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At the risk of sounding dumb, I must ask help for solving my doubt:The half-Gamma in the BS is multiplied by (sigma S)^2In the literature I often encounter this approximation: (dS)^2 ~ (sigma S)^2which I cannot completely understand as it seems it's missing dt.In fact, from the BM: dS = u S dt + sigma S dW ==> (dS)^2 ~ (sigma S)^2 dt Z^2where Z ~ N(0,1) ==> E[Z^2] = 1Therefore, (very) loosly speaking: (dS)^2 / dt ~ (sigma S)^2But I never see that dt in the approximation. What am I doing wrong here?Thanks for helping...

Actually, I finally got it. Being dt the time period for dS, then:Annualized: (dS)^2 / dt ~ (sigma S)^2Period-based: (dS)^2 ~ (sigma S)^2 dt