Stochastic Processes and Financial Mathematics
(part one)

5.3 Types of financial derivative

A contract that specifies that buying/selling will occur, now or in the future, is known as a financial derivative, or simply derivative. Financial derivatives that give a choice between two options are often known simply as options.

Here we collect together the three types of financial derivatives that we have mentioned in previous sections. As before, we use the term strike price to refer to a fixed price $K$ that is agreed at time $0$ (and paid at time $1$).

• • A forward or forward contract is the obligation to buy (or sell) a single unit of stock at time $1$ for a strike price $K$.

• • A European call option is the right, but not the obligation, to buy a single unit of stock at time $1$ for a strike price $K$.

• • A European put option is the right, but not the obligation, to sell a single unit of stock at time $1$ for a strike price $K$.

You are expected to remember these definitions! We will often use them in our examples.

There are many other types of financial derivative; we’ll mention some more examples later in the course, in Section 17.2.