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It is stated in the LLOB model (i.e. this paper, https://arxiv.org/pdf/1105.1694.pdf ) :

Our basic idea is that of a “latent order book” that at any instant of time t aggregates the total intended volume for sells at price p or above, $V+(p, t)$, and the total intended volume for buys at price $p$ or below, $V−(p, t)$. We want to emphasize that this is in general not the volume revealed in the real (observable) order book, in particular for p remote from the current price $p_t$ . It is rather the volume that would reveal itself in the order book, or as market orders, if the price came instantaneously closer to $p$. But since there is little incentive to reveal one’s intentions too early, most of the volume is latent and not revealed.

Can anyone explain why there is a certain volume that is not displayed?

Also, why do we have the condition $\rho_A(p_A,t)=\rho_B(p_B,t)$ if we denote $\rho_A$ and $\rho_B$ the ask and bid densities ?

Thanks

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Regarding unseen liquidity the easiest example would be iceberg order types. So only some percentage of the total interest of the order is visible but depending on the exchange and their priority rules a market order would execute against the entire unseen liquidity of that iceberg if it hit it.

More generally, not all limit order interest is shown early in the order book. Liquidity tends to fill in and out around the current market price. It's one of the reasons smaller order sizes tend to execute better as order book resilience works in your favour.

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  • $\begingroup$ What do you mean by "...around the current price"? $\endgroup$ – mbz0 Aug 3 '20 at 12:03
  • $\begingroup$ The current market price. If the market is 90/100 and you want to offer 100 lots at 200 you will not place the order now, but rather wait for it to be 185/195 for example $\endgroup$ – river_rat Aug 3 '20 at 12:04
  • $\begingroup$ I see, many thanks. And why do we have the density equilibrium? $\endgroup$ – mbz0 Aug 3 '20 at 12:07

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