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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
ss
​ for stable and
vv
​ for variable. The variable borrow interest rate
ivbti_{vb_t}
and stable borrow interest rates
isbti_{sb_t}
are calculated based on the optimal utilisation ratio
UoptU_{opt}
and optimal stable to total debt ratio
0ratio0_{ratio}
​ set by the protocol.
If
Ut<UOptU_t < U_{Opt}
​
ivbt=Rv0+UtUOpt∗Rv1i_{vb_{t}}=R_{v0}+ \frac{U_t}{U_{Opt}}*R_{v1}
If
Ut⩾UoptU_t \geqslant U_{opt}
​
ivbt=Rv0+Rv1+Ut−Uopt1−Uopt∗Rv2i_{vb_t}=R_{v0}+R_{v1}+\frac{U_t-U_{opt}}{1-U_{opt}}* R_{v2}
If
Ut⩽UoptU_t \leqslant U_{opt}
​
isbt=(Rv1+Rs0)+UtUOpt∗Rs1i_{sb_t}=(R_{v1}+R_{s0})+\frac{U_t}{U_{Opt}}*R_{s1 }
If
Ut>UoptU_t > U_{opt}
​
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}
If
Ratio>0ratioRatio > 0_{ratio}
, 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}}
The overall borrow interest rate
ibti_{b_t}
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}
Where:
  • ​
    ivbti_{vb_t}
    is the variable borrow amount,
  • ​
    BiB_i
    is the stable borrow amount,
  • ​
    isbii_{sb_i}
    is the stable borrow rate,
  • the subscript
    ii
    represents each stable borrow taken on the protocol.

Deposit interests rates

The deposit interest rate
idti_{d_t}
is directly dependent on the overall borrow interest rate
ibti_{b_t}
. 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)
Where:
  • ​
    RRRR
    is the retention rate i.e. the interest kept by the protocol as revenue.