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.
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$\begingroup$ Are you looking for anything specific in regards to research papers that cover equity index gamma and vanna modeling? $\endgroup$– user34971Apr 12, 2021 at 5:20
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$\begingroup$ 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 $\endgroup$– Literally an OrangeApr 12, 2021 at 5:29
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$\begingroup$ You should rather write the standard infinitesimal P&L of a delta-hedged option in a model where the volatility is stochastic and and develop that P&L at correct order (usually at order 2 in $\delta S$ and order 1 in $\delta V$) to make the vanna (and the gamma) appear and then look for breakevens. $\endgroup$– OlórinDec 19, 2022 at 9:59
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