I've searched all over the internet, but have not found the answer to this question.
When we 'delta-hedge', we make the value of a portfolio 0. Now, we know that an approximation of the change in a portfolios value is given by
THETA * dt + 0.5*GAMMA*S^2
where THETA and GAMMA are the greeks of the portfolio.
Now, here's my problem: everybody knows how to calculate the greeks of a derivative. Just differentiate with respect to some variable.
But, what is the derivative of a portfolio? Because that up there is a portfolio, not a derivative.
For simplicity, we might imagine a portfolio that has holdings in .... a call .... a stock .... and a bank account (to borrow and lend money).
What are the Gamma, Delta, Theta, Vega of such a portfolio?