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.
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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