QuoteOriginally posted by: CuchulainnQuoteThe most basic approach is to price an option with MC and then price it again with MC but then do it for S+h and S-h to get the delta/gamma. That's what my 5 year old son would do.Doesn't mean it's correct This approach is probably not even wrong, mathematically speaking.Hand-waving might be used but I can't see how you reconcile the fact that Wiener curve is continuous everywhere and differentiable nowhereSo the S+h and S-h would be an issue but I can be corrected by our resident stochastics experts. It's a can of worms looking for an optimal size h. Numerical Differentiation 101. Kienitz and Wetterau have a chapter on all this stuff. MC probably wasn't built for this kinds of computation?It's not about MC. It's the finite difference approximation that causes issues here.

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: barnyAs per Glasserman and what outrun says, it doesn't matter that the payoff is not differentiable at S=K since the probability is zero. But the context IMO is calculus and not probability and computing greeks at K??? Sets with measure zero are not the issue here.The discontinuity in the payoff affects the computation of delta and gamma.It's both calculus and probability in the context of calculating Greeks for a MC price. Sets with measure zero are the issue here, because it ensures us the discontinuity point of the first derivative won't give us troubles when calculating delta.For a vanilla call option, the payoff is continuous. However, the first derivative of the payoff is discontinuous, which thus affects the computation of gamma.