Modelling VWAP Slippage with HFT data

Usually the the difference between your average price between $t_0$ and $T$ and the price at $t_0$ is called the Implementation Shortfall (IS).

They are a lot of references to do this, just cite these two ones:

• Market Impacts and the Life Cycle of Investors Orders, by Bacry, Iuga, Lasnier and L
• Modelling Transaction Costs When Trades May Be Crowded: A Bayesian Network Using Partially Observable Orders Imbalance, by Brière, L, Nefedova and Raboun (it is one of the chapter of the book Machine Learning for Asset Management)

This Figure comes from the second paper (you see how it is square-rooted):

The formula is, for a traded quantity $Q$ $$IS(Q)simeq a cdot phi + b cdotsigmasqrt{frac{Q}{rm ADV}},$$ where

• $phi$ is the bid-ask spread
• $sigma$ is the volatility
• $rm ADV$ is the Average Daily Volume on the instrument.

$a$ and $b$ are two constants to be calibrated on your data. Typically: $a$ corresponds to your trading skills (if you are very smart in good liquidity chasing and if you have good execution predictors, $a$ can be close to 20%), and $b$ is somehow universal.

[EDIT] last paragraph removed (following @mbz0 remark).