I am reading a paper "A Simple Way to Estimate Bid-Ask Spreads from Daily High and Low Prices" cf.A Simple Way to Estimate Bid-Ask Spreads from Daily High and Low Prices

The authors proposed the method of estimation the bid-ask spread from high and low prices of consecutive two days.

From what I can understand, there is an important assumption there that the prices follow geometric Brownian motion and, therefore, the true variance over a 2-day period is twice as large as the expectation of the variance over a single day. This property is used for the spread estimation.

Next, assume that I have more data, than just high and low prices, say, 10 min bars.

Will it improve the spread estimator if I use high and low prices of consecutive two 10 min bars instead on days? Does it contradict to the derivation for daily case?


1 Answer 1


If you have access to intraday data, they are better ways to estimate the bid-ask spread. If you have Open, High, Low and Close price on each 5min bin $b$ (or any other interval): the Close of the previous bin and the Open of this one are consecutive. Hence $dP(b)=C(b-1)-O(b)$ allows to define an estimate $\psi(b)$ of the bid-ask spread $$\psi(b):=\min_{b:\, |dP(b)|>0} |dP(b)|.$$

It is not defined on every bin of each day (sometimes $dP(b)=0$), but often you have several of them. You can average them to obtain an estimate for the bid-ask of the day.

Of course you can add an estimate deduced from High and Low of the bin, but it is clearly worst than this $\phi$.

[EDIT following Kri's comment]
There is no academic paper comparing different approaches because anyone with empirical data can compare. Moreover, under common regularity assumption:

  • for the bid-ask spread: the higher frequency the better (of course it is not the same for the volatility --because of the bid-ask spread bounce at least, convicting to the well documented "signature plot" effect--),
  • nevertheless there is a difference at high-frequency between the tie-weighted average spread and the traded-quantity-weighted bid-ask spread. The spread is on average smaller around the trades.
  • $\begingroup$ I can't comment, but wanted to ask about @lehalle's answer - seems intuitive and straightforward - is there any papers empirically comparing these techniques? $\endgroup$
    – kri
    Sep 30, 2021 at 17:01
  • 1
    $\begingroup$ @kri I thought your comment deserved an edit of my answer: this is done $\endgroup$
    – lehalle
    Oct 1, 2021 at 10:46
  • $\begingroup$ Following up @lehalle's comments yet again. The estimate 𝜓(𝑏) is a point estimate over some time-interval right (i.e. 60 consecutive 1-min bars to make an hourly estimate). Then when you say "You can average them to obtain an estimate for the bid-ask of the day", do you mean to average separate such hourly estimates of 𝜓(𝑏) over some longer time span (e.g. 3-days, or 72 estimates of 𝜓(𝑏)). $\endgroup$
    – kri
    Oct 3, 2021 at 21:32
  • $\begingroup$ @kri you average over the day to have a bid-ask spread for the day. Of course there is in fact an intraday seasonality of the bid-ask spread, hence you can choose to average a time-weighted or trade-weighted way; results will be different. $\endgroup$
    – lehalle
    Oct 6, 2021 at 17:19

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