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I understand that it is the partial derivative of option price with respect to strike. What is it used for though? What does your dual delta signify?

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Dual Delta is the derivative of option value with respect to the strike: $\frac{\partial C}{\partial K}$. The ordinary Delta is of course $\frac{\partial C}{\partial S}$.

In the BSM framework Dual Delta evaluates to $\frac{\partial C}{\partial K}=-e^{-r T} N(d_2)$, it is therefore closely related to the pseudo probability of exercise $N(d_2)$. In fact it is minus the price of an Arrow Debreu security that pays 1 USD at time T if the Call is in the money and 0 otherwise.

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    $\begingroup$ probably derivative of Call by Strike K will be -e^(-rT) N(d_2). Cause when strike is increasing, the price of vanilla Call is decreasing. And I think yes, pseudo probability of exercise is N(d_2), it's correct $\endgroup$
    – Mike
    Jul 24, 2021 at 21:22
  • $\begingroup$ You are correct, I left out a minus sign en.wikipedia.org/wiki/… Thanks for noticing this. $\endgroup$
    – nbbo2
    Jul 24, 2021 at 21:30
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Dual Delta, dual Gamma and dual DdelV can be used to calculate the "local volatility" that is induced by a given volatility surface for example (the local volatility can be seen as the instantaneous volatility that the underlying would have at a given price and a given time).

See e.g. https://en.wikipedia.org/wiki/Local_volatility

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