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Estimating Limit Order Fill Probabilities by Size, Price, and Time

Article Quant Q&A · Author: naz
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Summary

The document frames an empirical problem in limit order placement: estimate the probability that an order of a specified size, placed a chosen distance from the mid-price, receives a fill within a given time. The proposed data include market-order prices, execution sizes, and timestamps. A Poisson process is suggested as a possible starting point, while the question also asks whether that model captures the problem adequately.

Key ideas

  • Fill probability depends on order size, distance from the mid-price, and the time horizon.
  • Market-order prices, sizes, and timestamps are proposed as empirical inputs for estimating fills.
  • A Poisson process is considered as a candidate model, but no model specification or fitted result is given.
  • The stated application is choosing order sizes and distances to improve expected fill value.
  • The document also raises expected executable size and the role of strategic interaction in order placement.

Tags

Market microstructureExecutionStatisticsMarket making
Full text
# Probability of getting a fill of a given size


# Probability of getting a fill of a given size












Question is quite simple, what is the probability of getting a fill for:

> (i) a limit order of size - $s$ (ii) that is $\Delta$ away from the mid-price (iii) in the next $t$ minutes

given empirical data of the market orders (prices and sizes of the fills, as well as the time of the fills). I think the Poisson process is useful here?

I have found this. Although it asks this question for the longer-timeframe, I suppose my question is a generalization of that question.

I would like to know this to optimally place the limit orders with varying sizes at varying distances from the mid-price to obtain the largest expected value of the fills. It would also be useful to know the expected order size at a given distance from the mid-price.

Also, according to this, what I am attempting to do might be nonsensical? And I should just base placing of the limit orders on game theory?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.