In my textbook that I am self-studying from it is given that (assuming the Black-Scholes framework):
- $\Delta_{stock} = \partial S / \partial S = 1$
- All other Greeks for the underlying stock = 0
I can see why $\Gamma_{stock} = 0$, from taking the partial derivative of $\Delta_{stock}$.
But why is there not some significance to $\theta_{stock}$ $\rho_{stock}$, $\psi_{stock}$, etc. and why are those necessarily 0?
It would seem to me that it could be useful taking the partial derivative of the stock price with respect to the risk free rate, the continuously compounded return on the stock, and the variance of the stock.