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I am looking at AAPL TAQ high-frequency trade data from NYSE and I have noticed that at several places the trade price (defined in Daily TAQ Client Specification as: "The Trade Price is the monetary value of an individual share of security at the time of the trade.") is quoted with three decimal digits. However, the TAQ quote data file does not contain quotes with three decimal digits, only two are present (as the minimal tick value for AAPL is 0.01$). Therefore, I am perplexed how to interpret the trades represented by three decimal digits, as there are no corresponding quotes at those prices. My question is, what is the reason behing this discrepancy?

EDIT: The sample trades can look like this: [time in nanoseconds, exchange, stock, ..., trade size, trade price, ...]

113750721732148 Y MSFT ... 100 60.55 ...
113750722078102 V MSFT ... 19 60.545 ...
113750746289535 K MSFT ... 100 60.55 ...

And for example, at 113748385546534 there was a trade with trade price 60.54. So trades fluctuate between the best bid and best ask prices, but there is this trade that is within the spread.

Source: NYSE TAQ trade sample data available here ftp://ftp.nyxdata.com/Historical%20Data%20Samples/Daily%20TAQ%20Sample/. I am talking about AAPL trades in a file EQY_US_ALL_TRADE_20161024 and AAPL quotes in a file SPLITS_US_ALL_BBO_A_20161024.

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    $\begingroup$ It's a rather large file - can you add examples of AAPL trade price quotes you are confused about in the text of the question? $\endgroup$ – LazyCat Jul 12 '17 at 15:11
  • $\begingroup$ Just two quick comments: I am not sure whether it is a good idea to provide every reader of this question with access to your downloaded TAQ data - is this legal? 2. May it be the case that three decimal numbers occur if large trade sizes eat up more than one level of the orderbook. In this case the quoted price could be the average price. $\endgroup$ – muffin1974 Jul 13 '17 at 16:44
  • $\begingroup$ No, these are publicly available data that NYSE provides as a sample data, so it should be fine. And the trade price seems always to be within the existing spread at the moment of trade. @LazyCat I edited the original post to show the precise appearance of these trades - thanks for the suggestion. $\endgroup$ – ragoragino Jul 14 '17 at 12:00
  • $\begingroup$ 60.545 is probably just a midpoint execution. $\endgroup$ – LazyCat Jul 14 '17 at 13:03
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say you have this order book, where left column are bids and right offers:

   60.56 1
1  60.55 
1  60.54

if you send a market order to sell 2 contracts, your trade will be completed with one contract at 60.55 and one at 60.54. The average price for your order is 60.545. The trade with 3 decimal was completed at multiple prices, and it's giving you the average.

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