How does one go about calculating the modified delta as proposed by Taleb in his book Dynamic hedging?

In his book he says its a change in the call price divided by a change in the underlying and provides the following example:

"If the call price picks up 0.05 points when the underlying asset moves from 100 to 100.1 then its delta will be 0.05/10 = 0.5."

How does he pick the price to change it at? Does he use the Black Scholes formula to calculate the the resulting option value when we change the price?


What you (and he?) describe is the numerical derivative. The delta of an option is the infinitesimal change in value when the stock moves (infinitesimally) - thus $$ \Delta = \frac{dO}{dS}. $$ If you approximate this quantity be finite differences then you get $$ \Delta \approx \frac{O(S+\Delta S)-O(S)}{\Delta S}, $$ where $\Delta S$ is a change in the stock price (10 poins in your case). These numerical approaches are applied with duration too - there this is called effective duration.


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