Can somebody prove that:
E[S2t×Γ(t,St)]=S20×Γ(0,S0)
where St follows a lognormal process as in the Black-Scholes model, and Gamma is the second derivative ∂2C/∂S2 of the option price with respect to S.
I can see it is true using simulation, but I can't prove it. It seems to be true for the Vega as well.
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