Interpreting Delta, Dual Delta, Gamma, and Dual Gamma

Summary

The document raises questions about how option delta and dual delta compare across strike prices, and whether either can represent the probability that a call expires in the money. It also asks whether gamma and dual gamma show a consistent relative pattern that could help describe the underlying asset’s distribution. The author suggests that hedging demand might make option prices exceed fair value and thereby cause delta to overstate this probability, but provides no derivation or evidence to confirm that explanation.

The text is a set of questions rather than a worked analysis, so it does not establish general relationships between these Greeks or provide a method for estimating probabilities or distributions. Any interpretation would depend on the pricing assumptions and market inputs used. The document is useful as a prompt to distinguish option price sensitivities from probability measures, but readers need a substantive answer or independent analysis before applying the suggested comparisons in trading or research.

Key ideas

• The document asks whether call delta systematically exceeds dual delta across strikes.
• It questions whether delta can be interpreted directly as the probability of expiring in the money.
• It proposes hedging demand as a possible explanation for differences between the two measures.
• It asks whether gamma and dual gamma have a consistent relationship across upside and downside strikes.
• The document supplies questions but no derivation or evidence that resolves them.

Tags

# Gamma and Delta vs Dual Gamma and Dual Delta


# Gamma and Delta vs Dual Gamma and Dual Delta












My understanding is that the dual delta is generally lower than the delta across all strike prices (they still have the same asymptotes at 0 and 1 for a call), primarily because options are often utilized for hedging. Consequently, buyers are inclined to pay a premium above the fair value. Therefore, relying on delta rather than dual delta to estimate the likelihood of an option expiring in the money tends to exaggerate this probability. Is this correct?

When comparing gamma to dual gamma as a proxy for the distribution of the underlying asset is there generally a pattern? (e.g dual gamma higher than gamma for upside strikes and lesser for downside strikes)

Thanks so much in advance and apologies if I'm being dumb :)

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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