Philippe Jorion - Financial Risk Manager - Trading Software

733 Pages·2004·2.69 MB·English

by  Jorion, Philippe

Financial Risk Manager
Handbook
Second Edition
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Financial Risk Manager
Handbook
Second Edition
Philippe Jorion
GARP
Wiley
John Wiley & Sons, Inc.
Copyright (cid:1) 2003 by Philippe Jorion, except for FRM sample questions, which are
copyright 1997–2001 by GARP. The FRM designation is a GARP trademark. All rights
reserved.
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Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data:
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10 9 8 7 6 5 4 3 2 1
About the Author
Philippe Jorion is Professor of Finance at the Graduate School of Management at the
University of California at Irvine. He has also taught at Columbia University, North-
westernUniversity,theUniversityofChicago,andtheUniversityofBritishColumbia.
He holds an M.B.A. and a Ph.D. from the University of Chicago and a degree in engi-
neering from the University of Brussels.
Dr. Jorion has authored more than seventy publications directed to academics
and practitioners on the topics of risk management and international finance. Dr.
Jorion has written a number of books, including Big Bets Gone Bad: Derivatives and
BankruptcyinOrangeCounty,thefirstaccountofthelargestmunicipalfailureinU.S.
history, and Value at Risk: The New Benchmark for Managing Financial Risk, which is
aimed at finance practitioners and has become an “industry standard.”
Philippe Jorion is a frequent speaker at academic and professional conferences.
He is on the editorial board of a number of finance journals and is editor in chief of
the Journal of Risk.
About GARP
The Global Association of Risk Professionals (GARP), established in 1996, is a not-
for-profitindependentassociationofriskmanagementpractitionersandresearchers.
Its members represent banks, investment management firms, governmental bodies,
academic institutions, corporations, and other financial organizations from all over
the world.
GARP’smission,asadoptedbyitsBoardofTrusteesinastatementissuedinFebru-
ary2003,istobetheleadingprofessionalassociationforriskmanagers,managedby
and for its members dedicated to the advancement of the risk profession through
education, training and the promotion of best practices globally.
In just seven years the Association’s membership has grown to over 27,000 indi-
viduals from around the world. In the just six years since its inception in 1997, the
FRM program has become the world’s most prestigious financial risk management
certification program. Professional risk managers having earned the FRM credential
are globally recognized as having achieved a minimum level of professional compe-
tencyalongwithademonstratedabilitytodynamicallymeasureandmanagefinancial
riskinareal-worldsettinginaccordwithglobalstandards.Furtherinformationabout
GARP, the FRM Exam, and FRM readings are available at www.garp.com.
v

Contents
Preface xix
Introduction xxi
Part I: Quantitative Analysis 1
Ch. 1 Bond Fundamentals 3
1.1 Discounting, Present, and Future Value . . . . . . . . . . . . 3
1.2 Price-Yield Relationship . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Valuation . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Taylor Expansion . . . . . . . . . . . . . . . . . . . . 7
1.2.3 Bond Price Derivatives . . . . . . . . . . . . . . . . . 9
1.2.4 Interpreting Duration and Convexity . . . . . . . . . . 16
1.2.5 Portfolio Duration and Convexity. . . . . . . . . . . . 23
1.3 Answers to Chapter Examples . . . . . . . . . . . . . . . . . 26
Ch. 2 Fundamentals of Probability 31
2.1 Characterizing Random Variables . . . . . . . . . . . . . . . 31
2.1.1 Univariate Distribution Functions . . . . . . . . . . . 32
2.1.2 Moments . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 Multivariate Distribution Functions . . . . . . . . . . . . . . 37
2.3 Functions of Random Variables . . . . . . . . . . . . . . . . 40
2.3.1 Linear Transformation of Random Variables . . . . . . 41
2.3.2 Sum of Random Variables . . . . . . . . . . . . . . . 42
2.3.3 Portfolios of Random Variables. . . . . . . . . . . . . 42
2.3.4 Product of Random Variables . . . . . . . . . . . . . . 43
2.3.5 Distributions of Transformations of Random Variables 44
2.4 Important Distribution Functions . . . . . . . . . . . . . . . 46
2.4.1 Uniform Distribution . . . . . . . . . . . . . . . . . . 46
2.4.2 Normal Distribution. . . . . . . . . . . . . . . . . . . 47
2.4.3 Lognormal Distribution . . . . . . . . . . . . . . . . . 51
2.4.4 Student’s t Distribution . . . . . . . . . . . . . . . . . 54
2.4.5 Binomial Distribution . . . . . . . . . . . . . . . . . . 56
2.5 Answers to Chapter Examples . . . . . . . . . . . . . . . . . 57
vii
viii CONTENTS
Ch. 3 Fundamentals of Statistics 63
3.1 Real Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1.1 Measuring Returns . . . . . . . . . . . . . . . . . . . 64
3.1.2 Time Aggregation . . . . . . . . . . . . . . . . . . . . 65
3.1.3 Portfolio Aggregation . . . . . . . . . . . . . . . . . . 66
3.2 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . 69
3.3 Regression Analysis . . . . . . . . . . . . . . . . . . . . . . 71
3.3.1 Bivariate Regression . . . . . . . . . . . . . . . . . . 72
3.3.2 Autoregression . . . . . . . . . . . . . . . . . . . . . 74
3.3.3 Multivariate Regression . . . . . . . . . . . . . . . . . 74
3.3.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3.5 Pitfalls with Regressions . . . . . . . . . . . . . . . . 77
3.4 Answers to Chapter Examples . . . . . . . . . . . . . . . . . 80
Ch. 4 Monte Carlo Methods 83
4.1 Simulations with One Random Variable . . . . . . . . . . . . 83
4.1.1 Simulating Markov Processes . . . . . . . . . . . . . . 84
4.1.2 The Geometric Brownian Motion . . . . . . . . . . . . 84
4.1.3 Simulating Yields . . . . . . . . . . . . . . . . . . . . 88
4.1.4 Binomial Trees . . . . . . . . . . . . . . . . . . . . . 89
4.2 Implementing Simulations . . . . . . . . . . . . . . . . . . . 93
4.2.1 Simulation for VAR . . . . . . . . . . . . . . . . . . . 93
4.2.2 Simulation for Derivatives . . . . . . . . . . . . . . . 93
4.2.3 Accuracy . . . . . . . . . . . . . . . . . . . . . . . . 94
4.3 Multiple Sources of Risk . . . . . . . . . . . . . . . . . . . . 96
4.3.1 The Cholesky Factorization . . . . . . . . . . . . . . . 97
4.4 Answers to Chapter Examples . . . . . . . . . . . . . . . . . 99
Part II: Capital Markets 103
Ch. 5 Introduction to Derivatives 105
5.1 Overview of Derivatives Markets . . . . . . . . . . . . . . . . 105
5.2 Forward Contracts . . . . . . . . . . . . . . . . . . . . . . . 107
5.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2.2 Valuing Forward Contracts . . . . . . . . . . . . . . . 110
5.2.3 Valuing an Off-Market Forward Contract . . . . . . . . 112
5.2.4 Valuing Forward Contracts with Income Payments. . . 113
5.3 Futures Contracts. . . . . . . . . . . . . . . . . . . . . . . . 117
5.3.1 Definitions of Futures . . . . . . . . . . . . . . . . . . 117
5.3.2 Valuing Futures Contracts . . . . . . . . . . . . . . . 119
5.4 Swap Contracts . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.5 Answers to Chapter Examples . . . . . . . . . . . . . . . . . 120
Financial Risk Manager Handbook, Second Edition
CONTENTS ix
Ch. 6 Options 123
6.1 Option Payoffs . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.1.1 Basic Options . . . . . . . . . . . . . . . . . . . . . . 123
6.1.2 Put-Call Parity . . . . . . . . . . . . . . . . . . . . . . 126
6.1.3 Combination of Options . . . . . . . . . . . . . . . . 128
6.2 Valuing Options . . . . . . . . . . . . . . . . . . . . . . . . 132
6.2.1 Option Premiums . . . . . . . . . . . . . . . . . . . . 132
6.2.2 Early Exercise of Options . . . . . . . . . . . . . . . . 134
6.2.3 Black-Scholes Valuation . . . . . . . . . . . . . . . . . 136
6.2.4 Market vs. Model Prices . . . . . . . . . . . . . . . . . 142
6.3 Other Option Contracts. . . . . . . . . . . . . . . . . . . . . 143
6.4 Valuing Options by Numerical Methods . . . . . . . . . . . . 146
6.5 Answers to Chapter Examples . . . . . . . . . . . . . . . . . 149
Ch. 7 Fixed-Income Securities 153
7.1 Overview of Debt Markets . . . . . . . . . . . . . . . . . . . 153
7.2 Fixed-Income Securities. . . . . . . . . . . . . . . . . . . . . 156
7.2.1 Instrument Types . . . . . . . . . . . . . . . . . . . . 156
7.2.2 Methods of Quotation. . . . . . . . . . . . . . . . . . 158
7.3 Analysis of Fixed-Income Securities . . . . . . . . . . . . . . 160
7.3.1 The NPV Approach . . . . . . . . . . . . . . . . . . . 160
7.3.2 Duration. . . . . . . . . . . . . . . . . . . . . . . . . 163
7.4 Spot and Forward Rates . . . . . . . . . . . . . . . . . . . . 165
7.5 Mortgage-Backed Securities. . . . . . . . . . . . . . . . . . . 170
7.5.1 Description . . . . . . . . . . . . . . . . . . . . . . . 170
7.5.2 Prepayment Risk . . . . . . . . . . . . . . . . . . . . 174
7.5.3 Financial Engineering and CMOs . . . . . . . . . . . . 177
7.6 Answers to Chapter Examples . . . . . . . . . . . . . . . . . 183
Ch. 8 Fixed-Income Derivatives 187
8.1 Forward Contracts . . . . . . . . . . . . . . . . . . . . . . . 187
8.2 Futures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
8.2.1 Eurodollar Futures . . . . . . . . . . . . . . . . . . . 190
8.2.2 T-bond Futures . . . . . . . . . . . . . . . . . . . . . 193
8.3 Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
8.3.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . 195
8.3.2 Quotations . . . . . . . . . . . . . . . . . . . . . . . 197
8.3.3 Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . 197
8.4 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
8.4.1 Caps and Floors . . . . . . . . . . . . . . . . . . . . . 202
8.4.2 Swaptions . . . . . . . . . . . . . . . . . . . . . . . . 204
8.4.3 Exchange-Traded Options. . . . . . . . . . . . . . . . 206
8.5 Answers to Chapter Examples . . . . . . . . . . . . . . . . . 207
Financial Risk Manager Handbook, Second Edition