Interest rate model

There are a number of interest rates used to determine the interest paid on borrowings and interest received on deposits. There are also interest indexes which are used to track the accrued interest.
Borrow interests rates
To differentiate the variable parameters from the stable ones, we are going to use the subscript sss
​ for stable and vvv
​ for variable.
The variable borrow interest rate ivbti_{vb_t}ivbt​​
 and stable borrow interest rates isbti_{sb_t}isbt​​
 are calculated based on the optimal utilisation ratio UoptU_{opt}Uopt​
 and optimal stable to total debt ratio 0ratio0_{ratio}0ratio​
​ set by the protocol.
If Ut<UOptU_t < U_{Opt}Ut​<UOpt​
​
ivbt=Rv0+UtUOpt∗Rv1i_{vb_{t}}=R_{v0}+ \frac{U_t}{U_{Opt}}*R_{v1} ivbt​​=Rv0​+UOpt​Ut​​∗Rv1​
If Ut⩾UoptU_t \geqslant	 U_{opt}Ut​⩾Uopt​
​
ivbt=Rv0+Rv1+Ut−Uopt1−Uopt∗Rv2i_{vb_t}=R_{v0}+R_{v1}+\frac{U_t-U_{opt}}{1-U_{opt}}* R_{v2}ivbt​​=Rv0​+Rv1​+1−Uopt​Ut​−Uopt​​∗Rv2​
If Ut⩽UoptU_t \leqslant U_{opt}Ut​⩽Uopt​
​
isbt=(Rv1+Rs0)+UtUOpt∗Rs1i_{sb_t}=(R_{v1}+R_{s0})+\frac{U_t}{U_{Opt}}*R_{s1 }isbt​​=(Rv1​+Rs0​)+UOpt​Ut​​∗Rs1​
If Ut>UoptU_t > U_{opt}Ut​>Uopt​
​
isbt=(Rv1+Rs0)+Rs1+Ut−UOpt1−UOpt∗Rs2i_{sb_t}=(R_{v1}+R_{s0})+R_{s1}+ \frac{U_t- U_{Opt}}{1 -U_{Opt}}*R_{s2}isbt​​=(Rv1​+Rs0​)+Rs1​+1−UOpt​Ut​−UOpt​​∗Rs2​
If Ratio>0ratioRatio > 0_{ratio}Ratio>0ratio​
, an excess is added to the stable borrow interest rate:
isbt+=Rs3∗ratio−0ratio1−0ratioi_{sb_t}+=R_{s3}*\frac{ratio-0_{ratio}}{1-0_{ratio}} 
isbt​​+=Rs3​∗1−0ratio​ratio−0ratio​​
The overall borrow interest rate ibti_{b_t}ibt​​
 factors in all variable and stable rate borrows and is calculated by taking the weighted average of the total variable and stable borrowed amounts and their respective interest rates.
ibt=TotalVariableBorrowAmount∗ivbt+∑Bi∗isbiTotalDebti_{b_t}=\frac{TotalVariableBorrowAmount*i_{vb_t}+\sum{B_i*i_{sb_i}}}{TotalDebt}ibt​​=TotalDebtTotalVariableBorrowAmount∗ivbt​​+∑Bi​∗isbi​​​
Where:
​ivbti_{vb_t}ivbt​​
is the variable borrow amount,
​BiB_iBi​
 is the stable borrow amount,
​isbii_{sb_i}isbi​​
is the stable borrow rate,
the subscript iii
 represents each stable borrow taken on the protocol.
Deposit interests rates
The deposit interest rate idti_{d_t}idt​​
 is directly dependent on the overall borrow interest rate ibti_{b_t}ibt​​
. The borrow interest is divided between the depositors, excluding what is retained by the protocol.
idt=Ut∗ibt∗(1−RR)i_{d_t}= U_t*i_{b_t}*(1-RR)
idt​​=Ut​∗ibt​​∗(1−RR)
Where:
​RRRRRR
 is the retention rate i.e. the interest kept by the protocol as revenue.
Last modified 9mo ago