[Release Candidate] Improve DSR Integration and Jump Rate Model

This patch makes a few important changes. We first fix an optimization of CDaiDelegate that simplifies a variety of logic in certain calculations. Secondly, we fix the jump rate model to have a fixed slope past the kink, as opposed to a certain multiplier.

contracts/CDaiDelegate.sol

@@ -157,18 +157,13 @@ contract CDaiDelegate is CErc20Delegate {
     function doTransferOut(address payable to, uint amount) internal {
         DaiJoinLike daiJoin = DaiJoinLike(daiJoinAddress);
         PotLike pot = PotLike(potAddress);
-        VatLike vat = VatLike(vatAddress);
 
         // Calculate the percentage decrease from the pot, and move that much out
         // Note: Use a slightly larger pie size to ensure that we get at least amount in the vat
-        uint pie = mul(add(amount, 1), RAY) / pot.chi();
+        uint pie = add(mul(amount, RAY) / pot.chi(), 1);
         pot.exit(pie);
 
-        // Checks the actual balance of DAI in the vat after the pot exit
-        uint bal = vat.dai(address(this));
-
-        // Remove our whole balance if rounding would lead us to remove more than we have
-        daiJoin.exit(to, bal >= mul(amount, RAY) ? amount : bal / RAY);
+        daiJoin.exit(to, amount);
     }
 
     /*** Maker Internals ***/

contracts/DAIInterestRateModel.sol

@@ -11,19 +11,29 @@ import "./SafeMath.sol";
 contract DAIInterestRateModel is JumpRateModel {
     using SafeMath for uint;
 
+    /**
+     * @notice The additional margin per block separating the base borrow rate from the roof (0.05% / block)
+     */
+    uint public constant gapPerBlock = 0.05e16 / blocksPerYear;
+
+    /**
+     * @notice The assumed (1 - reserve factor) used to calculate the minimum borrow rate (reserve factor = 0.05)
+     */
+    uint public constant assumedOneMinusReserveFactorMantissa = 0.95e18;
+
     PotLike pot;
     JugLike jug;
 
     /**
      * @notice Construct an interest rate model
-     * @param _pot The approximate target base APR, as a mantissa (scaled by 1e18)
-     * @param _jug The rate of increase in interest rate wrt utilization (scaled by 1e18)
-     * @param _kink The utilization point at which an additional multiplier is applied
-     * @param _jump The additional multiplier to be applied to multiplierPerBlock after hitting a specified utilization point
+     * @param jumpMultiplierPerYear The multiplierPerBlock after hitting a specified utilization point
+     * @param kink_ The utilization point at which the jump multiplier is applied
+     * @param pot_ The address of the Dai pot (where DSR is earned)
+     * @param jug_ The address of the Dai jug (where SF is kept)
      */
-    constructor(address _pot, address _jug, uint _kink, uint _jump) JumpRateModel(0, 0, _kink, _jump) public {
-        pot = PotLike(_pot);
-        jug = JugLike(_jug);
+    constructor(uint jumpMultiplierPerYear, uint kink_, address pot_, address jug_) JumpRateModel(0, 0, jumpMultiplierPerYear, kink_) public {
+        pot = PotLike(pot_);
+        jug = JugLike(jug_);
         poke();
     }
 
@@ -58,18 +68,24 @@ contract DAIInterestRateModel is JumpRateModel {
             .mul(15); // 15 seconds per block
     }
 
-
     /**
      * @notice Resets the baseRate and multiplier per block based on the stability fee and Dai savings rate
      */
     function poke() public {
         (uint duty, ) = jug.ilks("ETH-A");
-        uint stabilityFee = duty.add(jug.base()).sub(1e27).mul(1e18).div(1e27).mul(15);
+        uint stabilityFeePerBlock = duty.add(jug.base()).sub(1e27).mul(1e18).div(1e27).mul(15);
+
+        // We ensure the minimum borrow rate >= DSR / (1 - reserve factor)
+        baseRatePerBlock = dsrPerBlock().mul(1e18).div(assumedOneMinusReserveFactorMantissa);
 
-        baseRatePerBlock = dsrPerBlock().mul(1e18).div(0.9e18); // ensure borrow rate is higher than savings rate
-        multiplierPerBlock = stabilityFee.sub(baseRatePerBlock).mul(1e18).div(kink);
+        // The roof borrow rate is max(base rate, stability fee) + gap, from which we derive the slope
+        if (baseRatePerBlock < stabilityFeePerBlock) {
+            multiplierPerBlock = stabilityFeePerBlock.sub(baseRatePerBlock).add(gapPerBlock).mul(1e18).div(kink);
+        } else {
+            multiplierPerBlock = gapPerBlock.mul(1e18).div(kink);
+        }
 
-        emit NewInterestParams(baseRatePerBlock, multiplierPerBlock, kink, jump);
+        emit NewInterestParams(baseRatePerBlock, multiplierPerBlock, jumpMultiplierPerBlock, kink);
     }
 }
 

contracts/JumpRateModel.sol

@@ -10,7 +10,7 @@ import "./SafeMath.sol";
 contract JumpRateModel is InterestRateModel {
     using SafeMath for uint;
 
-    event NewInterestParams(uint baseRatePerBlock, uint multiplierPerBlock, uint kink, uint jump);
+    event NewInterestParams(uint baseRatePerBlock, uint multiplierPerBlock, uint jumpMultiplierPerBlock, uint kink);
 
     /**
      * @notice Indicator that this is an InterestRateModel contract (for inspection)
@@ -33,29 +33,29 @@ contract JumpRateModel is InterestRateModel {
     uint public baseRatePerBlock;
 
     /**
-     * @notice the utilization point at which an additional multiplier is applied
-    */
-    uint public kink;
+     * @notice The multiplierPerBlock after hitting a specified utilization point
+     */
+    uint public jumpMultiplierPerBlock;
 
     /**
-     * @notice the additional multiplier to be applied to multiplierPerBlock after hitting a specified utilization point
-    */
-    uint public jump;
+     * @notice The utilization point at which the jump multiplier is applied
+     */
+    uint public kink;
 
     /**
      * @notice Construct an interest rate model
      * @param baseRatePerYear The approximate target base APR, as a mantissa (scaled by 1e18)
      * @param multiplierPerYear The rate of increase in interest rate wrt utilization (scaled by 1e18)
-     * @param kink_ The utilization point at which an additional multiplier is applied
-     * @param jump_ The additional multiplier to be applied to multiplierPerBlock after hitting a specified utilization point
+     * @param jumpMultiplierPerYear The multiplierPerBlock after hitting a specified utilization point
+     * @param kink_ The utilization point at which the jump multiplier is applied
      */
-    constructor(uint baseRatePerYear, uint multiplierPerYear, uint kink_, uint jump_) public {
+    constructor(uint baseRatePerYear, uint multiplierPerYear, uint jumpMultiplierPerYear, uint kink_) public {
         baseRatePerBlock = baseRatePerYear.div(blocksPerYear);
         multiplierPerBlock = multiplierPerYear.div(blocksPerYear);
+        jumpMultiplierPerBlock = jumpMultiplierPerYear.div(blocksPerYear);
         kink = kink_;
-        jump = jump_;
 
-        emit NewInterestParams(baseRatePerBlock, multiplierPerBlock, kink, jump);
+        emit NewInterestParams(baseRatePerBlock, multiplierPerBlock, jumpMultiplierPerBlock, kink);
     }
 
     /**
@@ -89,8 +89,7 @@ contract JumpRateModel is InterestRateModel {
         } else {
             uint normalRate = kink.mul(multiplierPerBlock).div(1e18).add(baseRatePerBlock);
             uint excessUtil = util.sub(kink);
-            uint jumpMultiplier = multiplierPerBlock.mul(jump);
-            return excessUtil.mul(jumpMultiplier).div(1e18).add(normalRate);
+            return excessUtil.mul(jumpMultiplierPerBlock).div(1e18).add(normalRate);
         }
     }
 

spec/scenario/MCDai.scen

@@ -101,7 +101,6 @@ Test "Basic mint and redeem cDAI2 (upgrade to swept DSR)"
     UpgradeToDSR
     CheckBasicMintRedeemWithDSR
 
-
 Test "Basic borrow and repay cDAI2 (upgrade to swept DSR)"
     DeployCDAI
     CheckBasicMintRedeem

test/Models/DAIInterestRateModelTest.js

@@ -5,33 +5,41 @@ const BigNum = require('bignumber.js')
 const { call, etherUnsigned, getContract, getContractDefaults, getTestContract } = require('../Utils/MochaTruffle');
 const { getBorrowRate, getSupplyRate } = require('../Utils/Compound');
 
+const blocksPerYear = 2102400;
 const secondsPerYear = 60 * 60 * 24 * 365;
 
 function utilizationRate(cash, borrows, reserves) {
   return borrows ? borrows / (cash + borrows - reserves) : 0;
 }
 
-function baseRoofRateFn(dsr, duty, mkrBase, kink, jump, cash, borrows, reserves) {
-  const stabilityFee = (duty + mkrBase - 1) * 15;
+function baseRoofRateFn(dsr, duty, mkrBase, jump, kink, cash, borrows, reserves) {
+  const assumedOneMinusReserveFactor = 0.95;
+  const stabilityFeePerBlock = (duty + mkrBase - 1) * 15;
   const dsrPerBlock = (dsr - 1) * 15;
-  const base = dsrPerBlock / 0.9;
-  const slope = (stabilityFee - base) / kink;
+  const gapPerBlock = 0.0005 / blocksPerYear;
+  const jumpPerBlock = jump / blocksPerYear;
+
+  let baseRatePerBlock = dsrPerBlock / assumedOneMinusReserveFactor, multiplierPerBlock;
+  if (baseRatePerBlock < stabilityFeePerBlock) {
+    multiplierPerBlock = (stabilityFeePerBlock - baseRatePerBlock + gapPerBlock) / kink;
+  } else {
+    multiplierPerBlock = gapPerBlock / kink;
+  }
 
   const ur = utilizationRate(cash, borrows, reserves);
 
   if (ur <= kink) {
-    return ur * slope + base;
+    return ur * multiplierPerBlock + baseRatePerBlock;
   } else {
     const excessUtil = ur - kink;
-    const jumpMultiplier = jump * slope;
-    return (excessUtil * jumpMultiplier) + (kink * slope) + base;
+    return (excessUtil * jumpPerBlock) + (kink * multiplierPerBlock) + baseRatePerBlock;
   }
 }
 
-function daiSupplyRate(dsr, duty, mkrBase, kink, jump, cash, borrows, reserves, reserveFactor = 0.1) {
+function daiSupplyRate(dsr, duty, mkrBase, jump, kink, cash, borrows, reserves, reserveFactor = 0.1) {
   const dsrPerBlock = (dsr - 1) * 15;
   const ur = utilizationRate(cash, borrows, reserves);
-  const borrowRate = baseRoofRateFn(dsr, duty, mkrBase, kink, jump, cash, borrows, reserves);
+  const borrowRate = baseRoofRateFn(dsr, duty, mkrBase, jump, kink, cash, borrows, reserves);
   const underlying = cash + borrows - reserves;
   const lendingSupplyRate = borrowRate * (1 - reserveFactor) * ur;
 
@@ -66,10 +74,10 @@ contract('DAIInterestRateModel', async function (_accounts) {
 
       let model = await contract.deploy({
         arguments: [
-          "0xea190dbdc7adf265260ec4da6e9675fd4f5a78bb",
-          "0xcbb7718c9f39d05aeede1c472ca8bf804b2f1ead",
+          etherUnsigned(0.8e18),
           etherUnsigned(0.9e18),
-          etherUnsigned(5)
+          "0xea190dbdc7adf265260ec4da6e9675fd4f5a78bb",
+          "0xcbb7718c9f39d05aeede1c472ca8bf804b2f1ead"
         ]
       })
         .send({ from: root });
@@ -129,8 +137,8 @@ contract('DAIInterestRateModel', async function (_accounts) {
       [0e27, 0.1e27, 0.005e27, 3e18, 500],
 
     ].map(vs => vs.map(Number))
-      .forEach(([dsr, duty, base, cash, borrows, reserves = 0, kink = 0.9e18, jump = 5]) => {
-        it(`calculates correct borrow value for dsr=${(dsr / 1e25)}%, duty=${(duty / 1e25)}%, base=${(base / 1e25)}%, cash=${cash}, borrows=${borrows}, reserves=${reserves}`, async () => {
+      .forEach(([dsr, duty, base, cash, borrows, reserves = 0, jump = 0.8e18, kink = 0.9e18]) => {
+        it(`calculates correct borrow value for dsr=${(dsr / 1e25)}%, duty=${(duty / 1e25)}%, base=${(base / 1e25)}%, jump=${jump / 1e18}, cash=${cash}, borrows=${borrows}, reserves=${reserves}`, async () => {
           const [root] = _accounts;
 
           const onePlusPerSecondDsr = 1e27 + (dsr / secondsPerYear);
@@ -156,14 +164,14 @@ contract('DAIInterestRateModel', async function (_accounts) {
 
           const daiIRM = await DAIInterestRateModel.deploy({
             arguments: [
-              pot.options.address,
-              jug.options.address,
+              etherUnsigned(jump),
               etherUnsigned(kink),
-              etherUnsigned(jump)
+              pot.options.address,
+              jug.options.address
             ]
           }).send({ from: root });
 
-          const expected = baseRoofRateFn(onePlusPerSecondDsr / 1e27, onePlusPerSecondDuty / 1e27, perSecondBase / 1e27, kink / 1e18, jump, cash, borrows, reserves);
+          const expected = baseRoofRateFn(onePlusPerSecondDsr / 1e27, onePlusPerSecondDuty / 1e27, perSecondBase / 1e27, jump / 1e18, kink / 1e18, cash, borrows, reserves);
           assert.like(
             await getBorrowRate(daiIRM, cash, borrows, reserves),
             (x) => assert.approximately(Number(x) / 1e18, expected, 1e-8)
@@ -221,7 +229,7 @@ contract('DAIInterestRateModel', async function (_accounts) {
       [0e27, 0.1e27, 0.005e27, 3e18, 500],
 
     ].map(vs => vs.map(Number))
-      .forEach(([dsr, duty, base, cash, borrows, reserves = 0, kink = 0.9e18, jump = 5, reserveFactor = 0.1e18]) => {
+      .forEach(([dsr, duty, base, cash, borrows, reserves = 0, jump = 0.8e18, kink = 0.9e18, reserveFactor = 0.1e18]) => {
         it(`calculates correct supply value for dsr=${(dsr / 1e25)}%, duty=${(duty / 1e25)}%, base=${(base / 1e25)}%, cash=${cash}, borrows=${borrows}, reserves=${reserves}`, async () => {
           const [root] = _accounts;
 
@@ -248,14 +256,14 @@ contract('DAIInterestRateModel', async function (_accounts) {
 
           const daiIRM = await DAIInterestRateModel.deploy({
             arguments: [
-              pot.options.address,
-              jug.options.address,
+              etherUnsigned(jump),
               etherUnsigned(kink),
-              etherUnsigned(jump)
+              pot.options.address,
+              jug.options.address
             ]
           }).send({ from: root });
 
-          const expected = daiSupplyRate(onePlusPerSecondDsr / 1e27, onePlusPerSecondDuty / 1e27, perSecondBase / 1e27, kink / 1e18, jump, cash, borrows, reserves, reserveFactor / 1e18);
+          const expected = daiSupplyRate(onePlusPerSecondDsr / 1e27, onePlusPerSecondDuty / 1e27, perSecondBase / 1e27, jump / 1e18, kink / 1e18, cash, borrows, reserves, reserveFactor / 1e18);
           assert.like(
             await getSupplyRate(daiIRM, cash, borrows, reserves, reserveFactor),
             (x) => assert.approximately(Number(x) / 1e18, expected, 1e-8)