Finacial risk manager handbook

Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States. With offices in North America, Europe, Australia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding. The Wiley Finance series contains books written specifically for finance and investment professionals, as well as sophisticated individual investors and their financial advisors. Book topics range from portfolio management to e-commerce, risk management, financial engineering, valuation, and financial instrument analysis, as well as much more. For a list of available titles, please visit our Web site at www.WileyFinance.com. Copyright 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. Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008, e-mail: permcoordinator§wiley.com. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services, or technical support, please contact our Customer Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 or fax 317-572-4002. ISBN 0-471-43003-X Printed in the United States of America. Risk management has rapidly evolved over the last decade and has become an indispensable function in many institutions. This Handbook was originally written to provide support for candidates taking the FRM examination administered by GARP. As such, it reviews a wide variety of practical topics in a consistent and systematic fashion. It covers quantitative methods, capital markets, as well as market, credit, operational, and integrated risk management. It also discusses the latest regulatory, legal, and accounting issues essential to risk professionals. Modern risk management systems cut across the entire organization. This breadth is reflected in the subjects covered in this Handbook. This Handbook was designed to be self-contained, but only for readers who already have some exposure to financial markets. To reap maximum benefit from this book, readers should have taken the equivalent of an MBA-level class on investments. Finally, I wanted to acknowledge the help received in the writing of this second edition. In particular, I would like to thank the numerous readers who shared comments on the previous edition. Any comment and suggestion for improvement will be welcome. This feedback will help us to maintain the high quality of the FRM designation.

Financial Risk Manager Handbook Second Edition Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States With offices in North America, Europe, Australia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding The Wiley Finance series contains books written specifically for finance and investment professionals, as well as sophisticated individual investors and their financial advisors Book topics range from portfolio management to e-commerce, risk management, financial engineering, valuation, and financial instrument analysis, as well as much more For a list of available titles, please visit our Web site at www.WileyFinance.com Financial Risk Manager Handbook Second Edition Philippe Jorion GARP Wiley John Wiley & Sons, Inc Copyright 䊚 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 Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-750-4470, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008, e-mail: permcoordinator§wiley.com Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services, or technical support, please contact our Customer Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 or fax 317-572-4002 Library of Congress Cataloging-in-Publication Data: ISBN 0-471-43003-X Printed in the United States of America 10 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, Northwestern University, the University of Chicago, and the University of British Columbia He holds an M.B.A and a Ph.D from the University of Chicago and a degree in engineering 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 Bankruptcy in Orange County, the first account of the largest municipal failure in U.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 notfor-profit independent association of risk management practitioners and researchers Its members represent banks, investment management firms, governmental bodies, academic institutions, corporations, and other financial organizations from all over the world GARP’s mission, as adopted by its Board of Trustees in a statement issued in February 2003, is to be the leading professional association for risk managers, managed by 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 individuals 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 competency along with a demonstrated ability to dynamically measure and manage financial risk in a real-world setting in accord with global standards Further information about GARP, the FRM Exam, and FRM readings are available at www.garp.com v Contents Preface xix Introduction xxi Part I: Quantitative Analysis Ch Ch Bond Fundamentals 1.1 Discounting, Present, and Future Value 1.2 Price-Yield Relationship 1.2.1 Valuation 1.2.2 Taylor Expansion 1.2.3 Bond Price Derivatives 1.2.4 Interpreting Duration and Convexity 1.2.5 Portfolio Duration and Convexity 1.3 Answers to Chapter Examples 3 6 16 23 26 Fundamentals of Probability 2.1 Characterizing Random Variables 2.1.1 Univariate Distribution Functions 2.1.2 Moments 2.2 Multivariate Distribution Functions 2.3 Functions of Random Variables 2.3.1 Linear Transformation of Random Variables 2.3.2 Sum of Random Variables 2.3.3 Portfolios of Random Variables 2.3.4 Product of Random Variables 2.3.5 Distributions of Transformations of Random Variables 2.4 Important Distribution Functions 2.4.1 Uniform Distribution 2.4.2 Normal Distribution 2.4.3 Lognormal Distribution 2.4.4 Student’s t Distribution 2.4.5 Binomial Distribution 2.5 Answers to Chapter Examples 31 31 32 33 37 40 41 42 42 43 44 46 46 47 51 54 56 57 vii viii Ch Ch CONTENTS Fundamentals of Statistics 3.1 Real Data 3.1.1 Measuring Returns 3.1.2 Time Aggregation 3.1.3 Portfolio Aggregation 3.2 Parameter Estimation 3.3 Regression Analysis 3.3.1 Bivariate Regression 3.3.2 Autoregression 3.3.3 Multivariate Regression 3.3.4 Example 3.3.5 Pitfalls with Regressions 3.4 Answers to Chapter Examples Monte Carlo Methods 4.1 Simulations with One Random Variable 4.1.1 Simulating Markov Processes 4.1.2 The Geometric Brownian Motion 4.1.3 Simulating Yields 4.1.4 Binomial Trees 4.2 Implementing Simulations 4.2.1 Simulation for VAR 4.2.2 Simulation for Derivatives 4.2.3 Accuracy 4.3 Multiple Sources of Risk 4.3.1 The Cholesky Factorization 4.4 Answers to Chapter Examples 63 63 64 65 66 69 71 72 74 74 75 77 80 83 83 84 84 88 89 93 93 93 94 96 97 99 Part II: Capital Markets 103 Ch 105 105 107 107 110 112 113 117 117 119 119 120 Introduction to Derivatives 5.1 Overview of Derivatives Markets 5.2 Forward Contracts 5.2.1 Definition 5.2.2 Valuing Forward Contracts 5.2.3 Valuing an Off-Market Forward Contract 5.2.4 Valuing Forward Contracts with Income Payments 5.3 Futures Contracts 5.3.1 Definitions of Futures 5.3.2 Valuing Futures Contracts 5.4 Swap Contracts 5.5 Answers to Chapter Examples Financial Risk Manager Handbook, Second Edition CONTENTS Ch Ch Ch ix Options 6.1 Option Payoffs 6.1.1 Basic Options 6.1.2 Put-Call Parity 6.1.3 Combination of Options 6.2 Valuing Options 6.2.1 Option Premiums 6.2.2 Early Exercise of Options 6.2.3 Black-Scholes Valuation 6.2.4 Market vs Model Prices 6.3 Other Option Contracts 6.4 Valuing Options by Numerical Methods 6.5 Answers to Chapter Examples 123 123 123 126 128 132 132 134 136 142 143 146 149 Fixed-Income Securities 7.1 Overview of Debt Markets 7.2 Fixed-Income Securities 7.2.1 Instrument Types 7.2.2 Methods of Quotation 7.3 Analysis of Fixed-Income Securities 7.3.1 The NPV Approach 7.3.2 Duration 7.4 Spot and Forward Rates 7.5 Mortgage-Backed Securities 7.5.1 Description 7.5.2 Prepayment Risk 7.5.3 Financial Engineering and CMOs 7.6 Answers to Chapter Examples 153 153 156 156 158 160 160 163 165 170 170 174 177 183 Fixed-Income Derivatives 8.1 Forward Contracts 8.2 Futures 8.2.1 Eurodollar Futures 8.2.2 T-bond Futures 8.3 Swaps 8.3.1 Definitions 8.3.2 Quotations 8.3.3 Pricing 8.4 Options 8.4.1 Caps and Floors 8.4.2 Swaptions 8.4.3 Exchange-Traded Options 8.5 Answers to Chapter Examples 187 187 190 190 193 195 195 197 197 201 202 204 206 207 Financial Risk Manager Handbook, Second Edition ... 679 680 680 681 684 695 Financial Risk Manager Handbook, Second Edition Preface The FRM Handbook provides the core body of knowledge for financial risk managers Risk management has rapidly evolved... Credit Risk Management Ch 18 Introduction to Credit Risk 18.1 Settlement Risk 18.1.1 Presettlement vs Settlement Risk 18.1.2 Handling Settlement Risk 18.2 Overview of Credit Risk. .. Credit Risk 18.2.1 Drivers of Credit Risk 18.2.2 Measurement of Credit Risk 18.2.3 Credit Risk vs Market Risk 18.3 Measuring Credit Risk 18.3.1 Credit Losses