# Modelling VWAP Slippage with HFT data

I heard that VWAP slippage (relative difference between the VWAP and the initial mid-price, $$varepsilon . frac{P_{VWAP}-P_{arrival}}{P_{arrival}}$$ with $$varepsilon = +1 or -1$$ the trade sign) could be modelled as a function of volume, spread and volatility. Have you ever had experience for that?

Quantitative Finance Asked on December 31, 2020

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:

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).

Answered by lehalle on December 31, 2020

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