Excerpt from book - This chapter introduces the basic ideas in a finite-state one-period setting. In many basic senses, each subsequent chapter merely repeats this one from a new perspective. The objective is a characterization of security prices in terms of “state prices,” one for each state of the ... click here for more details.
Excerpt from book - This chapter extends the results of Chapter 1 on arbitrage, optimality, and equilibrium to a multiperiod setting. A connection is drawn between state prices and martingales for the purpose of representing security prices. The exercises include the consumption-based capital asset pricing model and the multiperiod “binomial” ... click here for more details.
Excerpt from book - This chapter presents portfolio choice and asset pricing in the framework of dynamic programming, a technique for solving dynamic optimization problems with a recursive structure. The asset pricing implications go little beyond those of the previous chapter, but there are computational advantages. After introducing the idea ... click here for more details.
Excerpt from book - This chapter presents infinite-period analogues of the results of Chapters 2 and 3. Although this setting requires additional technicalities and produces few new insights, it sometimes simplifies results and it serves the large-sample theory of econometrics, which calls for an unbounded number of observations. We start ... click here for more details.
Excerpt from book - This chapter presents the basic Black-Scholes model of arbitrage pricing in continuous time, as well as extensions to a nonparametric multivariate Markov setting. We first introduce the Brownian model of uncertainty and continuous security trading, and then derive partial differential equations for the arbitrage-free prices of ... click here for more details.
Excerpt from book - This chapter summarizes arbitrage-free security pricing theory in the continuous-time setting introduced in Chapter 5. The main idea is the equivalence between no arbitrage, the existence of state prices, and the existence of an equivalent martingale measure, paralleling the discrete-state theory of Chapter 2. This extends ... click here for more details.
Excerpt from book - This chapter reviews models of the term structure of interest rates that are used for the pricing and hedging of fixed-income securities, those whose future payoffs are contingent on future interest rates. Term structure modeling is one of the most active and sophisticated areas of application ... click here for more details.
Excerpt from book - This chapter applies arbitrage-free pricing techniques from Chapters 6 and 7 to derivative securities that are not always easily treated by the direct PDE approach of Chapter 5. A derivative security is one whose cash flows are contingent on the prices of other securities, or on ... click here for more details.
Excerpt from book - This chapter presents basic results on optimal portfolio and consumption choice, first using dynamic programming, then using general martingale and utility-gradient methods. We begin with a review of the Hamilton-Jacobi-Bellman equation for stochastic control, and then apply it to Merton’s problem of optimal consumption and portfolio ... click here for more details.
Excerpt from book - This chapter reviews security market equilibrium in a continuous-time setting and derives several implications for security prices and expected returns. These include Breeden’s consumption-based capital asset pricing model (in both complete- and incomplete-market settings) as well as the Cox-Ingersoll-Ross model of the term structure.