The Mathematics of Financial Modelingand Investment Management

Index Page 777 Wednesday, February 4, 2004 1:13 PM

Index 777

Tracking errors (Cont.)

bond portfolio strategies,

relationship, 651–652

determinants, 654

minimization, 558

multi-factor risk approach, 9

portfolio beta, 556–560

Tracking portfolio, 564

Trade horizon, 734

Trading. See Pair trading

activity, 532

constraints, 664

costs, control, 552

date, 180

gains, 443–445

halts, 28

restrictions, 28

strategies, 403–404, 443–445

Traditional asset classes, 3–4

Training data, 318

Transactions

costs, 32, 63. See also Capital

market

frequency, 23

Transforms. See Fourier trans-

forms; Integrals; Laplace

transform

Transition matrix, 542, 703–706

Transpose. See Matrices

operation, 153–154, 156–157

Treasury yield curve. See U.S.

Treasury yield curve

Trend stationary series, 309. See

also Multidimensional

trend stationary series

Trends. See Integrated trends

Triangular matrix. See Lower

triangular matrix; Upper

triangular matrix

Turnbull, Stuart, 684, 696, 698,

703, 730. See also Jar-

row-Turnbull Model

Turner, Christopher, 690

Two-factor stochastic volatility

model, 741

Two-sided Laplace transform,

134–135

Two-sided transform, 136

Two-stage stochastic optimiza -

tion problem, 676–677

Unbiased expectations theory,

616–617

Uncertainty, 737

representation, mathematics

(usage), 165–167

Uncorrelated variables, 188

Underlying asset

current price, 68

position, 65

Underwriting. See Securities

Undiversification, quantification,

472



Unexpected Loss (UL), 391, 747

Unique risk, 515

Uniqueness, theorem, 274

Univariate ARMA models. See

Nonstationary univariate

ARMA models; Stationary

univariate ARMA models

Univariate marginal distribu -

tions, 732

Univariate moving average. See

Stationary univariate mov-

ing average

Univariate normal distribution, 194

Univariate stationary series, 288–

289



Univariate time series, 340

University of Chicago, 81

University of Dijon, 79

University of Lausanne, 77

Unstructured data/information, 16

Unsystematic risk, 515

elimination, 556

factors, 86

Upper Riemann sum, 127

Upper triangular matrix, 148

Upstairs market, 50

Uryasev, Stanislav, 749

U.S. bonds, 3

U.S. Department of Energy (DOE),

11



U.S. Federal Reserve, 754–755

U.S. government bonds, 3

U.S. municipal bonds, 4

U.S. Office of the Controller of

the Currency. See Quar-

terly Derivatives Report

U.S. Treasury bonds, 600, 606

U.S. Treasury market, 632

U.S. Treasury spot rates, 606

U.S. Treasury strips, 667

U.S. Treasury yield curve, 599

construction, 600

measurement, 601

usage, 602. See also Spot rates

U.S. Treasury zero-coupon

bonds, 667

Utility functions, 77, 482–484,

487–490. See also Linear

utility function; Loga-

rithmic utility function;

Power utility function;

Quadratic utility func-

tion; Time-separable util-

ity function

defining, 82

Utility maximization framework,

491



Valuation. See American options;

European simple derivatives

formula, 429

principles. See Debt instruments

Value

stocks, 3

understanding, 83–85

Value at Risk (VaR), 748. See

also Conditional VaR

noncoherence, 749

Value Line Composite Average

(VLCA), 46, 47

Van Meer, Robert, 751

van Norden, Simon, 545

Vanguard Group, 650

Vapnik, Vladimir N., 317, 319

Vapnik-Chervonenkis (VC) the -

ory. See Learning

Vardharaj, Raman, 532, 556, 558,

582, 583, 586, 588. 590

Variable interest rates, convex -

ity, 120

Variable short-term rates, 619

Variables, 101. See also Gaussian

variables; Random vari-

ables; Stochastic variables;

Uncorrelated variables

calculus, usage, 138–139

characteristic function, 193

co-movement, 189

covariance, 328

definition, 101

IID sequence, 537

sum, 191–193

Variance portfolios. See Mini-

mum variance portfolios

Variance-covariance matrix, 82, 147,

324, 329. See also Diagonal

variance-covariance matrix;

n×n symmetrical variance-

covariance matrix

eigenvalue, 336

modeling, 347

PCA, performing, 543

usage, 335, 534

values. See Factor variance-

covariance matrix

Variances

growth, 277

standard deviations, substitu -

tions, 481

Variation margin, 58, 62

Variational methodologies, 674

Variational principle, 673–674

Variations. See Total variation

calculus, 201–202, 212–214

VARMA model, 542

Vasicek, Oldrich, 636

Vasicek Model, 635, 636

Vector Autoregressive (VAR). See

One-lag stationary VAR

models, 316, 338, 348. See

also Global VAR model;

Stationary VAR model

usage, 541

Vector support machines, 547

Vectors, 141–144. See also Column

vectors; Eigenvectors; Ran-

dom vectors; Row vectors

autoregressive models, 338–339

components, 141–142

Euclidean length, 143

norm, 143

operations, 153–156