Explanation of trade half life in Almgren-Chriss paper
Explanation of trade half life in Almgren-Chriss paper
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parky · External communityPost link
External question — Quantitative Finance Stack Exchange
Author: parky
Original post: https://quant.stackexchange.com/questions/81211
License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/
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In Section 2.3 of
Almgren, Robert, and Neil Chriss. "Optimal execution of portfolio transactions." Journal of Risk 3 (2001): 5-40
the authors define the half-life of a trade as
$\theta \equiv 1/\kappa$
and note that it is exactly the amount of time it takes to deplete the portfolio by a factor of
$e$
.
Eq(17) derives the amount of inventory remaining at a trading time
$t$
to be
$$
\frac{\sinh(\kappa(T - t))}{\sinh(\kappa T)} X.
$$
However, setting
$t = \theta \equiv 1 / \kappa$
in the above does not yield
$X / e$
.
I suspect I am misinterpreting the claim and seek some guidance to set me straight.
Thank you!
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Quoted from Forex.com.bd-Editorial External question — Quantitative Finance Stack Exchange Author: parky Source score (net votes, not local likes): 1 Original post: https://quant.stackexchange.com/questions/81211 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. In Section 2.3 of Almgren, Robert, and Neil Chriss. "Optimal execution of portfolio transactions." Journal of Risk 3 (2001): 5-40 the authors define the half-life of a trade as $\theta \equiv 1/\kappa$ and note that it is exactly the amount of time it takes to deplete the portfolio by a factor of $e$ . Eq(17) derives the amount of inventory remaining at a trading time $t$ to be $$ \frac{\sinh(\kappa(T - t))}{\sinh(\kappa T)} X. $$ However, setting $t = \theta \equiv 1 / \kappa$ in the above does not yield $X / e$ . I suspect I am misinterpreting the claim and seek some guidance to set me straight. Thank you!
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