I have two quasi definitions or interpretations of gamma risk in the context of the BSM model (please correct me if these don't make sense):
1) it is the option's sensitivity to jumps in the underlying
2) it is the option's sensitivity to realized volatility in the underlying
What I don't quite understand is this idea of "jump risk" in (1). What is jump risk? Or what is the source of jump risk in reality?
In addition, how is this risk any different to vega risk? I would have thought movements in implied vols would also incorporate the risk of jumps, in which case, why are vega and gamma seen as separate risks?
Thanks for the help on this