Why At-the-Money Option Delta Can Exceed One Half

Summary

The document raises a question about the relationship between maturity and the delta of an at-the-money option. It contrasts the common textbook statement that at-the-money delta is one half with the author’s observation that longer-dated options may show larger deltas in practice. It also distinguishes delta as a hedge ratio from the probability that an option expires in the money.

No answer or supporting analysis is included, so the document does not resolve why the observed delta may differ from one half. It gives no model assumptions, market data, option type, or definition of how “at the money” is determined. The topic is useful as a prompt for examining how delta depends on pricing conventions and market conditions, but the text itself provides no method for diagnosing the observation or evidence for a conclusion.

Key ideas

• Delta is described as a hedge ratio, distinct from the probability of exercise.
• The author reports observing at-the-money option deltas above one half for longer maturities.
• The document poses the question but supplies no explanation, model assumptions, or supporting data.

Tags

# Why a long-dated option has delta > 0.5?


# Why a long-dated option has delta > 0.5?












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?

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