Credit Risk: Pricing, Measurement, and Management

By David Lando | Go to book overview

Appendix A
Discrete-Time Implementation

Most of the explicit pricing formulas presented in this book are centered around computations related to Brownian motion and to affine processes. In many practical situations these solutions are not sufficient since securities and derivatives may have American features or complicated payoff structures which preclude explicit pricing formulas. Examples of this include the pricing of risky coupon debt with compound option features due to asset-sale restrictions and swap pricing with two-sided default risk, which we met in Chapter 7. A quick way to obtain numerical solutions is through discrete-time tree models for security prices. This section gives an overview of how this is solved conceptually for our two main cases. For the explicit implementation the reader will have to consult the cited references. The goal of this section is to convey the basic idea behind building discrete-time arbitrage-free models for bond prices.


A.1 The Discrete-Time, Finite-State-Space Model

We have given a probability space (Ω, F, P) with finite. Assume that there are T + 1 dates, starting at date 0. A security is defined in terms of two stochastic process—an ex-dividend price process S and a dividend process δ—with the following interpretation: St (ω) is the price of buying the security at time t if the state is ω. Buying the security at time t ensures the buyer (and obligates the seller to deliver) the remaining dividends δt+1(ω), δt+2(ω), …, δT(ω). We will follow the tradition of probability theory and almost always suppress the ω in the notation below. Of course, a buyer can sell the security at a later date, thereby transferring the right to future dividends to the new owner. Since there are no dividends after the final date T we should think of ST as 0 and δT as a final liquidating dividend if the security is still traded at this point.

In all models considered in this appendix (and in almost every model encountered in practice), we will assume that the model contains a money-market account which provides locally riskless borrowing and lending. The interest rate on this account is defined through the spot rate process:

-251-

Notes for this page

Add a new note
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

Items saved from this book

This book has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this book

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

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.

Cited page

Bookmark this page
Credit Risk: Pricing, Measurement, and Management
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

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

Full screen
/ 310

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, 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."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.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

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.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.