各种参数

此处整理，借贷协议AAVE的借贷利率相关参数：

AAVE中的LTV

AAVE中的LTV=Loan-To-Value=贷款价值
- ~= Collateral Factor=抵押率
  - 详见：
    - 抵押率 · DeFi借贷协议 (crifan.org)
- 举例
  - 存入100块，能贷出多少钱
    - 举例：存入100，能贷出75，就是：LTV=75%
- 借贷池参数
- 举例

Rv0=基础可变借贷利率

R(v0) = Base Variable Borrow Rate = 基础可变借贷利率
- 常数为Bt = 0。以射线表示
  - Constant for B(t)=0. Expressed in ray
- 相关代码
  - baseVariableBorrowRate

Rv=可变借贷利率

R(v) = Variable Borrow Rate =可变借贷利率
- 公式
- 此利率模型可校正主要利率:
  - 当 U = 0： R(v) = R(v0)
  - 当U = Uoptimal：R(v) = R(v0) + Rslope1
  - 高于 Uoptimal：考虑到资金成本，利率急剧上升

Rs=稳定借贷利率

R(s =) Stable Borrow Rate = Current Stable Borrow Rate = 稳定借贷利率
- 计算公式
- 说明
  - M(r)：平均市场贷款利率
    - the average market lending rate
  - R(slope1)：在非最优条件下的利率，斜率随着U的增加而增加
    - the interest rate slope below Uoptimal, increases the rate as U increases.
  - R(slope2) ：超出非最优的利率，斜率随着U与非最优之差的增大而增大
    - the interest rate slope beyond Uoptimal, increases as the difference between U and Uoptimal increases.
  - U：是利用率
    - is the utilization rate.
- 注意
  - Rs不会影响现有的稳定利率头寸-这只适用于新开的头寸
    - R(s) does NOT impact existing stable rates positions – this is applied only to new opened positions.
- 以射线表示
  - Expressed in ray

Rslope1=斜率1

R(slope1) = Interest Rate slope below U(optimal)
- 常数，当U <Uoptimal 时，表示利率与利用率的比例。以射线表示
  - Constant representing the scaling of the interest rate versus the utilization, when U < U(optimal). Expressed in ray

Rslope2=斜率2

R(slope2) = Interest Rate slope above U(optimal)
- 常数表示利率与利用率的比例，当U≥ U(optimal)。以射线表示
  - Constant representing the scaling of the interest rate versus the utilization, when U ≥ U(optimal). Expressed in ray

Ro=总体借贷利率

R(o) = Overall borrow rate=总体借贷利率
- 公式
- 说明
  - 准备金的总借款率，以总可变借款Bv与总稳定借款b的加权平均值计算
    - Overall borrow rate of the reserve, calculated as the weighted average between the total variable borrows Bv and the total stable borrows Bs

Mr=平均市场借贷利率

Mr=平均市场借贷利率=average Market lending rate
- 公式
  - 参数说明
    - i：平台个数
    - M(r：)平均市场借贷利率
    - P(r)(i)：借贷利率=贷款利率
    - P(i)(v)：借贷量
- 含义解释
  - 基本稳定借款利率，以射线表示
  - 市场价格将每日更新，最初由Aave

Rsa=平均稳定借贷利率

Rsa = Average Stable rate borrow rate=平均稳定借贷利率
- 公式
- 说明
  - 详见函数
    - decreaseTotalBorrowsStableAndUpdateAverageRate()
    - increaseTotalBorrowsStableAndUpdateAverageRate()
  - 以射线表示
    - Expressed in ray

Rl=当前流动性比例

R(l)=current Liquidity rate=当前流动性比例
- 公式
- 说明
  - 总借款利率R(O)与利用率U的函数
    - Function of the overall borrow rate RO and the utilization rate U

Bx=PB=用户本金借款余额

User Principal borrow Balance=用户本金借款余额
- 旧=AAVE V1
  - 变量：B(x)
  - 说明
    - 当用户打开借贷头寸时存储的余额。在多次借款的情况下，复利每次累积，它成为新的本金借款余额
      - Balance stored when a user opens a borrow position. In case of multiple borrows, the compounded interest is cumulated each time and it becomes the new principal borrow balance
- 新=AAVE V2
  - 变量：PB(x)
  - 说明
    - 当用户打开借贷头寸时存储的余额。在多次借款的情况下，复利每次累积，它成为新的本金借款余额。

Bvcx=VI=用户累计浮动借款指数

B(t)(vcx)=user Cumulated Variable borrow indeX=用户累计可变利率借款指数 = 用户借款累积指数=用户累计浮动借款指数
- 旧=AAVE V1
  - 公式
  - 说明
    - 特定用户的变量借款指数，在用户打开（新增？）变量借款头寸时存储
      - Variable borrow index of the specific user, stored when a user opens a variable borrow position
- 新=AAVE V2
  - 公式
  - 说明
    - 特定用户的可变借款指数，在用户新开可变借款头寸时存储

Bvc=VIt=累计可变利率借款指数

B(t)(vc)=Cumulated Variable Borrow index=累计可变利率借款指数 = 借款累积指数=累计浮动借款指数
- 旧=AAVE V1
  - 公式
  - 说明
    - 由变量借款Bv按利率Rv累积的利息，在借款、存款、偿还、赎回、切换利率、清算事件发生时更新
- 新=AAVE V2
  - 含义
    - 从池子首次发生用户操作时，累计到现在，每单位借款债务，共变成多少债务
    - 变量借款VB在一段时间∆T内以可变利率V R累计的利息
  - 公式
  - 说明
    - 在发生借款、存款、偿还、赎回、掉期、清算事件时更新
    - 这里使用复利公式计算利息，每次存钱、取钱、借钱、赎回、清算操作等动作
    - 因为在链上计算成本高，AAVE使用了泰勒展开式模拟这个公式，为了避免昂贵的求幂，使用二项式近似进行计算。
      - 参考链接
        
        https://github.com/aave/protocol-v2/blob/ce53c4a8c8620125063168620eba0a8a92854eb8/contracts/protocol/libraries/math/MathUtils.sol#L45
    - 不举例子了
    - 任务每次计算复利的时候，VIt都会大一点点，跟流动性累计指数相似。
    - 注意这里的复利周期是每秒计算的
  - 代码
    - CoreLibrary
      - 储备和用户数据的数据结构

struct UserReserveData { 
    //principal amount borrowed by the user. 
    uint256 principalBorrowBalance; 
    //cumulated variable borrow index for the user. Expressed in ray 
    uint256 lastVariableBorrowCumulativeIndex; 
    //origination fee cumulated by the user 
    uint256 originationFee; 
    // stable borrow rate at which the user has borrowed. Expressed in ray 
    uint256 stableBorrowRate; 
    uint40 lastUpdateTimestamp; 
    //defines if a specific deposit should or not be used as a collateral in borrows 
    bool useAsCollateral; 
} 

struct ReserveData { 
    /** 
    * @dev refer to the whitepaper, section 1.1 basic concepts for a formal description of these properties. 
    **/ 
    //the liquidity index. Expressed in ray 
    uint256 lastLiquidityCumulativeIndex; 
    //the current supply rate. Expressed in ray 
    uint256 currentLiquidityRate; 
    //the total borrows of the reserve at a stable rate. Expressed in the currency decimals 
    uint256 totalBorrowsStable; 
    //the total borrows of the reserve at a variable rate. Expressed in the currency decimals 
    uint256 totalBorrowsVariable; 
    //the current variable borrow rate. Expressed in ray 
    uint256 currentVariableBorrowRate; 
    //the current stable borrow rate. Expressed in ray 
    uint256 currentStableBorrowRate; 
    //the current average stable borrow rate (weighted average of all the different stable rate loans). Expressed in ray 
    uint256 currentAverageStableBorrowRate; 
    //variable borrow index. Expressed in ray 
    uint256 lastVariableBorrowCumulativeIndex; 
    //the ltv of the reserve. Expressed in percentage (0-100) 
    uint256 baseLTVasCollateral; 
    //the liquidation threshold of the reserve. Expressed in percentage (0-100) 
    uint256 liquidationThreshold; 
    //the liquidation bonus of the reserve. Expressed in percentage 
    uint256 liquidationBonus; 
    //the decimals of the reserve asset 
    uint256 decimals; 
    /** 
    * @dev address of the aToken representing the asset 
    **/ 
    address aTokenAddress; 
    /** 
    * @dev address of the interest rate strategy contract 
    **/ 
    address interestRateStrategyAddress; 
    uint40 lastUpdateTimestamp; 
    // borrowingEnabled = true means users can borrow from this reserve 
    bool borrowingEnabled; 
    // usageAsCollateralEnabled = true means users can use this reserve as collateral 
    bool usageAsCollateralEnabled; 
    // isStableBorrowRateEnabled = true means users can borrow at a stable rate 
    bool isStableBorrowRateEnabled; 
    // isActive = true means the reserve has been activated and properly configured 
    bool isActive; 
    // isFreezed = true means the reserve only allows repays and redeems, but not deposits, new borrowings or rate swap 
    bool isFreezed; 
}

更新
- 与v1版本不同的是，在更新储备状态时会将一部分产生的利息收入存入金库（treasury）中，具体的比例由储备的reserveFactor（configuration字段的一个值）来确定

/** 
 * @dev Updates the liquidity cumulative index and the variable borrow index. 
* @param reserve the reserve object 
**/ 
function updateState(DataTypes.ReserveData storage reserve) internal { 
  uint256 scaledVariableDebt = 
    IVariableDebtToken(reserve.variableDebtTokenAddress).scaledTotalSupply(); 
  uint256 previousVariableBorrowIndex = reserve.variableBorrowIndex; 
  uint256 previousLiquidityIndex = reserve.liquidityIndex; 
  uint40 lastUpdatedTimestamp = reserve.lastUpdateTimestamp; 


  (uint256 newLiquidityIndex, uint256 newVariableBorrowIndex) = 
    _updateIndexes( 
      reserve, 
      scaledVariableDebt, 
      previousLiquidityIndex, 
      previousVariableBorrowIndex, 
      lastUpdatedTimestamp 
    ); 


  _mintToTreasury( 
    reserve, 
    scaledVariableDebt, 
    previousVariableBorrowIndex, 
    newLiquidityIndex, 
    newVariableBorrowIndex, 
    lastUpdatedTimestamp 
  ); 
}

Bxc=用户复利借款余额

B(x)(c)=user Compounded borrow Balance=用户复利借款余额
- 旧=AAVE V1
  - 公式
  - 说明
    - 本金Bx加上累计利息
      - Principal Bx plus the cumulated interests
- 新=AAVE V2
  - 代码

struct RepayLocalVars { 
    uint256 principalBorrowBalance; 
    uint256 compoundedBorrowBalance; 
    uint256 borrowBalanceIncrease; 
    bool isETH; 
    uint256 paybackAmount; 
    uint256 paybackAmountMinusFees; 
    uint256 currentStableRate; 
    uint256 originationFee; 
} 

function repay(address _reserve, uint256 _amount, address payable _onBehalfOf) 
    external 
    payable 
    nonReentrant 
    onlyActiveReserve(_reserve) 
    onlyAmountGreaterThanZero(_amount) 
{ 
    // Usage of a memory struct of vars to avoid "Stack too deep" errors due to local variables 
    RepayLocalVars memory vars; 


    ( 
        vars.principalBorrowBalance, 
        vars.compoundedBorrowBalance, 
        vars.borrowBalanceIncrease 
    ) = core.getUserBorrowBalances(_reserve, _onBehalfOf); 
...

Dassett=债务总额

D(asset)(t = )Total Debt=债务总额
- 公式
- 说明
  - 借入的流动资金总额
    - Total amount of liquidity borrowed

VDassett=可变债务代币总额

VD(asset)(t = )Total Variable Debt Tokens=可变债务代币总额
- 说明
  - 以债务代币表示的可变利率借入的流动性总额
    - Total amount of liquidity borrowed at a variable rate represented in debt tokens

SDassett=稳定债务代币总额

SD(asset)(t = )Total Stable Debt Token=稳定债务代币总额
- 说明
  - 以债务代币表示的稳定利率借入的流动性总额
    - Total amount of liquidity borrowed at a stable rate represented in debt tokens

Lassett=资产的总流动性

L(asset)(t = )Total Liquidity of an asset=资产的总流动性
- 说明
  - 资产准备金中可用的流动资金总额。该值的小数取决于货币的小数
    - Total amount of liquidity available in the assets reserve. The decimals of this value depend on the decimals of the currency

Ci=LIt=流动性累计指数

C(t)(i)=Cumulated liquidity Index=流动性累计指数

旧=AAVE v1
- 公式
- 说明
  - 准备金在时间间隔∆T期间累积的利息，在发生借款、存款、偿还、赎回、掉期、清算事件时更新。
    - Interest cumulated by the reserve during the time interval ∆T , updated whenever a borrow, deposit, repay, redeem, swap, liquidation event occurs

新=AAVE v2

公式
说明
- 从池子首次发生用户操作时，累计到现在，每单位存款本金，变成多少本金（含利息收入）

存储

struct ReserveData { 
    //the liquidity index. Expressed in ray 
    uint128 liquidityIndex; 
  }

更新

function _updateIndexes( 
    DataTypes.ReserveData storage reserve, 
    uint256 scaledVariableDebt, 
    uint256 liquidityIndex, 
    uint256 variableBorrowIndex, 
    uint40 timestamp 
  ) internal returns (uint256, uint256) { 
    uint256 currentLiquidityRate = reserve.currentLiquidityRate; 
    uint256 newLiquidityIndex = liquidityIndex; 

    //only cumulating if there is any income being produced 
    if (currentLiquidityRate > 0) { 
      uint256 cumulatedLiquidityInterest = 
        MathUtils.calculateLinearInterest(currentLiquidityRate, timestamp); 

      newLiquidityIndex = cumulatedLiquidityInterest.rayMul(liquidityIndex); 
      require(newLiquidityIndex <= type(uint128).max, Errors.RL_LIQUIDITY_INDEX_OVERFLOW); 

      reserve.liquidityIndex = uint128(newLiquidityIndex); 
    } 

    reserve.lastUpdateTimestamp = uint40(block.timestamp); 
  } 
}

Itn=NIt=归一化收入

I(t)(n)=reserve Normalized Income=归一化收入
- 含义：每单位存款本金，未来将变成多少本金（含利息收入）
- 旧=AAVE V1
  - 公式
  - 说明
    - 准备金累积的持续利息
      - Ongoing interest cumulated by the reserve
- 新=AAVE V2
  - 公式
- 代码
  - getNormalizedIncome

  /** 
   * @dev Returns the ongoing normalized income for the reserve 
  * A value of 1e27 means there is no income. As time passes, the income is accrued 
  * A value of 2*1e27 means for each unit of asset one unit of income has been accrued 
  * @param reserve The reserve object 
  * @return the normalized income. expressed in ray 
  **/ 
  function getNormalizedIncome(DataTypes.ReserveData storage reserve) 
    internal 
    view 
    returns (uint256) 
  { 
    uint40 timestamp = reserve.lastUpdateTimestamp; 

    //solium-disable-next-line 
    if (timestamp == uint40(block.timestamp)) { 
      //if the index was updated in the same block, no need to perform any calculation 
      return reserve.liquidityIndex; 
    } 

    uint256 cumulated = 
      MathUtils.calculateLinearInterest(reserve.currentLiquidityRate, timestamp).rayMul( 
        reserve.liquidityIndex 
      ); 

    return cumulated; 
  }

各种参数

各种参数

AAVE中的LTV

Rv0=基础可变借贷利率

Rv=可变借贷利率

Rs=稳定借贷利率

Rslope1=斜率1

Rslope2=斜率2

Ro=总体借贷利率

Mr=平均市场借贷利率

Rsa=平均稳定借贷利率

Rl=当前流动性比例

Bx=PB=用户本金借款余额

Bvcx=VI=用户累计浮动借款指数

Bvc=VIt=累计可变利率借款指数

Bxc=用户复利借款余额

Dassett=债务总额

VDassett=可变债务代币总额

SDassett=稳定债务代币总额

Lassett=资产的总流动性

Ci=LIt=流动性累计指数

Itn=NIt=归一化收入

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