[Parametrization] Bootstrap Chicken In period

[bingen]

I think 1 week is a good trade off for safety (avoiding edge cases with tiny initial chicken in amounts and huge backing ratios) and good user experience (having to wait 1 week for the firs Chicken In seems quite reasonable).

Besides, making it longer doesn’t seem to improve results, actually the opposite.

We can revisit depending on the target average we finally set.

Below results for 1 week, 2 weeks and 1 month:

1 week

Performance

 - Total permament:               28,117.01
 - Permament percentage:          8.249%

 - Rebonders avg gain: 3.363%
 - LPs avg gain:       4.713%
 - Sellers avg gain:   1.937%
 - Traders avg gain:   8.697%

2 weeks

Performance

 - Total permament:               24,694.59
 - Permament percentage:          7.802%

 - Rebonders avg gain: 3.532%
 - LPs avg gain:       4.285%
 - Sellers avg gain:   2.013%
 - Traders avg gain:   9.694%

1 month

Performance

 - Total permament:               14,081.73
 - Permament percentage:          4.498%

 - Rebonders avg gain: 1.644%
 - LPs avg gain:       7.413%
 - Sellers avg gain:   1.381%
 - Traders avg gain:   8.159%

[bingen]

Quite related to #231 . For instance: https://github.com/liquity/ChickenBond/issues/231#issuecomment-1262857474

[bingen]

The longer the bootstrap period, the more rewards from yield generated from Pending are up for grabs for first users, so more incentive to LP. Without initial LPs, the system would have hard time kicking off.

[bingen]

Related to https://github.com/liquity/ChickenBond/issues/231#issuecomment-1262857474, maybe it’s important it’s not much less than target average.

See https://github.com/liquity/ChickenBond/issues/95#issuecomment-1207549471

it seems likely that minting of bLUSD would start as soon as the bootstrap period is over. If there’s even a single chicken who apes in ASAP, that kicks off the whole process of pouring the yield of pending and permanent buckets into acquired. This results in massive yield amplification for the first one who chickened in. Others are incentivized to follow suit by chickening in as well, until the yield amplification is reduced to a more reasonable level.

[bingen]

Maybe we can set initial accrual param for optimal rebonding, and then set the bootstrap period at the break even point. For instance, with a premium of 1.5, a Chicken In fee of 5% and a target of 30 days, using the optimal time formula we should have an initial alpha of 5.81. With that alpha, the break even point would be at 13.68. So we could set the bootsrapping period at 2 weeks. See: https://docs.google.com/spreadsheets/d/128KLqzjtuFM1oXSg_njGoi4_-VfCtOe-7EItNbgCr2E/edit#gid=0