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If neutralizing delta requires an addition of a fractional number of shares, e.g. 444.12345 do we generally keep the decimals or round up to the nearest integer? I reckon rounding would no longer make it "neutral"?

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    $\begingroup$ Yes, we round. And yes, that introduces an error. But it is a small error, especially in a large position, as a big bank might have. $\endgroup$
    – noob2
    Mar 14 at 19:58
  • $\begingroup$ Great, thank you. $\endgroup$ Mar 14 at 20:23
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    $\begingroup$ Years ago we would round (up or down) not just to a whole share, but to a round lot, which for almost all stocks was 100 shares. But as @noob2 wrote, for large positions this rounding did not make any material difference. $\endgroup$ Mar 16 at 15:35
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Answer: Round in practice. The error is relative small.

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