David Vose

Risk Analysis A quantitative guide

David Vose

third edition

John W iley & Sons, Ltd

Số hóa bởi Trung tâm Học liệu – ĐH TN

http://www.lrc-tnu.edu.vn

Copyright © 2008

David Vose

Published by

John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, P019 8SQ, England Telephone + 44 (0)1243 779777

Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. 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 under the terms o f the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by die Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W IT 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex P 019 8SQ, England, or emailed to [email protected], or faxed to + 44 (0)1243 770620. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought

Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 6045 Freemont Blvd, Mississauga, Ontario, Canada, L5R 4J3 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.

Library o f Congress Cataloging-in-PubUcation Data Vose, David. Risk analysis : a quantitative guide / David Vose. - 3rd ed. p. cm. Includes bibliographical references and index. ISBN 978-0-470-51284-5 (cloth : alk. paper) 1. Monte Carlo method. 2. Risk assessment-Mathematical models. I. Title. QA298.V67 2008 658.4'0352 - dc22 20070416%

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-470-51284-5 (H/B) Typeset in 10/12pt Times by Laserwords Private Limited, Chennai, India Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire

Số hóa bởi Trung tâm Học liệu – ĐH TN

http://www.lrc-tnu.edu.vn

S o ẹ l v ú ,

SáJL*->f i^w o

cC^

jL o r ^

JV -

Số hóa bởi Trung tâm Học liệu – ĐH TN

http://www.lrc-tnu.edu.vn

Contents Preface Part 1

xiii Introduction

1

1

W hy do a risk analysis? 1.1 M oving on from “W hat If” Scenarios 1.2 The Risk Analysis Process 1.3 Risk M anagem ent Options 1.4 Evaluating Risk M anagem ent Options 1.5 Inefficiencies in Transferring Risks to O thers 1.6 Risk Registers

3 3 5 7 10 11 13

2

Planning a risk analysis 2.1 Questions and Motives 2.2 D eterm ine the Assumptions that are Acceptable or Required 2.3 Time and Tim ing 2.4 You’ll N eed a Good Risk A nalyst or Team

21 21 22 23 23

3

The quality o f a risk analysis 3.1 T he Reasons W hy a Risk Analysis can be Terrible 3.2 Com m unicating the Quality o f Data Used in a Risk Analysis 3.3 Level o f Criticality 3.4 The Biggest Uncertainty in a Risk Analysis 3.5 Iterate

29 29 31 34 35 36

4

Choice o f m odel structure 4.1 Software Tools and the M odels they Build 4.2 Calculation M ethods 4.3 U ncertainty and Variability 4.4 H ow M onte Carlo Sim ulation Works 4.5 Sim ulation M odelling

37 37 42 47 57 63

5

U nderstanding and using the results o f a risk analysis 5.1 W riting a Risk Analysis Report 5.2 E xplaining a M odel’s Assum ptions

67 67 69

Số hóa bởi Trung tâm Học liệu – ĐH TN

http://www.lrc-tnu.edu.vn

V lll

Contents

5.3 5.4 Part 2

Graphical Presentation o f a M odel’s Results Statistical M ethods o f Analysing Results

70 91

Introduction

109

6

Probability m athem atics and sim ulation 6.1 Probability Distribution Equations 6.2 The Definition o f “Probability” 6.3 Probability Rules 6.4 Statistical M easures

115 115 118 119 137

7

Building and running a m odel 7.1 M odel Design and Scope 7.2 Building Models that are Easy to Check and Modify 7.3 Building Models that are Efficient 7.4 M ost Common M odelling Errors

145 145 146 147 159

8

Som e 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9

167 167 167 176 183 188 190 193

basic random processes Introduction The Binom ial Process The Poisson Process The Hypergeometric Process Central Limit Theorem Renewal Processes M ixture Distributions M artingales M iscellaneous Examples

194

194

9

D ata and statistics 9.1 Classical Statistics 9.2 Bayesian Inference 9.3 The Bootstrap 9.4 M aximum Entropy Principle 9.5 W hich Technique Should You Use? 9.6 Adding uncertainty in Simple Linear Least-Squares Regression A nalysis

207 208 215 246 254 255 256

10

Fitting distributions to data 10.1 Analysing the Properties o f the Observed Data 10.2 Fitting a Non-Param etric D istribution to the Observed Data 10.3 Fitting a First-Order Param etric D istribution to Observed D ata 10.4 Fitting a Second-Order Parametric D istribution to Observed Data

263 264 269 281 297

11

Sum s o f random variables 11.1 The Basic Problem 11.2 Aggregate Distributions

301 301 305

Số hóa bởi Trung tâm Học liệu – ĐH TN

http://www.lrc-tnu.edu.vn

Contents

lx

12

Forecasting with uncertainty 12.1 The Properties o f a Time Series Forecast 12.2 Com m on Financial Time Series Models 12.3 Autoregressive M odels 12.4 M arkov Chain M odels 12.5 Birth and Death M odels 12.6 Time Series Projection of Events Occurring Randomly in Time 12.7 Time Series M odels with Leading Indicators 12.8 Com paring Forecasting Fits for Different M odels 12.9 Long-Term Forecasting

321 322 327 335 339 343 345 348 351 352

13

M odelling correlation and dependencies 13.1 Introduction 13.2 Rank O rder Correlation 13.3 Copulas 13.4 The Envelope M ethod 13.5 M ultiple Correlation Using a Look-Up Table

353 353 356 367 380 391

14

Eliciting from expert opinion 14.1 Introduction 14.2 Sources o f Error in Subjective Estim ation 14.3 M odelling Techniques 14.4 Calibrating Subject M atter Experts 14.5 Conducting a Brainstorm ing Session 14.6 C onducting the Interview

393 393 394 401 412 414 416

15

Testing and m odelling causal relationships 15.1 C am pylobacter Exam ple 15.2 Types o f M odel to Analyse Data 15.3 From Risk Factors to Causes 15.4 E valuating Evidence 15.5 The Lim its o f Causal Argum ents 15.6 An Exam ple o f a Q ualitative Causal Analysis 15.7 Is Causal Analysis Essential?

423 424 426 427 429 429 430 434

16

O ptim isation in risk analysis 16.1 Introduction 16.2 O ptim isation M ethods 16.3 Risk Analysis M odelling and O ptim isation 16.4 W orking Example: Optim al A llocation of M ineral Pots

435 435 436 439 444

17

C hecking and validating a m odel 17.1 Spreadsheet M odel Errors 17.2 Checking M odel Behaviour 17.3 C om paring Predictions Against Reality

451

Số hóa bởi Trung tâm Học liệu – ĐH TN

451

456 460

http://www.lrc-tnu.edu.vn

X

Contents

18

Discounted cashflow m odelling 18.1 Useful Time Series M odels o f Sales and M arket Size 18.2 Summing Random Variables 18.3 Summing Variable Margins on Variable Revenues 18.4 Financial M easures in Risk Analysis

461 463 466 467 469

19

Project risk analysis 19.1 Cost Risk Analysis 19.2 Schedule Risk Analysis 19.3 Portfolios o f risks 19.4 Cascading Risks

473 474 478 486 487

20

Insurance and finance risk analysis m odelling 20.1 Operational Risk M odelling 20.2 Credit Risk 20.3 Credit Ratings and M arkov Chain M odels 20.4 Other Areas o f Financial Risk 20.5 M easures o f Risk 20.6 Term Life Insurance 20.7 Accident Insurance 20.8 M odelling a Correlated Insurance Portfolio 20.9 M odelling Extremes 20.10 Premium Calculations

493 493 494 499 503 503 506 509 511 512 513

21

M icrobial food safety risk assessm ent 21.1 Growth and Attenuation Models 21.2 D o se-R esponse Models 21.3 Is M onte Carlo Sim ulation the Right Approach? 21.4 Some M odel Simplifications

517 519 527 532 533

22

A nim al im port risk assessm ent 22.1 Testing for an Infected Animal 22.2 Estim ating True Prevalence in a Population 22.3 Importing Problems 22.4 Confidence of Detecting an Infected Group 22.5 M iscellaneous Animal Health and Food Safety Problem s

537 539 544

I

G uide for lecturers

567

II

About M odelRisk

569

III

A com pendium o f distributions III. 1 Discrete and Continuous D istributions 111.2 Bounded and Unbounded D istributions 111.3 Parametric and Non-Param etric D istributions 111.4 Univariate and M ultivariate Distributions

585

Số hóa bởi Trung tâm Học liệu – ĐH TN

553

556 559

585 586 587 588

http://www.lrc-tnu.edu.vn

Contents

III.5

Lists o f Applications and the M ost Useful Distributions H ow to Read Probability Distribution Equations III.7 The Distributions m .8 Introduction to Creating Your Own Distributions III.9 A pproxim ation of One Distribution with Another III. 10 Recursive Formulae for Discrete Distributions III. 11 A Visual Observation On The Behaviour O f Distributions

in.6

Xi

588 593 599 696 703 710 713

IV

Further reading

715

V

Vose C onsulting

721

R eferences

725

Index

729

Số hóa bởi Trung tâm Học liệu – ĐH TN

http://www.lrc-tnu.edu.vn

Preface I ’ll try to keep it short. This third edition is an almost complete rewrite. I have thrown out anything from the second edition that was really o f pure academic interest - but that w asn’t very much, and I had a lot o f new topics I wanted to include, so this edition is quite a bit bigger. I apologise if you had to pay postage. T here are two m ain reasons why there is so much material to add since 2000. The first is that our consultancy firm has grown considerably, and, with the extra staff and talent, we have had the privilege o f working on m ore am bitious and varied projects. We have particularly expanded in the insurance and finance m arkets, so you will see that a lot o f techniques from those areas, which have far wider applications, appear throughout this edition. We have had contracts where we were given carte blanche to think up new ideas, and that really got the creative juices flowing. I have also been involved in writing and editing various risk analysis guidelines that made me think more about the disconnect between what risk analysts produce and what risk m anagers need. This edition is split into two parts in an attem pt to help rem edy that problem. The second reason is that we have built a really great software team, and the freedom to design our own tools has been a double espresso for our collective imagination. We now build a lot o f bespoke risk analysis applications for clients and have our own com mercial software products. It has been enorm ous fun starting o ff w ith a typical risk-based problem, researching techniques that would solve that problem if only they were easy to use and then working out how to make that happen. M odelRisk is the result, and we have a few others in the pipeline.

S o m e th a n k yo u s . . . I have im posed a lot on Veerle and our children to get this book done. V has spent plenty o f evenings w ithout me while I typed away in my office, but I think she suffered much more living with a guy who was perpetually distracted by w hat he was going to write next. Sophie and Sebastien have also missed out. Papa always seemed to be working instead of playing with them. Worse, perhaps, it didn’t stop raining all sum m er in Belgium , and they had to forego a holiday in the sun so I could finish writing. I ’ll make it up to all three o f you, I promise. I have the luxury o f having some really smart and m otivated people working with me. I have leaned rather heavily on the partners and staff in our consultancy firm while I focused on this book, particularly on Huybert Groenendaal who has largely run the com pany in my “absence”. He also wrote Appendix 5. Tim our Koupeev heads our program m ing team and has been infinitely patient in converting m y neverending ideas for our M odelRisk software into reality. He also wrote Appendix 2. M urat Tomaev, oui head program m er, has made it all w ork together. Getting new m odules for me to look at always feels a little like Christm as.

Số hóa bởi Trung tâm Học liệu – ĐH TN

http://www.lrc-tnu.edu.vn