add get_targeted_long #882
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A detailed derivation of the solution can be found in section 2 of the attached document. |
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addresses #775
The solution first attempts to directly compute targeted reserve levels:$r_t$ , the pool share reserves, $z_t$ , must be:
For some target rate,
and the pool bond reserves,$y_t$ , must be:
where$c$ is the vault share price, $\mu$ is the initial vault share price, $t$ is the annualized position duration, and $T$ is the time stretch constant. The corresponding deltas are then:
If that is not successful, then it performs newtons method to minimize
for some realized fixed rate,$r(x) = (1 - p(x)) / (p(x) t)$ after a long was opened with $x$ base, where $p(x)$ is the spot price after the long was opened.