After selling a European call, we could hold 
shares of the same stock to hedge our position. This is named a delta hedge. Since the delta 
is a function of the underlying stock (S), to maintain an effective hedge we have to rebalance our holding constantly. This is called dynamic hedging. The delta of a portfolio is the weighted deltas of individual securities in the portfolio. Note that when we short a security, its weight will be negative:
Assume that a US importer will pay £10 million in three months. He or she is concerned with a potential depreciation of the US dollar against the pound. There are several ways to hedge such a risk: buy pounds now, enter a futures contract to buy £10 million in three months with a fixed exchange rate, or buy call options with a fixed exchange rate as its exercise price. The first choice is costly since the importer does not need pounds today. Entering a future contract is risky as well since an appreciation of the US dollar would cost...