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DeltaPrime

  • Launch App
On this page
  • Calculating borrowing interest
  • Utilisation Breakpoints
  • Slope
  • Offset
  • Calculating deposit rate
  • Graphs

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  1. Liquidity pools
  2. Interest

Calculations

PreviousReasoningNextPrime Account

Last updated 11 months ago

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Interest rates model might change to reflect the market. Stay in the loop in our Discord. InIn the near future this static model, will be updated to a dynamic interest rate model, to automatically reflect supply and demand.

Calculating borrowing interest

The borrowing rate RtR_{t}Rt​ is based on the current pool utilisation. It is a segmented (piecewise-linear) function defined by , and the .

 Rb={a1∗u+b1if u<=u1,a2∗u+b2if u1<u<=u2,a3∗u+b3if u2<u<=u3,a4∗u+b4if u>u3 Rb−borrowing rateu−pool utilisationa1,2,3,4−slopesb1,2,3,4−offsetsu1,2,3−utilisation breakpoints \ R_{b} = \begin{cases} a_{1}*u +b_{1} & \quad \text{if } u <= u_{1},\\ a_{2}*u +b_{2} & \quad \text{if } u_{1}<u <= u_{2},\\ a_{3}*u +b_{3} & \quad \text{if } u_{2}<u <= u_{3},\\ a_{4}*u +b_{4} & \quad \text{if } u > u_{3} \end{cases} \ \\ \\ R_{b} - \text{borrowing rate}\\ u - \text{pool utilisation}\\ a_{1,2,3,4}-\text{slopes}\\ b_{1,2,3,4}-\text{offsets}\\ u_{1,2,3}-\text{utilisation breakpoints}\\  Rb​=⎩⎨⎧​a1​∗u+b1​a2​∗u+b2​a3​∗u+b3​a4​∗u+b4​​if u<=u1​,if u1​<u<=u2​,if u2​<u<=u3​,if u>u3​​ Rb​−borrowing rateu−pool utilisationa1,2,3,4​−slopesb1,2,3,4​−offsetsu1,2,3​−utilisation breakpoints

Utilisation Breakpoints

The utilisation breakpoints define the points at which the should change. They are tuned to ensure ideal pool utilisation, and might change in the future. For both stables and non-stables, ideal utilisation ratio is set at 75%. For USDC that ratio is set at 85%.

By having multiple utilisation breakpoints instead of just one, DeltaPrime creates an optimal utilisation range. Instead of suddenly increasing the slope, there are ranges, to stabilize the interest rate around the ideal pool utilisation.

Non-stables (AVAX, ARB, etc)
Stables (USDC, DAI, etc)

0.6

0.6

0.8

0.8

0.9

0.9

Slope

The slope defines the steepness with which the interest rates rise. In the beginning, it equals 0 (a constant function) to ensure low borrowing APR and encourage borrowing. In the second range rates moderately rise.The ideal pool utilisation percentage is in this range. In the third part, rates grow rapidly to encourage deposits and repayments and keep liquidity available for withdrawals. In the final range, liquidity must be freed up to bring the utilization back to a healthy ratio. In this last part rates grow with exceptional speed.

Non-stables (AVAX, ARB, etc)
Stables (USDC, DAI, etc)

0.050

0.167

0.200

0.250

0.500

1.000

29.800

6.500

Offset

Non-stables (AVAX, ARB, etc)
Stables (USDC, DAI, etc)

0

0

-0.090

-0.050

-0.330

-0.650

-26.700

-5.600

Calculating deposit rate

Deposit rate is calculated based on current borrowing rate and pool utilisation and balances total interests of all borrowers and all depositors.

Graphs

Non-stables

Stables

If we combine the utilisation breakpoints with the , there needs to be an offset to make the graph connect. The following numbers are the result of the formula which brings the full graph together.

​

​

​

​

Rd=Rb∗uRd−deposit rateR_d = R_b * u\\ R_d - \text{deposit rate}\\ Rd​=Rb​∗uRd​−deposit rate

u1u_1u1​
u2u_2u2​
u3u_3u3​
a1a_{1}a1​
a2a_{2}a2​
a3a_{3}a3​
a4a_{4}a4​
b1b_1b1​
b2b_2b2​
b3b_3b3​
b4b_4b4​
desired interest rates
utilisation breakpoints
slopes
offsets
slope
Non-stable interest graph, "utilisation -> borrowing interest -> depositing interest": 60% -> 3% -> 1.8%; 80% -> 7% -> 5.6%; 90% -> 12% -> 10.8%; 100% -> 310% -> 310%
Stable interest graph, "utilisation -> borrowing interest -> depositing interest": 60% -> 10% -> 6%; 80% -> 15% -> 12%; 90% -> 25% -> 22.5%; 100% -> 90% -> 90%