For example, consider S&P options.

My reasoning is rooted in the fact that VIX returns and S&P returns have a negative relationship, since VIX is a measure of S&P options' implied vol. Doesn't that imply that when the S&P goes down, the implied vol of S&P options is going up? So if you were to answer "what happens to the price of this option when the underlying increases 1%"... instead of just using the delta of the option, would it be intuitively more correct to then make an expected vega adjustment? If I a mistaken about something, please let me know.


  • $\begingroup$ This concept of "shadow Delta" is related to the so-called volatility "stickiness assumption" following the seminal work of Derman on volatility regimes. Maybe this related question will help: quant.stackexchange.com/questions/25244/… $\endgroup$ – Quantuple Nov 22 '18 at 8:31
  • $\begingroup$ Exactly what I was looking for... thanks! $\endgroup$ – doctorpigeonhole Nov 22 '18 at 23:31
  • $\begingroup$ Glad I could help $\endgroup$ – Quantuple Nov 23 '18 at 8:54


Two extreme models are assuming: a) ATM vol stays constant for a given moneyness (called sticky moneyness) or b) vol stays constant at fixed strikes (called sticky moneyness). A variation on a) is sticky delta. It's also possible to come up with models that are sort of a weighted average of these two extremes.

As Quantuple pointed out, work has been done by Derman to identify what the market is using; the answer is that it depends/varies over time. Googling on his name plus the terms above will get you a long way in finding more resources.


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.