Introduction To Quantitative Finance, An: A Three-Principle Approach

273 Pages·2015·5.965 MB·English

by  Ting Christopher Hian Ann

An Introduction to
Quantitative
Finance
A Three-Principle Approach
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
An Introduction to
Quantitative
Finance
A Three-Principle Approach
Christopher Hian Ann Ting
Singapore Management University, Singapore
World Scientific
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Cataloging-in-Publication Data
Ting, Christopher Hian Ann, author.
An introduction to quantitative finance : a three-principle approach / Christopher Hian Ann Ting.
pages cm
Includes bibliographical references and index.
ISBN 978-9814704304 (alk. paper)
1. Finance--Mathematical models. I. Title.
HG106.T56 2015
332.01'5195--dc23
2015025675
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Copyright © 2016 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance
Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy
is not required from the publisher.
In-house Editor: Qi Xiao
Typeset by Stallion Press
Email: [e-mail]
Printed in Singapore
Dedicatedto
Reiko,Eri,Ai,andJoshua.
Inmemoryof
Mr.LeeKuanYew.
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Contents
Foreword xiii
Preface xv
AbouttheAuthor xix
Acknowledgments xxi
Notations xxiii
1. Introduction 1
1.1 ABriefHistoryofQuantitativeFinance . . . . . . . 1
1.2 The2008GlobalFinancialCrisis
andQuantitativeFinance . . . . . . . . . . . . . . . 4
1.3 FallacyofPrediction:WhiteKiwi . . . . . . . . . . . 6
1.4 BeattheMarket . . . . . . . . . . . . . . . . . . . . . 9
1.5 TopicsandProspectsofQuantitative
Finance . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 16
2. BriefIntroductiontoFourMajorAssetClasses 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Stocks . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Currencies . . . . . . . . . . . . . . . . . . . . . . . . 25
viii AnIntroductiontoQuantitativeFinance
2.4 Commodities . . . . . . . . . . . . . . . . . . . . . . 29
2.5 FixedIncome . . . . . . . . . . . . . . . . . . . . . . 32
2.6 OtherInvestments . . . . . . . . . . . . . . . . . . . 38
2.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 39
3. PrinciplesofQuantitativeFinance 47
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 UncertaintyandRisk . . . . . . . . . . . . . . . . . . 48
3.3 PrinciplesofQuantitativeFinance . . . . . . . . . . 50
3.3.1 Firstprinciple:Returnisfixed
intheabsenceofrisk . . . . . . . . . . . . . 50
3.3.2 Secondprinciple:Expectedreturn
isdirectlyproportionaltorisk . . . . . . . . 51
3.3.3 Thirdprinciple:Everywillingbuyer
hasawillingseller . . . . . . . . . . . . . . . 55
3.4 RelativeValuation . . . . . . . . . . . . . . . . . . . 59
3.5 AnApplicationofthePrinciples
ofQuantitativeFinance. . . . . . . . . . . . . . . . . 62
3.6 ViolationsofThreePrinciples? . . . . . . . . . . . . 65
3.7 PrinciplesversusModels . . . . . . . . . . . . . . . 68
3.8 PhysicsEnvy? . . . . . . . . . . . . . . . . . . . . . . 69
3.9 MarketFriction . . . . . . . . . . . . . . . . . . . . . 73
3.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 75
4. InterestRates 79
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 CompoundingSchemes . . . . . . . . . . . . . . . . 80
4.3 Zero-CouponYieldCurveandRisks . . . . . . . . . 82
4.3.1 Zero-couponbondsandinterestraterisks . 83
4.3.2 Gurkaynak–Sack–Wright(GSW)dataset . . 87
4.3.3 Downward-slopingyieldcurve . . . . . . . 88
4.3.4 U-shapeandhump-shapeyieldcurves . . . 91
4.4 InterestRateRiskandBondReturn . . . . . . . . . . 94
4.4.1 Returnfromthepassageoftime . . . . . . . 95
4.4.2 Returnduetothechangeininterestrate . . 96
Contents ix
4.5 InterestRateRiskandtheYield
CurveShape . . . . . . . . . . . . . . . . . . . . . . . 98
4.5.1 Amodeloflong-termrisks . . . . . . . . . . 99
4.5.2 Amodelofshort-termrisks . . . . . . . . . 102
4.5.3 Summaryofataleoflong-
andshort-termrisks . . . . . . . . . . . . . . 104
4.6 LiquidityRisk . . . . . . . . . . . . . . . . . . . . . . 107
4.7 CreditRisk . . . . . . . . . . . . . . . . . . . . . . . . 108
4.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 110
5. DerivativeswithLinearPayoffs 113
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 113
5.1.1 Linearpayoffs . . . . . . . . . . . . . . . . . 114
5.1.2 Nonlinearpayoffs . . . . . . . . . . . . . . . 115
5.2 ForwardForexRate . . . . . . . . . . . . . . . . . . . 116
5.2.1 Interestrateparity . . . . . . . . . . . . . . . 117
5.2.2 ForwardFXratesinpractice . . . . . . . . . 119
5.2.3 Non-DeliverableForward(NDF) . . . . . . 120
5.3 ImpliedForwardInterestRate . . . . . . . . . . . . . 121
5.4 ForwardRateAgreement . . . . . . . . . . . . . . . 122
5.5 InterestRateSwap . . . . . . . . . . . . . . . . . . . 126
5.6 Cross-CurrencyInterestRateSwap(CIRS). . . . . . 129
5.7 DiscountFactorsinPractice . . . . . . . . . . . . . . 130
5.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 135
6. DerivativeswithNonlinearPayoffs 137
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 137
6.2 EuropeanandAmericanPutsandCalls . . . . . . . 139
6.3 OverallShapeofEuropeanCallOption
PriceFunction . . . . . . . . . . . . . . . . . . . . . . 142
6.3.1 Monotonouswithrespecttothestrike
price . . . . . . . . . . . . . . . . . . . . . . . 142
6.3.2 Lowerandupperboundsfortheslope . . . 143
6.3.3 Convexity . . . . . . . . . . . . . . . . . . . . 145
6.4 OverallShapeofEuropeanPutOption
PriceFunction . . . . . . . . . . . . . . . . . . . . . . 147