This chapter now turns to nonlinear derivatives, or options. As described in the previous chapter, options account for a large part of the derivatives markets. On organized exchanges, options represent more than $50 trillion in derivatives outstanding. Over-the-counter options add up to more than $60 trillion in notional amounts.
Although the concept behind these instruments is not new, option markets have blossomed since the early 1970s, because of a breakthrough in pricing options (the Black-Scholes formula) and advances in computing power. We start with plain-vanilla options: calls and puts. These are the basic building blocks of many financial instruments. They are also more common than complicated, exotic options.
The purpose of this chapter is to present a compact overview of important concepts for options, including their pricing. We will cover option sensitivities (the “Greeks”) in a future chapter. Section 8.1 presents the payoff functions on basic options and combinations thereof. We then discuss option prices, or premiums, in Section 8.2. The Black-Scholes pricing approach is presented in Section 8.3. Next, Section 8.4 briefly summarizes more complex options. Finally, Section 8.5 shows how to value options using a numerical, binomial tree model.
8.1 OPTION PAYOFFS
8.1.1 Basic Options
Options are instruments that give their holder the right to buy or sell an asset at a specified price until a specified expiration date. The specified delivery ...