Estimating delta and gamma without a formula

An option has no closed-form price and you value it numerically. How would you estimate its delta and gamma?

Use finite differences on the pricer with common random numbers, or pathwise and likelihood-ratio estimators. Central differences give $\Delta\approx\frac{V(S+h)-V(S-h)}{2h}$ and $\Gamma\approx\frac{V(S+h)-2V(S)+V(S-h)}{h^2}$; reuse the same random draws for each bump so the noise largely cancels. In a tree or PDE grid, read them off neighbouring nodes. Pathwise derivatives work for smooth payoffs; likelihood-ratio weights handle discontinuous ones.