The presence of skew causes a correlation between volatility and spot. This correlation produces a negative shadow delta for all forward starting products (forward starting options have a theoretical delta of zero).

How does this produce a negative shadow delta? The exact mechanism is not clear to me.


Basically, the author is saying that the delta of an option,

$dC/dS = \frac{\partial C}{\partial S} + \frac{\partial C}{\partial v}\frac{\partial v}{\partial S}$,

where the $\frac{\partial C}{\partial S}$ is the delta assuming constant volatility, the $\frac{\partial C}{\partial v}$ is the vega of the option, and the $\frac{\partial v}{\partial S}$ describes how the implied volatility of the option moves as the spot price moves. This second term is the "shadow delta" being referred to.

  • $\begingroup$ The use of a total derivative was what I was missing here $\endgroup$ – Permian Feb 19 '17 at 17:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.