Taleb Modified Delta

Question

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?

Answer 1

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.