TLDR：
- Interest Rate Model is one of the deceive factors related to equilibrium and system revenue
- MakerDAO’s Stability Fees is not high
- Different Protocols have their own opinions on optimized utilization rate, Compound’s design is a double-edged sword
- MakerDAO and Parasset both take the Stability Fee Model, while having some differences
- Liquity’s 1time cost is effective but not friendly for some users
- Parasset combines some advantages of Liquity and MakerDAO
Stability Fee & Interest Rate Model
The cost of borrowing on Liquity can be treated as a one-time fixed cost.
The cost of borrowing on MakerDAO or Parasset can be considered as a variable cost.
The cost of borrowing on Compound or AAVE can be considered as fixed cost + variable cost
Although Compound and AAVE using the jump interest rate model, often the Optimized utilization rate will become the equilibrium and Schelling point.
MakerDAO
Collateralized assets in MakerDAO have 3 different tags A/B/C，e.g. ETH has the following subtypes:
- ETH-A
- ETH-B
- ETH-C
A type asset has Debt Ceiling
Dai ETH-A (34%)
From the chart we can see the after MakerDAO officially support USDC as a collateral asset, the collaterals backing DAI have about 45% is USDC
PSM is a module that helps the DAI keep the peg, and charges 1% fee during the process
Stability Fee Calculation
Stability Fee = ( ( Borrowed DAI * ( 1 + Annualized Stability Fee ) ) ^ ( Borrowing Term in Days/365 ) ) — Borrowed DAI
The formula itself is not complicated
*From the short term user’s perspective the Stability Fee is not a very big deal, part of the revenue is sent to DSR (DAI Saving Rate)
Liquity
Fixed Cost components
One time Borrowing Fee and Liquidation Reserve for the gas fee in the situation troves got liquidated
Fees Calculation
Each time there is a redemption, the base rate will increase by the proportion of redeemed LUSD and then applied to the current redemption as follows:
b ( t ) = b ( t − 1 ) + α × m / n
the base rate will change over time, δ decay factor that is applied with every redemption and issuance of LUSD before calculating the resulting fee.
b ( t ) = b ( t − 1 ) × δ ^ △t
The decay factor δ is chosen such that the half-life of the base rate is 12 hours.
200 LUSD is about them as 0.08 ETH, so for users, they need to think 0.08ETH is a small cost, then they will be more willing to borrow LUSD (Many users deposited LUSD into Stability Pool)
From this chart, the Troves in Liquity have mainly consisted 10–100 ETH, which indicates there’s a certain “level” need to be reached first to make more sense for using Liquity (Some users do use lending protocols as a leverage tool, in that case, the fees will also be amplified)
From this LUSD utilization chart, we can see about 80% of LUSD flows into Stability Pool. In the early stage, 20% flowed into Uniswap V2 later this portion went to Curve LUSD/3Pool. Because of the design of the Stability Pool, it is kind of similar to pool 2 liquidity mining (using ETH to acquire LQTY）
Compound
Interest Rate Model
In short Interest Rate changes when utilization changes.
Utilization Rate
utilizationRate = totalBorrows / (totalCash + totalBorrows — totalReserves)
when utilizationRate<= kink
borrowRate = baseRate + utilizationRate*multiplier
when utilizationRate>kink
borrowRate = baseRate + utilizationRate*multiplier + (utilizationRate-kink)*jumpMultiplier
*base rate
For DAI base rate depends on Dai Savings Rate (DSR)
for other Tokens，baseRate = baseRatePerYear/blocks per year
Compound Standard Interest Rate Model
Borrow Interest Rate=Multiplier∗Utilization Rate+Base Rate
The Jump Rate model
Borrow Interest Rate = Multiplier∗min(Ua,Kink)+Jump Multiplier∗max(0,Ua−Kink)+Base Rate
2 Parameters
- Base rate per year, the minimum borrowing rate
- Multiplier per year, the rate of increase in interest rate concerning utilization
2 New
- Kink, the point in the model in which the model follows the jump multiplier
- Jump Multiplier per year, the rate of increase in interest rate concerning utilization after the “kink”
USDC
- Base rate: 0%/yr
- Multiplier: 5%/yr
- Kink: 80%（all Jump models Kink set to 80%）
- Jump multiplier: 109%/yr
- Reserve factor: 7%
The Interest rate model of Compound is relatively complicated, which can be a double-edged sword, especially the optimized utilization rate is the key for the whole model and system risk.
Parasset
Stability Fee
Bt−1 / Xt−1 ∗Pt reflects the C-Ratio’ change due to the price change between t-1 and t
Because the K constant for the liquidation in the system is set to 1.2 or 1.33,
We can assume the average collateralized ratio is 150%, then Ct and Ct-1 in the function can be treated as 2/3
Under this assumption the function can be written as follows:
Stability Fee = System Debt * base market rate * ( 1 + 2 ) * block height differences
Stability Fees under this case should be about 3 times the base market rate, which is not high and can be very competitive with MakerDAO.
Conclusion
Parasset’s design is combined with Liquity and MakerDAO.
Similar to Liquity, the Insurers can participate in the Insurance pool to get the reward of ASET, and liquidation remainders.
Similar to MakerDAO, Stability Fees serves the following purposes:
- Higher the C-Ratio keeps the system healthy
- Create the revenue for the system, create a closed-loop for users in the system
