Dynamic Asset Pricing Theory

By Darrell Duffie | Go to book overview

11
Corporate Securities

THIS CHAPTER OFFERS a basic review of the valuation of equities and corporate liabilities, beginning with some standard issues regarding the capital structure of a firm. Then, we turn to models of the valuation of defaultable debt that are based on an assumed stochastic arrival intensity of the stopping time defining default. The work presented in this chapter is widely extended in work cited in the Notes.

We begin in the first few sections with an extremely simple model of the stochastic behavior of the market values of assets, equity, and debt. We may think of equity and debt, at this first pass, as derivatives with respect to the total market value of the firm, and priced accordingly. Later, we introduce market imperfections and increase the degree of control that may be exercised by holders of equity and debt. With this, the theory becomes more complex and less like a derivative valuation model. There are many more interesting variations than could be addressed well in the space available here. Our objective is merely to convey some sense of the types of issues and standard modeling approaches.

We let B be a standard Brownian motion in Rd on a complete probability space (Ω, F, P), and fix the standard filtration {Ft : t ≥ 0} of B. Later, we allow for information revealed by “Poisson-like arrivals,” a significant departure from our usual case of Brownian information.


A. The Black-Scholes-Merton Model

For a simple start, we outline the classic Black-Scholes-Merton model of corporate debt and equity valuation. We suppose that the firm’s future cash flows have a total market value at time t given by At, where A is a

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Dynamic Asset Pricing Theory
Table of contents

Table of contents

  • Title Page iii
  • Contents vii
  • Preface xiii
  • I - Discrete-Time Models 1
  • 1 - Introduction to State Pricing 3
  • 2 - The Basic Multiperiod Model 21
  • 3 - The Dynamic Programming Approach 49
  • 4 - The Infinite-Horizon Setting 65
  • II - Continuous-Time Models 81
  • 5 - The Black-Scholes Model 83
  • 6 - State Prices and Equivalent Martingale Measures 101
  • 7 - Term-Structure Models 135
  • 8 - Derivative Pricing 167
  • 9 - Portfolio and Consumption Choice 203
  • 10 - Equilibrium 235
  • 11 - Corporate Securities 259
  • 12 - Numerical Methods 293
  • Appendixes 321
  • Bibliography 373
  • Symbol Glossary 445
  • Author Index 447
  • Subject Index 457
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