🤓In Depth - How It Works
(Info via TJ Docs)
Algorithm to Calculate Risk-Free Value (RFV)
This algorithm has the added benefit of never having a gap of liquidity between Floor and active price.
We simulate if there's enough totalETH to absorb sell pressure if we dumped all circLILY at the price in the bin activeId - 1. The value of ETH if we sold all the circulating LILY at that price is circLILY * price(activeId - 1) = valueETH.
If valueETH > totalETH, then the price price(activeId - 1) is too high to absorb all sells of circulating LILY so we iterate to the next bin down, activeId - 2.
Once again we calculate valueETH, but with a caveat this time: we simulate that the ETH in the bin above, activeId - 1, has all its ETH converted to LILY and then check if we have enough ETH to absorb the rest of the circulating supply of LILY.
To do this, first we convert all the ETH to LILY in bin activeId - 1, which is reserveETH(activeId - 1) / price(activeId - 1).
Then we subtract this from the circulating supply of LILY to get the new circulating supply and multiply this new circulating supply with the price in activeId - 2: valueETH = (circLILY - reserveETH(activeId - 1) / price(activeId - 1)) * price(activeId - 2)
Then we check if valueETH <= totalETH - reserveETH(activeId - 1). If not, we iterate down to the next bin and so on.
We do this until we land on a bin where value_ETH <= total_ETH - sum_i(reserveETH(activeId - i)). Once it does, it means we have found a bin, activeId - i, that can absorb all the sells of LILY, and thus, that bin becomes the new Floor price.
Here comes the fun part - to rebalance, we only take ETH from all bins smaller than activeId - i and place them in bin activeId - i. All bins with ETH above activeId - i remain untouched. This also means that there is never a gap of liquidity between Floor and active bin.
That was quite hard to follow so let's illustrate it with an example below.
Example
Initial Distribution
Protocol seeds 2100 LILY tokens into the LILY/ETH pool which has a bin step of 0.01 ETH.
The liquidity is equally distributed with 100 LILY in each bin across 21 bins from starting price of 1 ETH per LILY to 1.2 ETH per LILY.
First Buy
Alice is the first buyer of the pool and opts to buy 1000 LILY tokens. Because 1000 LILY has been removed from the initial bins, circulating supply is now 1000.
Assuming a 1% swap fee, the current price is now 1.09 ETH per LILY and the bins look like this:
Rebalance
After the buy, a rebalance is triggered by the protocol to redistribute ETH into the Floor bin.
To find the Floor price, we use an iterative algorithm that simulates whether there's enough ETH in the pool if the entire circulating supply of LILY (1000) is sold at the current price (1.09 ETH per LILY).
First we sum up the ETH in the pool and get 1055.45 ETH - this is the totalETH.
Then we get the circulating supply of LILY valued in ETH, which is 1000 * 1.09 = 1090 - this is the valueETH.
Because valueETH > totalETH, we cannot make 1.09 the Floor price so we move down to next bin 1.08 and then we repeat the algorithm again.
First we subtract the amount of ETH currently in the 1.09 bin from totalETH, which is 1055.45 - 110.09 = 945.36 ETH - this is the new totalETH.
Then we get the new circulating supply if the price moved down to 1.09. We get this by finding the amount of LILY that would fill the 1.09 bin if all the ETH in there had been converted to LILY, which is 110.09/1.09 = 101 LILY.
Then we subtract current circulating supply by this number to get 1000 - 101 = 899 LILY - this is the new circLILY.
We then calculate the new valueETH which is 899 * 1.08 = 970.92 ETH.
As valueETH > total_ETH still, we iterate down to the 1.07 bin and repeat once again.
We've already calculated the first bin where valueETH <= totalETH in the table below, which is 1.04 ETH per LILY. Thus, 1.04 becomes the new Floor.
Now that we have our Floor price of 1.04, we execute our rebalance. Remember:
All bins above 1.04 remain untouched
All bins below 1.04 are rebalanced into 1.04
Therefore, we simply take all the ETH in bins 1, 1.01, 1.02 and 1.03, and put them into 1.04.
What About Sells?
If Alice then sells LILY back into the pool, no rebalancing is necessary as we've already proven that the invariant holds and the current Floor price is low enough to absorb as much sell pressure.
What if Circulating Supply Increases?
Circulating supply can only increase if more LILY is bought from the initial bins.
As these LILY tokens are bought in exchange for ETH which is locked into the pool forever, any circulating supply increase will always have a corresponding increase in ETH in the pool that can absorb sell pressure.
Disclaimer
Onyx Lily tokens are released via a Trader Joe v2.1 Liquidity Pool. The purchase of Onyx Lily tokens does not constitute an investment contract or any form of investment advice.
Onyx Lily no guarantees or promises about the future value or performance of the token, and the value of the token may fluctuate significantly.
Also note that it might be illegal for you to own Onyx Lily depending on your jurisdiction, check with your local laws.
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