Estimating Bid–Ask Spreads from Transaction Prices

Summary

The document asks whether bid and ask quotes, or an average spread, can be reconstructed when only transaction prices are available. One answer cautions that trades alone do not contain enough information to recover the quotes directly. Closely spaced transactions with different prices may offer limited clues about the spread during that short interval, especially for a very liquid instrument, but this is not a general reconstruction method.

A second answer proposes Roll’s model as an academic starting point. It estimates the percentage spread from the negative serial covariance between consecutive log returns, under the model’s assumptions. The answer warns that the estimate may perform poorly in practice and that modifications exist; assessing whether the data fit the assumptions is part of deciding whether the method is useful. The discussion gives neither a worked empirical example nor a complete survey of alternatives, so its estimate should be treated as a model-dependent proxy rather than recovered historical quotes.

Key ideas

• Transaction prices alone generally do not identify the historical bid and ask quotes.
• Very closely spaced trades with differing prices may provide brief, context-specific spread clues.
• Roll’s model estimates a percentage spread from negative serial covariance in log returns.
• The Roll estimate depends on assumptions and may perform poorly, so it should be treated as a starting point.

Tags

# Recreating Bid-Ask from Transactions data


# Recreating Bid-Ask from Transactions data












A database only has transactions/trades for a given instrument. In order to recreate bid-ask of the instrument to estimate the average bid-ask spread, what process does one need to follow? what are the various assumptions involved. have not found anything concrete.

## Answer by Richard at NorgateData (score 2)

https://quant.stackexchange.com/a/60558

Unfortunately there is no information available to do this.

You might be able to infer some brief bid-ask spread data from consecutive transactions that have are very tightly spaced time-wise but have a price variance, but this is would only be relevant for that particular short time period, unless you really do have an extremely liquid instrument.

## Answer by Sharad (score 0)

https://quant.stackexchange.com/a/60579

The standard academic way to do this is to start by using Roll's model (1984). If $p_t$ is the (log) price of an asset then setting $r_t = p_t - p_{t-1}$, we can estimate the percentage bid-ask spread as:

$\widehat{s} = 2 \sqrt{-\mbox{Cov}(r_t, r_{t-1})}$

In practice, this measure may not perform very well and all sorts of extensions and modifications have been proposed. Having said that, using Roll's model as a starting point and ascertaining to what extent the data satisfies the model's assumptions can be a very useful stepping stone in terms of selecting/developing a more satisfactory model.

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