10000% in three and a half days? How exactly is Fraxlend's interest rate calculated?

As Curve founder Michael Egorov's personal debt warehouse risk situation fermented, discussions surrounding Fraxlend's interest rate issues have also increased.

The reason for this is that Fraxlend has adopted a relatively special interest rate adjustment mechanism. As a result, the loan interest rate in the CRV/FRAX market in Fraxlend has been rising rapidly for most of the time from yesterday to the present, which "forced" Egorov to take the lead in this afternoon. $7.13 million in debt was repaid on the platform.

So, how exactly is Fraxlend's interest rate calculated? Why can the number rise so fast? Combining the official documentation of Frax Finance and the tweet explanation of its developer Drake Evans, we briefly sorted out this algorithm.

First, according to Frax Finance's documentation, Fraxlend uses three different interest rate change algorithms for different markets:

• Linear interest rate: Simply put, it is a basic algorithm in which the interest rate increases linearly with the market utilization rate.
• Time-weighted variable interest rate: An algorithm that determines the increase or decrease of the interest rate according to the market utilization rate, and adjusts the interest rate through a fixed time interval.
• Variable interest rate V 2 : A composite algorithm that combines the former two, uses the function of linear interest rate to determine the current interest rate, but also uses the formula of time-weighted variable interest rate to adjust the maximum interest rate.

Well, you may feel that this explanation is more vague, don't worry, let's continue.

According to Drake's explanation, Fraxlend's CRV/FRAX market uses the second algorithm (i.e. time-weighted variable rate), which works as follows:

• First, Fraxlend will set a target utilization rate range for a specific market. When the market utilization rate is within this range, the interest rate does not need to change.
• When the market utilization rate is lower than the target range, the interest rate will gradually decrease with a certain multiplier every certain period of time until the lowest interest rate.
• When the market utilization rate is higher than the target range, the interest rate will gradually increase with a certain multiplier at specific intervals until the lowest interest rate.

This specific period of time, called the half-life in Fraxlend's design, refers to the time it takes for the interest rate to halve when the market utilization rate is 0, and it is also the time it takes for the interest rate to double when the market utilization rate is 0.

According to the contract in the CRV/FRAX market, the target utilization rate range is 75% -85%, the minimum interest rate is 0.5%, the maximum interest rate is 10000%, and the half-life is 12 hours.

This also means that for the CRV/FRAX market:

• When the market utilization rate is in the range of 75% -85%, there is no need to change the interest rate.
• When the market utilization rate is lower than 75%, every 12 hours, the interest rate will gradually decrease with a certain "multiplier" until 0.5%.
• When the market utilization rate is higher than 85%, every 12 hours, the interest rate will gradually increase with a certain "multiplier" until 10000%.

Therefore, for quite a long period of time since yesterday, since the overall utilization rate of the CRV/FRAX market in Fraxlend has continued to exceed 85%, or even close to 100%, the loan interest rate of this pool has continued to rise.

However, this does not mean that the interest rate in this market will double every 12 hours as some rumors say, and rush to 10000% in three and a half days (this statement comes from Delphi Digital, but in fact Delphi Digital only listed 100% utilization rate, it is not said to be the general situation after exceeding 85%), because in reality, the utilization rate of the market has not been maintained at 100% (this is impossible), so the above mentioned That "multiplier" is not always 2x.

According to Drake's supplementary introduction, when the utilization rate of the CRV/FRAX market exceeds 85%, corresponding to the utilization rate of each level, the multipliers of interest rate growth are also different.

As shown in the figure above, when the market utilization rate is 85%, the "multiplier" is 1 times, which also means that the interest rate will remain unchanged; but as the utilization rate rises, the "multiplier" will gradually increase; until Once utilization reaches 100%, the "multiplier" becomes 2x, which begins what Delphi Digital calls doubling.

Currently, with Egorov's repayment, the utilization rate of the CRV/FRAX market has dropped to 53.68%, which means that if the situation is maintained, the interest rate will drop further after 12 hours. In this way, the pressure on Egorov will also be greatly reduced.

So it is not difficult to understand why Egorov wants to replace some of Fraxlend's debts in advance, at least to lower the interest rate first, otherwise the rising range is really unbearable.