Interpreting Market-Order Screening in a Limit Order Book Model

Summary

The document asks how a relationship for the screening of market-order flow is derived in a statistical model of a continuous double auction. In the quoted passage, a market order that survives to a price bin can be prevented from reaching the next bin when it encounters a resting limit order there. The quantity of interest is how the surviving market-order rate changes as price increases.

The questioner identifies the zero-occupation probability at a price site as a key term and seeks an intuitive derivation or related physics references. The excerpt also relates screening to mean order density and a parameter denoted by sigma, under an independent-fluctuation assumption. However, the document offers no derivation, references, or answer to the question. Its usefulness is therefore conceptual: it highlights how resting liquidity can attenuate market-order flow across price levels, while leaving the mathematical details and model assumptions unresolved.

Key ideas

• A resting limit order at a price level can prevent an arriving market order from continuing to the next level.
• The model describes the resulting attenuation as screening of market-order flow.
• The probability that a price site is empty is central to the relationship being questioned.
• The excerpt connects screening with mean order density under an independent-fluctuation assumption.
• The document requests an explanation but does not provide a derivation or references.

Tags

# Screening Market Order - Limit Order Books and Modeling


# Screening Market Order - Limit Order Books and Modeling












I am reading the paper "A statistical theory of continuous double auction". The paper can be found at,

https://www.santafe.edu/research/results/working-papers/statistical-theory-of-the-continuous-double-auctio

On page 20, section F-3 titled "Screening of the market-order rate", the author states as follows. I am trying to undestand how the relationship $d\mu = -\mu (1-\pi_0)$ is arrived at. Here $\pi_0$ is the probability of zero occupation at site with price $p$. I would imagine that this is a fairly known result in physics, or physical chemistry. I would imagine there is probably a result in eletrostatic screening or diffusion problems in the presense of barriers.

I was hoping someone could point me to references or introductory exposition of anything related to this derivation.

Thank you,

> Screening of the market-order rate

> In the context of independent fluctuations, Eq. (26) implies a relation between the mean density and the rate at which market orders are screened as price increases. The effect of a limit order, resident in the price bin p when a market order survives to reach that bin, is to prevent its arriving at the bin at p + dp. Though the nature of the shift induced, when such annihilation occurs, depends 21 on the comoving frame being modeled, the change in the number of orders surviving is independent of frame, and is given by $\mu = - \mu (1 - \pi_0) = -\frac{\mu <n>}{\sigma}$. (29)

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