.91.\
   ![](https://1569313259-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fn6wwJ0pvrhjXGxxDpmNa%2Fuploads%2FdkqUUUwOWZIcaFJ5EiVZ%2Fimage.png?alt=media\&token=97670d2c-7007-4036-920c-5f38805ea11e)

Following these steps, you can check the Risk-Adjust Factor for any asset in the protocol by simply replacing the market contract address with the one corresponding to the desired asset.

## F. Variable Rate Pool Fee

$$
\begin{align\*} \delta = 10% \end{align\*}
$$

$$\delta$$ is the fraction of the [fixed interest rate fees](https://docs.exact.ly/getting-started/math-paper#4.2.1-supply-interest-rate) retained by the Variable Rate Pool upon leaving the Fixed Rate Pool.

## G. Supply E.M.A. Parameters

$$
\begin{align\*} \beta\_{slow} = 0.000053 \end{align\*}
$$

The time decay parameter is used when the supply is above average.

$$
\begin{align\*} \beta\_{fast} = 0.4000 \end{align\*}
$$

The time decay parameter is used when the supply is below average.

## H. Target Solvency Ratio

$$
\begin{align\*} \Gamma = 1.25 \end{align\*}
$$

Target solvency ratio after [liquidation](https://docs.exact.ly/getting-started/math-paper#6.-liquidations).

## I. Liquidation Bonuses

$$
\begin{align\*} \nu\_{liquidator} = 5.00% \ \nu\_{bad-debt} = 0.25% \end{align\*}
$$

During the [liquidation process](https://docs.exact.ly/getting-started/math-paper#6.-liquidations), the liquidator gets a commission fee, and the Variable Rate Pool receives a percentage of extra liquidation fees to compensate for potential bad debt residuals.

## J. Extraordinary Earnings Distribution Factor

$$
\begin{align\*} \xi\_{extearn} = 2.00 \end{align\*}
$$

## K. Penalty Rate

$$
\begin{align\*} DailyPenaltyRate = 0.45% \end{align\*}
$$

The daily penalty rate fee is charged to fixed interest rate borrowers who didn't pay their loans on time. This fee is charged daily after the maturity day.&#x20;

For example, if your total debt after the maturity date is $100, and you pay 10 days later, the penalty fees will be $4.5 (0.45%\*10\*$100).