# 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.

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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

First: once you will have your liquidity indicator, you will need to know if the signal is worth the risk to go faster (or slower if it is a negative signal). Impulse control will tell you that: http://www.ceremade.dauphine.fr/~bouchard/pdf/BML09.pdf Optimal control of trading algorithms: a general impulse control approach, by Bruno Bouchard, Ngoc Minh Dang, Charles-Albert Lehalle

If you want to couple liquidity and price limits, you can use market making like techniques: http://arxiv.org/abs/1105.3115 Dealing with the Inventory Risk. A solution to the market making problem by Olivier Guéant, Charles-Albert Lehalle, Joaquin Fernandez Tapia

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.

Estimate it on real,time and you will have a full framework.

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Major measures of liquidity is volume and the spread. I would look for correlation between returns and volume and the bid-ask spread. On each time there is a negative anticipation I would add the stock sizing by the POV target at that point and the difference between arrival price and current price and buy sell imbalances in the order book. The specifics on how these are done would be a differentiating factor between each execution algo implementation.

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