Interest Rate Strategy

Risk Management
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Interest Rate Strategy
This section describes the lending pool's interest rate parameters.
The interest rate strategy of Trava pool is designed to control liquidity risk while also maximizing utilization. The Utilisation Rate determines the borrow interest rates. 
Each token in each Pool has a utilization rate UtU_tUt​
  at each time  ttt
, which is defined by the ratio Ut=Lt/AtU_t = L_t/A_tUt​=Lt​/At​
where  LtL_tLt​
 represents total borrows and AtA_tAt​
 represents total liquidity. This ratio regulates how much of a deposited token is used in the market.
When this ratio approaches 100%, there will be a scarcity of tokens in the Pool. The borrower will be unable to borrow at this time, and the lender will be unable to withdraw funds from the Pool. To avoid this, interest rate and risk parameters must be calculated in precise detail for each token.
Interest Rate Model
Interest Rate Model tends to be a cost-effective way for the Pool to run itself. The parameters of the pool will aid in the adjustment of borrow and deposit rates to a balanced and reasonable point.
In practice, numerous models are used: linear rate, non-linear rate, and kinked rate. The kinked rate model is used in the Trava protocol. As with the non-linear model, such models have the virtue of significantly shifting the incentives for borrowers and lenders beyond some usage level. In contrast to non-linear models without a kink, they also introduce a point of abrupt change in the interest rate, beyond which interest rates begin to sharply rise.
The kinked model is based on several parameters and is described as follows. Firstly, the ratio optimal utilization rate UoptimalU_\text{optimal}Uoptimal​
 is a parameter that determines the best-fit utilization rate for the protocol. It varies from token to token and depends on the risk and volatility of the token. For example, it could be 80% for stable tokens like DAI, or just 65% for unstable coins like LINK.
Next, the interest rate is a function that varies based on utilization rate. Three parameters are used to define this function: (1) Initial rate R0R_0R0​
, (2)  the constant Rslope1R_\text{slope1}Rslope1​
  is used when  Ut<UoptimalU_t < U_\text{optimal}Ut​<Uoptimal​
,  and  (3)  the constant Rslope2R_\text{slope2}Rslope2​
 is used when Ut≥UoptimalU_t \geq U_\text{optimal}Ut​≥Uoptimal​
. 
Specifically, the interest rate RtR_tRt​
 is defined by:
If Ut<UoptimalU_t <U_\text{optimal}Ut​<Uoptimal​
  then     Rt=R0+UtUoptimal×Rslope1R_t = R_0 + \frac{U_t}{U_\text{optimal}} \times  R_\text{slope1}Rt​=R0​+Uoptimal​Ut​​×Rslope1​
 
If Ut≥UoptimalU_t \geq	 U_\text{optimal}Ut​≥Uoptimal​
 then Rt=R0+Rslope1+Ut−Uoptimal1−Uoptimal×Rslope2R_t= R_0 + R_\text{slope1} + \frac{ U_t - U_\text{optimal}}{1 -U_\text{optimal}} \times R_\text{slope2}Rt​=R0​+Rslope1​+1−Uoptimal​Ut​−Uoptimal​​×Rslope2​
​
The interest rates have a kink in them: they sharply change at a certain point. A variety of protocols use interest rates like this, including Aave and Compound. As users mint, redeem, borrow, repay, or liquidate tokens, the interest rate changes with the utilization rate  UtU_tUt​
 . As a result, it's also known as a variable interest rate. 
Interest rate parameters in Trava protocol
Token
Uoptimal
Base
Slope1
Slope2
DAI
80%
0%
4%
75%
USDC
90%
0%
4%
60%
USDT
90%
0%
4%
60%
ETH
65%
0%
8%
100%
BNB
65%
0%
10%
100%
BUSD
80%
0%
4%
100%
BTCB
65%
0%
7%
100%
AAVE
65%
0%
7%
100%
ADA
65%
0%
8%
100%
CAKE
65%
0%
8%
100%
XRP
65%
0%
8%
100%
DOGE
60%
0%
8%
150%
DOT
65%
0%
8%
100%
XVS
65%
0%
7%
100%
FTM
65%
0%
8%
100%
Borrow rate
The borrow rate is calculated using the current interest rateRtR_tRt​
(per year)  and is updated every second.  That is, borrowers will be charged interest that changes every second. He must pay more interest if the Utilisation Rate is higher, and vice versa. Mathematically, at each time t, the Borrow rate (per second)  is Bt=Rt/YB_t = R_t/YBt​=Rt​/Y
  where Y=31536000Y= 31536000Y=31536000
 is the number of seconds in a year. If the user is currently borrowing TtT_tTt​
 tokens then the interest payable is Tt×BtT_t \times B_tTt​×Bt​
 . The interest payable is accrued to the loan in the next second, that is Tt+1=Tt(1+Bt)T_{t+1}=T_t(1+B_t)Tt+1​=Tt​(1+Bt​)
 .
Deposit rate
Deposit rate and Borrow rate are closely linked. Precisely, at each time ttt
, deposit rate  DtD_tDt​
 is determined based on  Utilization Rate UtU_tUt​
 and borrow rate BtB_tBt​
 and reserve factor rrr
. Precisely, deposit rate is defined by Dt=Ut×Bt×(1−r)D_t = U_t \times B_t\times  (1-r)Dt​=Ut​×Bt​×(1−r)
.
In terms of probability, UtU_tUt​
 is probability that each token is borrowed, thus DtD_tDt​
 is the average value of interest earned from each token deposited into the Pool. 
For deposit, the calculation of interest is updated after each operation deposit, withdraw, borrow, repay. In particular, if a user is currently depositing TtT_tTt​
 tokens, after a period of time Δt\Delta{t}Δt
 (in seconds) he will receive an interest of Tt×Dt×Δt,T_t \times  D_t \times \Delta{t},Tt​×Dt​×Δt,
 and this interest is accrued to the deposited token, i.e. after time Δt\Delta{t}Δt
 he have Tt+Δt=Tt×(1+Dt×Δt).T_{t+\Delta{t}} = T_t \times  (1 + D_t \times \Delta{t}).Tt+Δt​=Tt​×(1+Dt​×Δt).
​
Introduction
Risk parameters
Last modified 5mo ago
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Contents
Interest Rate Model
Borrow rate
Deposit rate