What is the link between option Greeks (i.e. vega, delta, gamma, theta) and implied volatility surface (IVS) movements? Could you say that their 'information content' is the same. i.e. that out of movements of the one you could derive the movements of the other at the same point in time?
Some Background to why I am asking this question:
I have two sets of data from Optionmetrics:
- An interpolated IVS (of the SPY) as constant point of time to maturity (30,60,..180 days) and constant points of Delta
- Option greeks data (vega, delta, gamma, theta) for an option that is modeled to be perpetually at the money and at 30 days of expiration.
Regression these sets on each other, and also using principal components techniques reveals that both sets of data are essentially the same 'information' (or you could say they have the same variation).
My question is whether is due to the manner in which Optiometrics handles/interpolates the data or that this is something structural and founded in theory. That why I ask the above - I would like to know whether to what extent theoretically this similarity is also the case.