# Tag Info

Let $$\ln\left(S_T/S_t\right)$$ have mean $\mu_\tau$ and standard deviation $\sigma_\tau$, where $\tau=T-t$, and density of its standardized form $$X= \frac{\ln(S_T/S_t)-\mu_\tau}{\sigma_\tau}$$ approximated by Gram-Charlier expansion $$f_X(x) = \phi(x) - \gamma_{1\tau} \frac{1}{3!} D^3 \phi(x) + \gamma_{2\tau} \frac{1}{4!} D^4 \phi(x),$$ with $\phi$ ...