# Dynamic Asset Pricing Theory

By Darrell Duffie | Go to book overview

7
Term-Structure Models

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. Termstructure modeling is one of the most active and sophisticated areas of application of financial theory to everyday business problems, ranging from managing the risk of a bond portfolio to the design and pricing of collateralized mortgage obligations.

Included in this chapter are such standard examples as the Merton, Ho-Lee, Dothan, Brennan-Schwartz, Vasicek, Black-Derman-Toy, BlackKarasinski, and Cox-Ingersoll-Ross models, and variations of these “singlefactor” term-structure models, so named because they treat the entire term structure of interest rates at any time as a function of a single state variable, the short rate of interest. We will also review multifactor models, including multifactor affine models, extending the Cox-Ingersoll-Ross and Vasicek models.

All of the named single-factor and multifactor models can be viewed in terms of marginal forward rates rather than directly in terms of interest rates, within the Heath-Jarrow-Morton (HJM) term-structure framework. The HJM framework allows, under technical conditions, any initial term structure of forward interest rates and any process for the conditional volatilities and correlations of these forward rates.

Numerical tractability is essential for practical applications. The “calibration” of model parameters and the pricing of term-structure derivatives are typically done by such numerical methods as “binomial trees” (Chapter 3), Fourier transform methods (Chapter 8), Monte Carlo simulation (Chapter 12), and finite-difference solution of PDEs (Chapter 12).

This chapter makes little direct use of the pricing theory developed in Chapter 6 beyond the basic idea of an equivalent martingale measure,

-135-

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes

#### Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited page

Dynamic Asset Pricing Theory

• 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
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this book
• Bookmarks
• Highlights & Notes
• Citations
/ 465

### How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

## Cited passage

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.