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Hello,

I am working on modelling the probability of a limit order being filled given a state of the order book, say till the top 5 levels on bid and ask side.
I was wondering if anyone here has any experience with the same and can share a few insights/papers ?

Also, is it at all possible to do this with just the state of the order book at various times in the day?
What I mean is can this be done without data on order flow since we lose information as we only have the top n (5 in the case) level of the order book.

Regards

Not sure if it's helpful but I once looked at this too a couple of years ago, and I thought this thesis was interesting:

http://discovery.ucl.ac.uk/1359852/1/Ch ... Thesis.pdf

At what time resolution do you have the 5 level snapshots? By any change liquid future markets like the emini S&P ?

Thanks a ton for the reply outrun, I will read the paper you have shared. 
For the 2nd part, I have top 5 levels at the end of every second and yes, i am looking at emini S&P and similarly liquid markets.

Cool, I'm also looking at the same markets (40 most liquid futures), same second resolution, except I only have second resolution ohlcv of trades: 2009-2016.

Good luck!

Cool, I'm also looking at the same markets (40 most liquid futures), same second resolution, except I only have second resolution ohlcv of trades: 2009-2016.

Good luck!

Same to you Sire.

i've looked at this quite extensively for ir futures and have found that higher levels of the order book are not very predictive. a simple model using the best level data (e.g. something along the lines of: probability to get filled on bid side = 1 - bid_volumes / total volumes) works reasonably well. but it's a quite volatile measure and its predictive power is different for different products (e.g. slower moving stuff like bobl vs buxl). an indicator based on last traded levels (volume weighted) in my experience adds value. 

also, it depends on the application. if you are modelling this to estimate fill probabilities in a back tester, i would say don't bother. rather, first order, i would assume to only get the passive fill as the market ticks through you (and perhaps additionally use simple conservative rules to estimate queue position in case of cancellations). 

this is based on my experience of rates futures and might look different for other products.