New answers tagged greeks
1
I assume you work in the Black Scholes framework. Then,
\begin{align*}
P(S_0,K,T) = Ke^{-rT}\Phi(-d_2)-S_0\Phi(-d_1),
\end{align*}
where
\begin{align*}
d_1 &= \frac{\ln\left(\frac{S_0}{K}\right)+\left(r+\frac{1}{2}\sigma^2\right)T}{\sigma\sqrt{T}}, \\
d_2 &= \frac{\ln\left(\frac{S_0}{K}\right)+\left(r-\frac{1}{2}\sigma^2\right)T}{\sigma\sqrt{T}}= ...
3
overall gamma is second derivative of whole portfolio over underlying.
adding any function (such as underlying*constant) which second derivative is 0 does not alter overall second derivative.
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