**16**

**GENERAL PRINCIPLES OF ASSET PRICING**

*I*n this chapter, we discuss the general principles of asset pricing. Previously, we have discussed them only in special cases. Our focus here is to analyze asset pricing in a more comprehensive setup. Due to its generality, this chapter is inevitably abstract and challenging, but important for understanding the foundations of modern asset pricing theory. After extending the state-dependent contingent claims discussed in Chapter 10 to allow for an arbitrary number of states, we then introduce the economic notions of complete market, the Law of One Price, and arbitrage. Then, we provide the fundamental theorem of asset pricing that ties these concepts to asset pricing relations. Subsequently, we discuss stochastic discount factor models, providing the unified framework of asset pricing theories, including the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT) as special cases. We also explain the Hansen-Jagannathan bound on the volatility of possible stochastic discount factors and apply it to analyze the equity risk premium.

## 16.1 ONE-PERIOD FINITE STATE ECONOMY

Recall from Chapter 10 that if a security has payoffs,

it means that the economy will have two states next period, up or down, and the security will have a value of $1 or 0 in the up and down states, respectively. Similarly, as a simple extension, we can think that ...