The formula of $Gamma = (Vplus + Vminus - 2V0)/(V0 * dS^2)$, where
- $V$ is the contract value,
- $S$ is the stock price.
We also know that $Gamma = (Dplus-Dminus)/(Splus-Sminus)$, where
- $D$ is the contract Delta,
- $Splus = S0 + dS$,
- $Sminus = S0 - dS$,
- $Dplus = (Vplus - V0)/(V0 * dS)$,
- $Dminus = (V0 - Vminus)/(V0 * dS)$.
Substituting $Dplus$, $Dminus$, and replacing $Splus-Sminus$ with $2dS$ we get:
$(Vplus + Vminus - 2V0)/(V0 * dS)/2dS = (Vplus + Vminus - 2V0)/(V0 * 2 * dS^2)$
I must be doing something wrong, because 1/2 is not present in the book formula.
Could you, please, help me with the derivation?