# 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?

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 $$Q$$ $$IS(Q)\simeq a \cdot \phi + b \cdot\sigma\sqrt{\frac{Q}{\rm ADV}},$$ 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).

• 1. According to Brière paper, the IS definition fits perfectly with the one I gave for the VWAP slippage, i.e. that is the signed relative difference between the VWAP and the arrival price, ... not sure I got the point of translating from IS to VWAP, as they are still similar to me? 2. How is IS different from what is known as Market Impact, defined by $$\mathbb{I} (Q) = < \varepsilon (p_T - p_0) >$$ ? They seem very resembling, namely for the empirical law? – mbz0 Aug 25 '20 at 9:16
• Please correct me if I'm mistaking but The cost of trading can decomposed into two components. First, the impact that trading has on the move of the market price (the mid-price for instance), which is referred to as market impact. The second component corresponds to market frictions such as slippage. – mbz0 Aug 25 '20 at 9:49
• sorry @mbz0 : you are right, I though you targeted to model the difference between your average price and the VWAP of the market. I edited my answer to remove the last section. About your last remark: market impact is part of the "slippage", it is better to say that the slippage is decomposed in bid-ask costs (or trading skills) and market impact driven costs. – lehalle Aug 26 '20 at 4:56