So looking at the revision notes the vega is said to be zero for the share price St. But why is this true for a when a share price is modelled by a geometric Brownian motion - it is dependent on the volatility sigma?
The Greeks are defined as partial derivatives, which are only defined under a certain set of parameters. Partial derivatives keep all other parameters constant, since St is one of those parameters then its partial derivative under any other parameter than itself is zero.
