In my finance course, we were talking about the flaws of modelling Stock Prices with the geometric Brownian Motion. According to my professor:
"Since the geometric Brownian Motion has continous time sample path, it does not allow for jumps in its values when rare events occur"
I fail to really understand this explication for the no-jump problem. If we take a look at the log normal distribution of the prices, then there should be the small possibility of an "extreme change", resp. a very rare event occurring and therefore experiencing a jump?
If anyone has a more detailed explanation than just the quote above, I would be very thankful