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Why Option Strike Premium Differences Do Not Equal Exercise Probabilities

Article Quant Q&A · Author: Shay
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Summary

This question asks whether the difference in premiums between nearby options of the same type and expiry must be at least the farther-strike option’s exercise probability multiplied by the contract multiplier. It uses put options as an example and interprets the Black–Scholes–Merton value N(−d2) as the probability of exercise. The proposed inequality treats that probability as a lower bound on the premium difference.

The document does not provide an answer or supporting analysis, so the claim remains unresolved. In particular, it does not distinguish risk-neutral exercise probabilities from option price sensitivities, or account for the strike spacing and payoff profile that determine how prices vary across strikes. It is therefore a useful question about interpreting the BSM formula, but not a validated arbitrage rule or pricing method.

Key ideas

  • The question proposes linking adjacent option premium differences to the farther-strike option’s exercise probability.
  • It interprets N(−d2) as a put exercise probability under the BSM model.
  • The document provides no derivation or answer to establish the proposed inequality.
  • Exercise probability alone does not specify the premium difference across strikes.

Tags

OptionsDerivatives pricingArbitrage
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# Options Arbitrage


# Options Arbitrage












I have a basic question regarding the BSM formula, would be thankful for any assistance.

As far as I understand $N(d2)$ and $N(-d2)$ stand for the probability of a Call and Put respectively being exercised.

If so, isn't it the case that two adjacent same type options with the same expiry must have a difference in premiums of at least the farther strike's exercisable probability times the Multiplier of the contract?

For example:

Option Type - Put

Strike $X - N(-d2) \geq 0.4$

Strike $Y - N(-d2) \geq 0.3$

Option Multiplier - 100

In general, isn;t it the case that:

X Premium $\geq Y Premium + Y \cdot N(-d2) *$ Multiplier

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