Adjusts the time stretch calculation to hold the ratio of reserves constant #716
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Fixes: #715.
The gist of this PR is that all we need to do to maintain an approximately constant inventory across pool's with similar initial conditions but different position durations is to solve for a time stretch that implies the same ratio of reserves.
To derive this, we use the spot price calculation:
We start by solving for the benchmark time stretch$t_{s_b}$ using the existing $ratio = \tfrac{\mu \cdot z}{y}$ using $z_e = 1$ and $\mu = 1$ , but this won't effect the ending result since the ratio will be the same regardless of the starting initial share price and effective share reserves. Finally, we solve for the target spot price $p_{target}$ from the position duration $d_{position}$ and target APR $r_{target}$ :
calculateTimeStretch
function. Then we use this time stretch to solve for the ratio of reservescalculateInitialSharePrice
. For simplicity we use a benchmark ofFinally, we use the spot price calculation to solve for the adjusted time stretch: