ARC: Update AMPL interest rate curve to account for over-approximation in compounded interest

Thanks for this well explained post @Naguib

In the last forum discussion about the calibration of AMPL interest rate parameters, multiple users among which @pakim249, @DFC, @danbainbridge and @BlockEnthusiast highlighted their concerns around 10,000% max APY not beeing enough given the rebasing opportunity

The AMPL reserved was fully utilised at multiple occasions and for lengthy periods with depositors unable to withdraw the liquidity they deposited since rational actors were borrowing the available liquidity to take advantage of the superior yield offered by the rebasing. To avoid this situation again, I believe that the max borrow rate should be aligned with the rebasing returns

Stats Rebase %
Min -6.8
5% Percentile -3.3
25% Percentile -1.6
Median 0.0
Average 0.2
75% Percentile 1.0
95% Percentile 5.0
Max 27.1

Historical statistics on rebasing data place a 5% rebase as the 95% percentile of the distribution. It seems the interest rate model max rate should cover this scenario as it’s not sustainable to call upon governance for frequent parameters adjustments. 5% daily yield takes us to 1825% APR which takes us to ​5,421,184,057% APY with daily compounding. Based on this the current 10,000% slope 2 seems excessive while the 750% seems too low

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