Fixed Income Finance: A Quantitative Approach

by Wise, Mark; Bhansali, Vineer

• ISBN13: 9780071621205
• ISBN10: 0071621202
• Edition: 1st
• Format: Hardcover
• Copyright: 2010-01-13
• Publisher: McGraw-Hill Education

Summary

The fundamentals of finance for advancedmathematical mindsWritten by authors at the top of their respective fields,Fixed Income Financeis a thorough introduction to theconcepts, formulas, methodologies, and applicationsthat are critical to pursuing a career in fixed incomefinance and beyond. Bridging the gap between basicintroductory guides and advanced tomes, it providesfinancial engineers who already have strong mathematicalbackgrounds and analytical skills with a hands-on,quantitative guide to the basic concepts and tools theyneed to apply their knowledge in a financial context.

Author Biography

Mark Wise is the John A. McCone professor.of high-energy physics at the California Institute of.Technology..Vineer Bhansali is a senior member.of PIMCOn++s portfolio management group.

Table of Contents

Preface	p. vii
Bond Basics	p. 1
Treasury Bonds and the Yield Curve	p. 1
Duration and Convexity	p. 6
Corporate Bonds and Credit Risk	p. 8
Stocks	p. 14
Arbitrage Opportunities	p. 15
Derivatives	p. 17
Mortgages	p. 20
Municipal Bonds	p. 28
Real Bonds	p. 31
Convertible Bonds	p. 33
CDOs and Tranches	p. 33
The Mathematics of Financial Modeling	p. 35
Normal Random Variables	p. 35
The Central Limit Theorem	p. 39
The Probability Distribution for Corporate Bond Returns	p. 41
Correlated Random Variables	p. 44
Random Walks	p. 52
Survival Probabilities	p. 59
Lognormal Variables	p. 63
Mean-Reverting Random Walks	p. 63
Correlated Random Walks	p. 65
Simulation	p. 67
Appendix 1: Gaussian Integrals	p. 72
Appendix 2: Dirac Delta Function	p. 74
Structural Models	p. 77
Risk-Neutral Pricing of European Stock Options	p. 77
Arbitrage Argument for the Pricing of Stock Options	p. 83
A Structural Model Relating Equity and Debt	p. 91
Risk-Neutral Default Probabilities	p. 103
The Risk Premium	p. 108
Including Dividends	p. 110
Bond Portfolio Management	p. 115
Investor Preferences and Utility Functions	p. 115
Mean-Variance Portfolio Allocation	p. 120
Beyond Mean-Variance Portfolio Allocation	p. 121
Three Exactly Solvable Portfolio Allocation Problems	p. 126
Portfolio Allocation to a CDO	p. 136
Portfolio Allocation with Many Risky Assets	p. 142
The Efficient Frontier	p. 145
Value at Risk	p. 150
Fixed-Income Risk Factors and Hedging	p. 156
Term Structure Models	p. 163
The Yield Curve	p. 163
One- and Two-Factor Vasicek Models for the Yield Curve	p. 165
Spot Yield Volatility	p. 175
The Taylor Rule	p. 176
A Macroeconomic Two-Factor Model	p. 182
Relationship between the Macroeconomic and Vasicek Models	p. 184
Another Two-Factor Model	p. 188
Models with Explicit Time Dependence	p. 196
Derivatives of Bonds	p. 199
Eurodollar Futures Rates and Volatilities	p. 199
Future and Forward Contracts	p. 201
European Options on a Zero Coupon Bond	p. 203
Interest-Rate Swaps	p. 208
Interest-Rate Caps	p. 210
Trees	p. 213
Basics	p. 213
Binomial Trees and Stock Options	p. 218
The Black-Derman-Toy Model for Interest Rates	p. 223
A Heath-Jarrow-Morton Model on a Recursive Tree	p. 233
Appendix: Discussion of HJM Code	p. 239
Index	p. 243
Table of Contents provided by Ingram. All Rights Reserved.