Black–Scholes Dual Delta and Strike Sensitivity

Summary

The document introduces the Black–Scholes derivative of an option’s value with respect to its strike, often called dual delta. It gives the call and put formula and asks how to interpret the measure in practice when an option’s strike is fixed during the contract’s life.

The text frames a useful distinction: sensitivity to strike can describe how option values vary across strikes, even though an individual contract does not change its strike. It mentions a possible connection to local volatility but does not explain how to use dual delta for that purpose. Because the source is an unanswered question, it provides no worked application, empirical evidence, or caveats beyond the fixed-strike concern.

Key ideas

• Dual delta measures how Black–Scholes option value changes as the strike varies.
• The document gives the formula for calls and puts.
• A fixed strike raises the question of how strike sensitivity is useful in practice.
• The source mentions local volatility as a possible application but does not develop it.

Tags

# Practical use of Dual Delta?


# Practical use of Dual Delta?












I am wondering what the practical use of the Black-Scholes Dual-Delta is?

I know it is the first derivative wrt the strike price:

$$ \frac{\partial V}{\partial K} = -\omega e^{-r T} \Phi(\omega d_2) $$

where $\omega = +1$ for a call and $\omega = -1$ for a put.

But I don't have any intuition of the practical use, since the strike is fixed over the life of an option contract.

There are some questions here and here, but a practical use does not seem to be given. One answer suggests that it is used to compute local volatility, but I do not know how this would be done.

Thanks in advance !

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