# What is the relationship between Vanna and Gamma?

I'm trying to build a crude model for the effects of delta hedging on major indices like the S&P 500. My background is more in pure mathematics so a lot of this stuff is new to me. That said I would like to know if there is a function $$f$$ such that $$vanna=f(gamma)$$, where these greeks are from the black-scholes equation. I would also appreciate it if someone pointed me to some good research papers that cover equity index gamma and vanna modeling. Thanks in advance.

• Are you looking for anything specific in regards to research papers that cover equity index gamma and vanna modeling?
– user34971
Apr 12, 2021 at 5:20
• I'll take what I can get but I'm especially interested in how gamma and vanna play off of each other. I.e. gamma increases which suppresses volatility or volatility increases which reduces gamma Apr 12, 2021 at 5:29