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Why is Vega for a share price 0???

R

Raj_121

Member
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.
 
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