The mathematics of derivatives: tools for designing numerical algorithms

208 Pages·2007·0.775 MB·English

by  Robert L. Navin

The Mathematics
of Derivatives
Tools for Designing Numerical
Algorithms
ROBERT L. NAVIN
John Wiley & Sons, Inc.

The Mathematics
of Derivatives
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The Mathematics
of Derivatives
Tools for Designing Numerical
Algorithms
ROBERT L. NAVIN
John Wiley & Sons, Inc.
Copyright(cid:1)c 2007byRobertL.Navin.Allrightsreserved.
PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey.
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LibraryofCongressCataloging-in-PublicationData:
Navin,RobertL.
Themathematicsofderivatives:toolsfordesigningnumericalalgorithms/RobertL.Navin.
p.cm.–(Wileyfinanceseries)
Includesbibliographicalreferences.
ISBN-13:978-0-470-04725-5(cloth)
ISBN-10:0-470-04725-9(cloth)
1.Derivativesecuritie–Valuation–Mathematicalmodels.I.Title.II.Series.
HG6024.A3N372007
332.64’57015181–dc22
2006017013
PrintedintheUnitedStatesofAmerica.
10987654321
This book is dedicated with love to Thais Roda Noya.

Contents
Preface xi
Acknowledgments xiii
PART I The Models 1
CHAPTER 1
Introduction to the Techniques of Derivative Modeling 3
1.1 Introduction 3
1.2 Models 3
1.2.1 WhatIsaDerivative? 3
1.2.2 WhatIsaModel? 5
1.2.3 TwoInitialMethodsforModelingDerivatives 6
1.2.4 PriceProcesses 7
1.2.5 TheArchetypalSecurityProcess:NormalReturns 8
1.2.6 BookOutline 10
CHAPTER 2
Preliminary Mathematical Tools 11
2.1 ProbabilityDistributions 11
2.2 n-DimensionalJacobiansandn-FormAlgebra 14
2.3 FunctionalAnalysisandFourierTransforms 16
2.4 Normal(Central)LimitTheorem 18
2.5 RandomWalks 20
2.6 Correlation 22
2.7 FunctionsofTwo/MoreVariables:PathIntegrals 24
2.8 DifferentialForms 26
CHAPTER 3
Stochastic Calculus 27
3.1 WienerProcess 27
vii