Vega-Gamma relation

am looking for published, discussed information on gamma-vega reltionships as spelt out for example in Taleb's old book and how it applies in particular to stochastic volatility option pricing models? Any help greatly appreciated. I find that this relationship is very important in practical terms, but relatively little documented. Thanks, mtsm
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frenchX Senior Member Posts: 5586 Joined: Mar 2010

Thu Apr 28, 11 08:15 PM I didn't manage to find on the internet the solution but I have the path. You have to do as in this paper of Mercurio http://www.fabiomercurio.it/VegaGammaRelationship.pdf FIrst you have the pricing equation and you have the invariant transform equation (obtained by studying the symmetry of the Lie group of the pricing PDE). Equal the both PDE and you have your Gamma-Vega relation for your SV model. With that it's possible to have your Gamma-Vega relation (in a far much easier way that the conventional one of taking the closed form heston formula differentiate twice in S and compared with the closed form differentiated by volatility by eyes). Since the SV models are linear one the scale invariance of time shouldn't be very hard to obtain. That's my 2$ and I think it's feasible. By the way, it won't be a simple Vega-Gamma relation, you would have the Vanna and the Vomma implicated I think (In the BS world it works well due the lognormal density). Carol Alexander has done some work about scale invariance properties.