Each option book states that the delta, considered as the hedge ratio and not the probability to have the option exercised, is 50% for ATM options. Anyway, empirically speaking I see it is more than this as the maturity of the option is longer.

Can you please clarify this?

  • 2
    $\begingroup$ ATM is usually never 50D. See here for an explanation. It is with higher vol as opposed to time there but if you look at the equation you can see it's the same explanation. Usually books should state ATM is close to 50d, not claim it is 50d. $\endgroup$
    – AKdemy
    Aug 12 at 7:45
  • 1
    $\begingroup$ Thanks @AKdemy, really helpful! $\endgroup$ Aug 12 at 11:13

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