Decaying Order Imbalance for Market Making

Summary

The document examines how to measure order imbalance for a market maker. A cited definition accumulates the excess size of buy orders over sell orders at the current quote since the market maker last changed that quote. This measure resets to zero after any quote update, discarding earlier order information.

The discussion recognizes that some historical order flow may remain informative after a small quote change, while a large price shift can make old observations less relevant. It asks whether an imbalance process could use exponential decay that speeds up when prices move substantially. No specific standard formula, calibration method, or empirical evidence is supplied, so the text frames a modeling question rather than presenting a tested solution. The core lesson is that imbalance memory and quote-price changes may need to be modeled together when designing market-making signals.

Key ideas

• A quote-reset imbalance measure forgets all earlier order flow whenever the quote changes.
• Buy and sell order sizes can be summarized as a signed imbalance at the current quote.
• Past order information may deserve partial weight after small quote changes.
• A larger price shift may justify faster decay of previously observed order flow.
• The document poses this design problem but does not provide a tested decay rule.

Tags

# Market imbalance measures for market making


# Market imbalance measures for market making












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 However it makes sense that if we make a large jump in our quoted prices that we will want to forget past now outdated information.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?

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