After selling a European call, we could hold shares of the same stock to hedge our position. This is named delta hedge. Since 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 pounds in three months. He or she is concerned with a potential depreciation of the US dollar against the UK pound. There are several ways to hedge such a risk: buy pounds now, enter a futures contract to buy 10 million pounds 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 UK pounds today. Entering a future contract is risky as well, since an appreciation of the US...