# Liquidity estimators: VWAP and IS

I am looking for some info on how to estimate liquidity (intraday). I have read some researches and created intraday measurements of liquidity on time yet not on price. What I mean by this is that I am not looking for a liquidity profile based on time but a profile based on price, i.e. how much liquidity there is at each price level. For this I am assuming I need to look into adaptive algos that calculate real-time data. However, I was looking at some Implementation Shortfall algos and couldn't find anything except that old article from 1988.

For example, if I was an VWAP algo I would know the TIMES to send the orders (let's say there is an U-shaped historical volume profile), but I, as an extremely sophisticated investor (:P) would like to have an algo that "looks" at each level and estimates if it can transact orders here or not. I.e. looking at depth, volatility etc.

In short, I am looking for a study or something to illuminate me on the basics of liquidity seeking algorithms to understand some more as I can't find anything!

Thanks for taking time.

• If you're interested in visuals, Robert Almgren has narrated a few interesting videos about his brokerage's algos. – chrisaycock Dec 13 '11 at 19:47
• Since you have indicated that you are interested in VWAP, you could also attempt to model VWAP, and try to estimate parameters from the volume data / price in the market. – Peter Irojah Mar 15 '12 at 15:58

This second paper suggests to model liquidity vs price balance this way: (1) the mid price $S_t$ dynamics is not directional (anyway if you have a trend detector, plug it in it, otherwise take a martingale); (2) put an order at distance $\delta$ of $S_t$; (3) the trade you get follows a Poisson process with intensity $A_t \exp -k_t \delta$. the pair $(A_t, k_t)$ is you liquidity signal.