Weighting Order Book Midpoints by Execution Probability

# Mid-Point calculation with execution probability


# Mid-Point calculation with execution probability












Referring

Cao, Hansch, and Wang (2004) "The Informational Content of an Open Limit Order Book"

$$ \mbox{WP}^{n_1 - n_2} = \frac{\sum_{j=n_1}^{n_2} (Q_j^d P_j^d + Q_j^s P_j^s)}{(Q_j^d + Q_j^s)} $$

Did someone know maybe some variation of that equation that penalizing quotes that are more away from best quotes? I think result of that formula is easy to manipulate by placing limit orders in large amount at prices that have very low execution probability in some time.

I'm trying to modify that formula, with inputing additional touching probability for each ask and bid level calculated from book market orders inflow in some sampled time T to ability for penalize levels on what orders can be easy cancelled before execution.

## Answer by lehalle (score 1)

https://quant.stackexchange.com/a/77804

Using as weights the probability of execution (or indeed the probability that the price reaches the considered level) makes sense. In essence, you would like to assign weights that reflects how much this limit is "meaningful" in contributing to the price formation process.

In Huang, Weibing, C-A L, and Mathieu Rosenbaum. "Simulating and analyzing order book data: The queue-reactive model" Journal of the American Statistical Association 110, no. 509 (2015): 107-122, author have shown that for "large ticks assets" (i.e. when the bid-ask spread is around 1.2 to 1.6 ticks) first and second queues where enough to model the full price formation process. Nevertheless, you have to keep in mind that order book only contains information on the endogenous part of the price formation; it means that if a News suddenly impact a company, the price will move a way that is (more or less) independent of the orderbook shape.

For the sake of simplicity, let's only consider the first limits Bid and Ask. Imagine now that you find weights $w^B$ and $w^A$ to adjust the bid and ask limits, as you said in your question, $w^A$ is related to the probability $p_A$ that the price reaches the best bid before the first ask (say, again for simplicity, that $w^A=p_A$) and $w^B=1-p_A$.

Before going further, I let you convince yourself that your indicator is similar to the imbalance: $$\mathbf{I}={Q^B-Q^A \over Q^B+Q^A}.$$ And that the imbalance should be related to the probability that the price reaches $P^B$ before $P^A$. It is why it is interesting, you should think something like $$p_A\propto 1+\mathbf{I}.$$

Now you may feel the difficulty: the imbalance (and hence your indicator) is meant to tell you the direction of the price, and you want to change its formula using an indicator of where the price should go... There is a deadlock somewhere, no?

Nevertheless, if you want to do something in practice, I would suggest to use non directional weights (based on volatility) to adjust the limits. It is better than nothing but it does not solve the deadlock I mentioned.