The paper An Electronic Market-Maker define the market order imbalance as follows:

We will define the order imbalance as the total excess demand size since the last change of quote by the market maker. Suppose there are $x$ buy orders and $y$ sell orders of one share at the current quoted price; the order imbalance is $x - y$. (p. 15)

An issue with the above definition is that the slightest update of the quote sets the imbalance back to $0$ and forgets all previous order information. However it makes sense that if we make a large jump in our quoted prices that we will want to forget past now outdated information.

Are there any 'standard' ways to define an order imbalance process that captures this information i.e. some exponential decay on previous orders that decays faster when there has been a large shift in prices?

  • $\begingroup$ For the most lucrative (to market-makers) stocks, what you call "the slightest update" and "a large jump" are the same thing :) $\endgroup$ – LazyCat Sep 23 '16 at 16:12
  • $\begingroup$ Good point, the function should also depend on the liquidity of the stock. $\endgroup$ – rwolst Sep 23 '16 at 22:05

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