Modeling Fixed Income Securities and Interest Rate Options

385 Pages·2019·7.897 MB·English

by  Jarrow, Robert A.

Modeling Fixed Income
Securities and Interest Rate
Options
Third Edition
CHAPMAN & HALL/CRC
Financial Mathematics Series
Series Editors
M.A.H. Dempster
Centre for Financial Research
Department of Pure Mathematics and Statistics
University of Cambridge
Dilip B. Madan
Robert H. Smith School of Business
University of Maryland
Rama Cont
Department of Mathematics
Imperial College
Aims and scope:
The field of financial mathematics forms an ever-expanding slice of the financial sector. This
series aims to capture new developments and summarize what is known over the whole spec-
trum of this field. It will include a broad range of textbooks, reference works and handbooks
that are meant to appeal to both academics and practitioners. The inclusion of numerical
code and concrete real-world examples is highly encouraged.
Equity-Linked Life Insurance
Partial Hedging Methods
Alexander Melnikov, Amir Nosrati
High-Performance Computing in Finance
Problems, Methods, and Solutions
M. A. H. Dempster, Juho Kanniainen, John Keane, Erik Vynckier
An Introduction to Computational Risk Management of Equity-Linked Insurance
Runhuan Feng
Derivative Pricing
A Problem-Based Primer
Ambrose Lo
Portfolio Rebalancing
Edward E. Qian
Interest Rate Modeling
Theory and Practice, 2nd Edition
Lixin Wu
Metamodeling for Variable Annuities
Guojun Gan and Emiliano A. Valdez
Modeling Fixed Income Securities and Interest Rate Options
Robert A. Jarrow
For more information about this series please visit: https://www.crcpress.com/Chapman-and-
HallCRC-Financial-Mathematics-Series/book-series/CHFINANCMTH
Modeling Fixed Income
Securities and Interest Rate
Options
Third Edition
Robert A. Jarrow
CRC Press
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This book is dedicated to my wife Gail.

Contents
Preface to the Third Edition, xv
Section i Introduction
chapter 1 ◾ Introduction 3
1.1 THE APPROACH 3
1.2 MOTIVATION 4
1.3 THE METHODOLOGY 8
1.4 AN OVERVIEW 10
REFERENCES 12
chapter 2 ◾ Traded Securities 13
2.1 TREASURY SECURITIES 13
2.2 TREASURY SECURITY MARKETS 15
2.3 REPO MARKETS 17
2.4 TREASURY FUTURES MARKETS 18
2.5 INTEREST RATE DERIVATIVES ON TREASURIES 19
2.6 EURODOLLAR SPOT, FORWARD, AND FUTURES
MARKETS 20
2.7 INTEREST RATE DERIVATIVES ON LIBOR 21
REFERENCES 21
chapter 3 ◾ The Classical Approach 23
3.1 MOTIVATION 23
3.2 COUPON BONDS 23
vii
viii ◾ Contents
3.3 THE BOND’S YIELD, DURATION, MODIFIED
DURATION, AND CONVEXITY 26
3.4 RISK MANAGEMENT 33
REFERENCE 38
Section ii Theory
chapter 4 ◾ The Term Structure of Interest Rates 41
4.1 THE ECONOMY 42
4.2 THE TRADED SECURITIES 42
4.3 INTEREST RATES 44
4.4 FORWARD PRICES 48
4.5 FUTURES PRICES 50
4.6 OPTION CONTRACTS 52
4.6.1 Definitions 53
4.6.2 Payoff Diagrams 53
4.7 SUMMARY 56
REFERENCES 56
chapter 5 ◾ The Evolution of the Term Structure of
Interest Rates 57
5.1 MOTIVATION 57
5.2 THE ONE-FACTOR ECONOMY 61
5.2.1 The State Space Process 62
5.2.2 The Bond Price Process 65
5.2.3 The Forward Rate Process 72
5.2.4 The Spot Rate Process 78
5.3 THE TWO-FACTOR ECONOMY 80
5.3.1 The State Space Process 80
5.3.2 The Bond Price Process 81
5.3.3 The Forward Rate Process 82
5.3.4 The Spot Rate Process 83
5.4 N ≥ 3-FACTOR ECONOMIES 83
Contents   ◾   ix
5.5 CONSISTENCY WITH EQUILIBRIUM 83
REFERENCES 84
chapter 6 ◾ The Expectations Hypothesis 85
6.1 MOTIVATION 85
6.2 PRESENT VALUE FORM 86
6.3 UNBIASED FORWARD RATE FORM 90
6.4 RELATION BETWEEN THE TWO VERSIONS OF THE
EXPECTATIONS HYPOTHESIS 94
6.5 EMPIRICAL ILLUSTRATION 95
6.5.1 Present Value Form 96
6.5.2 Unbiased Forward Rate Form 97
REFERENCES 98
chapter 7 ◾ Trading Strategies, Arbitrage Opportunities,
and Complete Markets 99
7.1 MOTIVATION 99
7.2 TRADING STRATEGIES 100
7.3 ARBITRAGE OPPORTUNITIES 110
7.4 COMPLETE MARKETS 114
chapter 8 ◾ Bond Trading Strategies – An Example 121
8.1 MOTIVATION 121
8.2 METHOD 1: SYNTHETIC CONSTRUCTION 122
8.2.1 An Arbitrage-Free Evolution 123
8.2.2 Complete Markets 124
8.3 METHOD 2: RISK-NEUTRAL VALUATION 130
8.3.1 Risk-Neutral Probabilities 130
8.3.2 Risk-Neutral Valuation 133
8.3.3 Exploiting an Arbitrage Opportunity 134
chapter 9 ◾ Bond Trading Strategies – The Theory 137
9.1 THE ONE-FACTOR ECONOMY 137
9.1.1 Complete Markets 138