The Mathematics of Financial Models + Website: Solving Real-World Problems with Quantitative Methods

345 Pages·2014·2.61 MB·English

by  Kannoo Ravindran

The Mathematics
of Financial
Models
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The Mathematics
of Financial
Models
Solving Real-World Problems
with Quantitative Methods
KANNOO RAVINDRAN
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Copyright©2014byKannooRavindran.Allrightsreserved.
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10 9 8 7 6 5 4 3 2 1
Contents
Preface ix
Acknowledgments xi
CHAPTER1
SettingtheStage 1
WhyIsThisBookDifferent? 2
RoadMapoftheBook 3
References 5
CHAPTER2
BuildingZeroCurves 7
MarketInstruments 8
LinearInterpolation 16
CubicSplining 25
Appendix:FindingSwapRatesUsingaFloatingCoupon
BondApproach 41
References 43
CHAPTER3
ValuingVanillaOptions 45
Black-ScholesFormulae 47
AdaptationsoftheBlack-ScholesFormulae 53
LimitationsoftheBlack-ScholesFormulae 70
ApplicationinCurrencyRiskManagement 74
Appendix 78
References 80
CHAPTER4
Simulations 81
UniformNumberGeneration 82
Non-UniformNumberGeneration 86
ApplicationsofSimulations 93
v
vi CONTENTS
VarianceReductionTechniques 100
References 104
CHAPTER5
ValuingExoticOptions 107
ValuingPath-Independent,European-StyleOptionsona
SingleVariable 108
ValuingPath-Dependent,European-StyleOptionsona
SingleVariable 114
ValuingPath-Independent,European-StyleOptionson
TwoVariables 135
ValuingPath-Dependent,European-StyleOptionson
MultipleVariables 152
References 157
CHAPTER6
EstimatingModelParameters 159
CalibrationofParametersintheBlack-ScholesModel 161
UsingImpliedBlack-ScholesVolatilitySurfaceand
ZeroRateTermStructuretoValueOptions 169
UsingVolatilitySurface 178
CalibrationofInterestRateOptionModelParameters 190
StatisticalEstimation 196
References 203
CHAPTER7
TheEffectivenessofHedgingStrategies 205
DeltaHedging 206
AssumptionsUnderlyingDeltaHedging 216
BeyondDeltaHedging 223
TestingHedgingStrategies 230
AnalysisAssociatedwiththeHedgingofaEuropean-Style
VanillaPutOption 235
References 244
CHAPTER8
ValuingVariableAnnuityGuarantees 245
BasicGMDB 246
DeathBenefitRiders 261
OtherDetailsAssociatedwithGMDBProducts 269
ImprovingModelingAssumptions 273
LivingBenefitRiders 276
References 279
Contents vii
CHAPTER9
RealOptions 281
SurrenderingaGMABRider 282
AddingServersinaQueue 300
References 314
CHAPTER10
PartingThoughts 315
AbouttheAuthor 317
AbouttheWebsite 319
Index 321

Preface
T
he purpose of this book is to give the reader a better appreciation and
insight into the use of quantitative tools to solve real-world problems
whenthereisanotionofcost(ormoney)involved.Examplesofsuchprob-
lemsexistinabundanceinpractice(e.g.,budgeting,managementoffinancial
risks, valuation of financial instruments, optimizing the efficiency of oper-
ations, extension or termination of a contract, etc.) where one is interested
in either minimizing the cost or maximizing the profit/revenue associated
withabusinessdecision.Despitethevastnumberofexampleswherequan-
titative methods are applied to solve practical problems in finance, due to
time constraints, I can only discuss a limited number of them. As such, it
isimperativeforthereadertorealizethattheexamplesinthisbookareby
no means exhaustive and it is my sincere desire to discuss more examples
spanningacrossdifferentindustriesinfutureeditionsofthebook.
To discuss the application of quantitative methods in this book, I have
organized the book into four sections. The first section focuses on prob-
lemsassociatedwiththeconstructionofzerocurves,discounting,andfuture
valuing.Thesecondsectiondiscussesproblemsassociatedwithvaluingboth
vanilla and exotic options. The third section focuses on estimation and the
calibration of parameters used in pricing/hedging models, and the last sec-
tionmentionshedgingstrategies,realoptions,andvariableannuities.
Todiscussthesetopics,insteadofgettingintodetailsregardingtheuseof
the underlying models, I provide sufficient background necessary to ensure
thatthereaderisabletophilosophicallyunderstandtheproblemthatneeds
to be solved. Once this is done, I apply the relevant quantitative methods
and underlying models to solve the problems, while keeping details on the
quantitativemethodsusedassupplementalmaterialsonthewebsite.
ThoughIhaveassumedthatreaderswillhavesomegeneralunderstand-
ingofbasicfinance,derivatives,first-yearcalculus,andprobability,thisbook
is appropriate for any student, academic, and practitioner (which includes
everyone from an end user to a market maker and anyone from a back-
office function to a front-office function). More precisely, for readers who
are quantitatively biased, this book provides the necessary practical exam-
plesandinformationsothatnuancesassociatedwiththepracticalityofthe
ix