Why Trade-Time Bid-Ask Spreads Can Differ from Time-Sampled Spreads
Summary
The document compares two ways to estimate bid-ask spreads: sampling quotes on a regular time grid and sampling the quotes immediately before trades. Trade-time sampling can be cheaper and easier because it may require fewer quote observations, but it does not produce a neutral snapshot of market conditions. Trades occur at selected times, and traders may choose whether to trade based partly on the spread and other costs or signals. As a result, pre-trade spreads may differ systematically from spreads measured at regular intervals.
The response adds a separate timing effect: execution can remove the best bid or ask orders, widening the spread observed at the moment of the trade. Its order-book example illustrates how the spread can increase after the top quote is depleted, with larger effects possible when a trade consumes multiple levels. The discussion does not establish that pre-trade spreads are always lower than time-grid averages; the sampling bias and post-trade book changes are distinct considerations.
Key ideas
- Regular time-grid and pre-trade quote samples measure spreads at different kinds of times.
- Trade timing may depend on spread costs and other factors, creating selection effects in pre-trade samples.
- A trade can remove the best quote and widen the spread observed during or after execution.
- Large trades that consume several book levels can cause greater spread changes.
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Full text
# The bid-ask spread before transactions # The bid-ask spread before transactions They are a lot of ways to compute an "estimated bid-ask spread". The most straightforward one is to sample the bid-ask on a regular time grid (for instance every second), but that for you need all the quote changes (a quote is the best bid and ask, price and quantity). Usually it is easier (and cheaper) to get the quotes sampled just before the transactions of the day. Hence it is natural the compute the average bid-ask spread on such a database. Unfortunately this sample time is a stopping time and not a deterministic good that is known "a priori". Worst than that it is probable that the occurence of a trade is not independent of the bid-ask spread: most probably traders or algorithms are making a trade-off between the cost of crossing the spread and some predictors or a waiting cost. Because of that the bid-ask spread compute just before a trade is in general smaller than the "average bid-ask spread" (on a regular time grid). In this context, the original question is: "is the bid-ask spread sampled just before a trade always lower than the bid-ask spread sampled on a regular time grid?" ## Answer by Lisandro Nasini (score 2) https://quant.stackexchange.com/a/78566 Consider that sometimes the spreads at the exact moment a trade is executed can be larger than the spread before that trade, due to the effect of removing hit orders from the order book, specifically the best bid or best ask orders (assuming they have been completely filled). If you have bids of 10-11-12 and offers of 13-14-15, the spread is 1. However, when, let's say, the 3rd offer crosses the spread and hits the 1st bid, it removes both orders, and the bids are now 10-11 while the offers are 13-14. Now the spread is 2. If the trade size sweeps through many orders, the spread will be even larger at the time of the trade.
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