The Greeks: Delta, Gamma, and Theta Intuition

You own a European call option on a stock at $S = 100$ with strike $K = 100$, 30 days to expiry, $\sigma = 20\%$, and $r = 5\%$. (a) The delta is $\Delta = 0.54$. Explain what this means. If the stock goes to 101, approximately what happens to the call price? (b) The gamma is $\Gamma = 0.035$. If the stock moves to 105, what is the new approximate delta? Why does this matter for hedging? (c) The theta is $\Theta = -0.05$ (per day). You hold the option over a weekend (3 days, no trading). How much value do you lose? How does gamma relate to theta?