I'm using Montecarlo to estimate the value of an option,

$$\overline V(S_T, r, \sigma, T;N)=\mathbb{E} \left[V(S_T, r, \sigma, T)\right]$$ which comes with a standard error $SE$.

I'm using "bump-and-reval" (finite differences) to compute the greeks. So for example for Delta:

$$ \Delta \approx \frac{\overline V(S_T+\Delta S, r, \sigma, T;N)-\overline V(S_T-\Delta S, r, \sigma, T;N)}{2\Delta S} $$

my question is, what's the right way to combine the standard errors to get the right one for $\Delta$?

What about for a second order greek, like Gamma:

$$ \Gamma \approx \frac{\overline V(S_T+\Delta S, r, \sigma, T;N)-2\overline V(S_T, r, \sigma, T;N)+\overline V(S_T-\Delta S, r, \sigma, T;N)}{(\Delta S)^2} $$



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