Given the same undelying, the same strike and them term to maturity, are the Greeks (esp. delta) for a European option pretty close to the ones for an American option? Any intuitions behind this?

Yes, ther are generaly very similar. There are probably interesting (and quite possibly unrealistic) exceptions, but seeing as it is common to use european options values as control variates for american lattice estimates, it seems consistent that the greeks would be similar. Also, risk management people learned some time ago that you don't have to be super precise about pricing to do good risk management, the idea here being that small pricing errors cancel out when investigating differences in value. Greeks are of course small differences, so this too seems to confirm the validity of your observation. If you were thinking about whether you could substitute euro greeks for american greeks in risk management, I'd say yes go ahead, at least for vanilla products.

for vanilla options, since a american option is essentially a european one + the right to exercize early, greeks should be roughly identical except when close to early exercize conditions...

QuoteOriginally posted by: zrjfor vanilla options, since a american option is essentially a european one + the right to exercize early, greeks should be roughly identical except when close to early exercize conditions...In general sense, what are early exercise conditions for American option?