# Tag Info

Pathwise finite difference Gamma formula is indeed: $$\Gamma(S_0,T, dS; Z) = (dS)^{-2} \left[ (S_T^{up} (Z) - K)^+ -2 (S_T (Z) - K)^+ + (S_T^{dn} (Z) - K)^+ \right],$$ where $Z$ is a standard normal rv, and $$S_T (Z) = S_0\eta (Z),$$ $$S_T^{up} (Z) = (S_0+dS)\eta(Z) = (S_0+dS)S_0^{-1} S_T (Z)$$  S_T^{dn} (Z) = (S_0-dS)\eta(Z) = (S_0-dS)S_0^{-1} S_T (...