The Mathematics of Financial Modelingand Investment Management

Index Page 766 Wednesday, February 4, 2004 1:13 PM

766 Index

Independent and identically dis -

tributed (Cont.)

processes, extreme value the -

ory, 362–378

returns, 522

assumption, 492

variables, 362, 368, 437, 531

sequence, 364

Independent and identically dis -

tributed (IID) sequences,

268, 325, 495. See also

Fat-tailed IID sequences;

Stationary IID sequence

assumption, 378

assumption, elimination, 376–388

estimation procedures, 381

normalized maxima, 374

Independent distributed sequences,

191



Independently distributed (ID)

variables, 359

Indeterminacy principle, 243

Index. See Benchmarks; Markets

tracking/cointegration, 565

Indexed portfolio, construction,

564–565

Indexing. See Enhanced indexing

strategy, 564

Indicator function. See Events

Indifference curves, 482–484

Individual investors, 2

Inequality constraints, Markow -

itz mean-variance model

(extension), 485–487

Infinite autoregressive form, 295

Infinite moving average. See Time

series

representation, 292, 301

Infinite noncountable set, 99

Infinite variation, 106

Infinitesimal calculus, 107

Infinitesimal notation, 109

Infinitesimal quantities, calculus,

107



Inflation, 593

Information. See Unstructured

data/information

acquisition, cost, 28, 83

advantage, 744

costs, 26–27

criteria. See Akaike Informa -

tion Criteria; Bayesian

Information Criteria

overload, 15–16

processing costs, 37

propagation, 181, 402–403

set, 85

structures, 181–183

technology, role, 11–13

Information coefficient (IC), 568–

570



Information ratio (IR), 568, 570,

751, 753

Information Theory, 747

Informationless trades, 33

Ingersoll, Jonathan, 616, 637,

709. See also Cox-Inger-
     soll-Ross Model
     Initial conditions, 295
     Initial margin, 58
     requirement, 49–50
     Inner product, 155
     Innovation. See Processes
     Inputs, requirement. See Assets
     Instantaneous interest rate, 219.
     See also Risk-free bank
     account
     Institutional investors, 2, 37–41.
     See also Common stocks
     Insurance
     companies, 41, 80
     premiums, establishment, 80
     ruin problem, 80–81
     Intangible assets, 21–22
     Integrals, 172–174. See also
     Improper integrals; Indefi-
     nite integrals; Lebesque-
     Staieltjes integrals; Rie-
     mann integrals
     definition. See Stochastic inte -
     grals
     transforms, 134–138
     Integrated GARCH (IGARCH),
     347, 548
     Integrated nonstationary process,
     268

Integrated processes, 311
Integrated series, 309–313
Integrated trends, 309–313
Integration, 127–130
chain rule, 129
Darboux-Young approach, 173
operation, linearity, 133
process, 14–15
Intensity of belief. See Belief
Interest
instantaneous rate, 620
payments, receiving, 52
risk-free rate, 447
Interest rate risk, 599, 615
exposure, 44
problem, 44
Interest rate-equity swap, 70
Interest rate-risk based capital
requirements, 5
Interest rates. See Deterministic
short-term interest rates;
Guaranteed interest rate;
Risk-free short-term con-
tinuously compounding
interest rate
calibration. See Random
interest rates
changes, 43, 716
constancy, 119–120
convexity. See Constant inter-
est rates; Continuously
compounding constant

interest rate; Variable

interest rates

derivatives, pricing, 638–640

parallel shift, 114, 668

term structure, 126, 599–612

continuous time, 623–638

Interest ratio. See Short interest

ratio

Interest-rate derivatives, class

(pricing), 639

Interior-point algorithms, 210–211

Interior-point methods, 208, 210–

211



International Swaps and Derivatives

Association (ISDA), 683

Credit Derivatives Definition

(1999), 683

Master Agreement, 683

International treaties, 34–35

Intertek Group, study, 13

Inter-trades intervals, distribu -

tional properties, 383

Interval of convergence. See

Convergence

Intrinsic value, 66–67. See also

Stocks

Inverse characteristic equation,

297–298

Inverse floaters, 54

Inverse Fourier transform, 137

Inverse function, 101

Inverse Laplace transform, 249

Inverse operation, 159–160

Inverse operators, 291

Inverted yield curve, 612

Investing. See Active investing

Investment. See Direct invest -

ments

alternatives, 4, 45

budget, constraint, 666

companies, 42–43

constraints, 5–6

decision-making process, 13

horizon, 502–503, 607. See

also One-period invest -

ment horizon

management

applications, CAPM (role),

525–526

milestones, 75

objectives, 64

setup, 2

opportunities, 569

performance

measurement/evaluation, 2

monitoring, 552

policy, establishment, 2–6

principles, 81–82

processes. See Semiautomated

investment processes

risk-return trade-off, 81

strategy, 41

selection, 2

vehicles, 51