This chapter introduces the fundamentals of security pricing. It begins with a discussion on utility theory and risk and introduces the stochastic discount factor, or pricing kernel, as the fundamental determinant of all security prices. Some basic applications are introduced as examples and to help develop martingale pricing principles. This is initially accomplished in a discrete-time setting and then taken to continuous time. The stochastic discount factor and martingale pricing are subsequently used to develop various option-pricing results. Throughout the chapter, every effort is made to relate the mathematics of pricing to the underlying economic concepts.

UNCERTAINTY, UTILITY THEORY, AND RISK

One of the most important concepts in finance is that of risk. The fact that there is so much risk in the world is what makes finance a very complicated subject. As we will see later, the existence of financial markets and institutions can be explained by the need to control risk in our lives. Therefore, before we can dive into the theory of finance, we must first understand what risk is and how it affects us. The mathematical characterization of risk is one of the main goals of economic theory and the building block of modern finance theory. In this section, we will present the basics of this theory.

Generally, when thinking of risk, we think of an uncertain factor affecting our “happiness” in a negative manner. For example, a homeowner may be very concerned about the risk of fire destroying his home.