This report shows how to extract the default probability from the price or yield of a bond. It is not hard to do. All you need is a little elementary probability theory and some simple logic. Armed with the market based estimate of default probability, and your own model based estimate, you can decide if a bond is a good investment.
Included in this report is:
- What kind of simple betting game is a lot like buying a zero coupon bond.
- Exact formula for default probability of zero coupon bonds.
- Simple approximation formulas for the default probability of zero coupon bonds using either discount rate or yield.
- How to numerically solve for the default probability of the more complicated case of a coupon bond.
- Formulas for the probabilities of two correlated bonds both defaulting, one or the other defaulting, or neither defaulting.
- Functions for calculating default probability given price, or price given default probability, written in Open Office Basic which should be compatible with Microsoft's Visual Basic, and usable as spreadsheet macros.
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Free with your purchase of the report, is an accompanying Open Office spreadsheet, providing an example of how to use the included functions.
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About the authors: Stefan Hollos and J. Richard Hollos are physicists by training, and have in recent years been working on problems in quantitative finance. They are the authors of Simple Trading Strategies That Work and Bet Smart: The Kelly System for Gambling and Investing, and are brothers and business partners at Exstrom Laboratories LLC in Longmont, Colorado. The website for their quantitative finance related work is QuantWolf.com. They are interested in anything related to the calculation of probabilities (odds).
Table of Contents
- Section 1 Zero Coupon Bonds
- 1.1 Formula Reference
- 1.1.1 Default probability in terms of price
- 1.1.2 Default probability in terms of discount rate
- 1.1.3 Approximate default probability in terms of discount rate
- 1.1.4 Default probability in terms of yield
- 1.1.5 Approximate default probability in terms of yield
- 1.1.6 Converting discount rate to yield
- 1.1.7 Converting yield to discount rate
- 1.2 Formula Derivations
- Section 2 Coupon Bonds
- 2.1 Formula Reference
- 2.1.1 Default probability
- 2.1.2 Initial guess for z
- 2.2 Formula Derivation
- Section 3 Correlated Bond Default
- 3.1 Formula Reference
- 3.1.1 Probability of double default
- 3.1.2 Probability of 1st bond defaulting and 2nd not defaulting
- 3.1.3 Probability of 2nd bond defaulting and 1st not defaulting
- 3.1.4 Probability of neither bond defaulting
- 3.2 Formula Derivation
- Section 4 Software
- 4.1 Program Listing
Send comments to: Stefan Hollos (stefan[AT]exstrom DOT com)
Copyright 2011 by Exstrom Laboratories LLC