How Option Premium Sensitivity to Strike Differs from One-for-One

Summary

The document explains why increasing an option’s strike by one unit does not necessarily increase its premium by the same amount. It notes that displayed option quotes may come from different times, so apparent price and implied-volatility comparisons can be misleading. The accepted answer gives an extreme example: if the underlying has no chance of finishing below either put strike, both puts would be worth zero despite the strike difference.

For a put under the stated model, the sensitivity of price to strike is expressed as a discounted probability term, which is below one. This helps explain why premium changes can be smaller than strike changes. The discussion is brief and does not develop the model assumptions, derive the sensitivity formula, or assess how other market factors affect quoted premiums. It offers a basic pricing intuition rather than a complete method for comparing options.

Key ideas

• Option premiums do not generally change one-for-one with strike prices.
• Unsynchronized quotes can make comparisons between option premiums unreliable.
• If both puts have zero probability of finishing in the money, both can be worth zero despite different strikes.
• The stated put price sensitivity to strike is below one under the model described.

Tags

# Oughtn't option premiums increase by the same amount as strike prices?


# Oughtn't option premiums increase by the same amount as strike prices?












- Pls see this question's title. In the screenshot below, as the strike prices below increase by +1, oughtn't the option premiums increase by +1 too?

- Why buy the \$104 put for \$13.71? The \$105 put looks more attractive to me; it has lower IV and costs only 4 cents more!

## Answer by Ivan (score 1, accepted)

https://quant.stackexchange.com/a/51636

These quotes may not be synchronised. Also if the probability of being below either strike is zero, then why would the price change, both options will be worth zero ? Just an extreme example that shows why not. The sensitivity of the price wrt strike is $N(d_0)e^{-rT}<1$.

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