As titled, I am having trouble estimating the VaR of a portfolio mapped as a function of a single risk factor $S$, in the form :
$$V(S) = S^3 - 30S^2 + 300S + 150$$
with current value $S = 10$.
$S$ is supposed to be normally distributed, with mean $\mu = 10$ and annual volatility $\sigma= 0.3$.
I found that both delta and gamma evaluated at $S = 10$ are zero, then clearly I cannot implement any of Delta-Gamma method or Delta-Gamma-Delta method.
Are these methods not applicable on non-monotonic function?
Then what kinds of other practical methods can I use to estimate the portfolio VaR?
Can someone please briefly explain, please?