The Mathematics of Financial Modelingand Investment Management

(Brent) #1

Index Page 770 Wednesday, February 4, 2004 1:13 PM


770 Index

National Association of Insurance
Commissioners (NAIC)
scenarios, 675
National Association of Securi-
ties Dealers Automated
Quotation (NASDAQ)
Composite index, 47
system, 46–47
Natural numbers, one-to-one
relationship, 100
NAV. See Net asset value
n-dimensional Borel sets, 227–
228

N-dimensional Brownian motion,
634

n-dimensional Brownian motion,
228

n-dimensional Cartesian space, 143
n-dimensional cumulative distri -
bution function, 176
n-dimensional distribution func -
tion, 176
n-dimensional Euclidean space, 170
N-dimensional Itô process, 634, 638
N-dimensional price process, 458
n-dimensional probability den -
sity, 176
n-dimensional real space, 179
n-dimensional space, 175
n-dimensional vector, 97, 158
n-dimensional zero-mean white
noise process, 293, 307
Negative sign restriction, 208.
See also Nonnegativity
sign restriction
Net asset value (NAV), 42
Neural networks, usage, 345
New York Stock Exchange (NYSE),
42–43, 46
Composite Index, 46, 94
index, 521
market capitalization, 95
Newton, Isaac, 91
Newton-Raphson iterative tech -
nique, 596
Nielsen, Steen, 344
No-arbitrage models, 634
Noise. See Colored noise; White
noise
multiplicative nature, 383
term, 328, 576
Nominal rate, 52
Nonanticipativity property, 215
Noncorporate issuers, 27
Non-decreasing function, 363
Nondiversifiable risk factors, 86
Nonequality constraints, 211
Nonfactor error term, 533
Nonfinancial businesses, 34–35
Non-Gaussian processes, 387
Nonhomogeneous system, 150
Non-IID framework, 384
Nonliability driven entities,
benchmarks, 40–41

Nonliability driven objectives, 2
Nonlinear dynamics, 256–259
chaos, 573–574
development, 243
models, 573–574. See Prices;
Returns
Nonlinear models, 288
Nonlinear pattern recognition.
See Statistical nonlinear
pattern recognition
Nonnegative adapted process, 404
Non-negative diagonal elements,
162

Nonnegative integer values, 371
Nonnegativity sign restriction, 207
Nonobservability, consequences,
521

Nonreproducible assets, 21–22
Nonsingular variance-covariance
matrix, 293
Nonstandard analysis, 107
Nonstationary models. See Finan -
cial time series
Nonstationary multivariate ARMA
models, 304
Nonstationary process. See Inte -
grated nonstationary process
Nonstationary series, 295–297, 304
Nonstationary univariate ARMA
models, 300–301
Nonsystematic factor risk, 652
Nonsystematic risk, 513–516, 518
exposure, 660
reduction, 661
Nonterm structure
factors, 656
risk factors, 653
Nontrivial solutions, 161
Non-U.S. bonds, 3
Non-U.S. common stocks, 3
Non-U.S. foreign stocks, 3
Normal distribution, 194. See
also Joint multivariate
normal distribution; Stan-
dard normal distribution;
Univariate normal distri-
bution
Normal probability. See Cumu-
lative normal probability
Normal random variable, 196–197
Normal yield curve, 612
Normality assumption, relax -
ation, 491–492
Normally distributed IID vari-
ables, 534
Normative theory, 471
Notional amount, 69
Notional principal amount, 69–71
Nth to default swaps, 681–682
n-tuples, 96–98, 168
Null hypothesis, usage, 340
Numeraire, definition, 101
Numerical algorithms, 206–212

Numerical solutions. See Ordi-
nary differential equa-
tions; Partial differential
equations
Numerical values, 101
N-vector process, 460
Objective function, 201
Observations, definition, 306
Observed information matrix, 322
Odd lots, 664
Office of the Comptroller of the
Currency, Quarterly
Derivatives Report, 1

Ohlson, J.A., 574
O’Kane, Dominic, 711
Okazaki, M.P., 388
Oksendal, Bernd, 268
Olesen, Overgaard, Jan, 344
Olsen & Associates. See High-
frequency data studies
One price, law. See Law of one
price
One-dimensional Brownian motion,
228, 271
One-dimensional Itô formula,
272–274
One-dimensional standard Brown -
ian motion, 226, 232
One-dimensional zero-mean
white noise process, 289
One-factor equilibrium model, 636
One-factor model, 632
One-factor term structure mod -
els, examples, 635–638
One-lag stationary VAR, 537
One-period finite-state market, 399
One-period investment horizon,
513

One-sided Laplace-transform,
application, 248–249
One-sided transform, 136
Onigo, Iris, 10
On-the-run maturities, 601
On-the-run yield, estimation, 601
Open-end funds, 42
Operation, 153
Operational efficiency, 32–34
Operational risk, 746–747
Opportunity costs, measurement,
34

Optimal control theory, 212–214
Optimal portfolio
CML, usage, 482–485
selection, 484–485
Optimal solution, 207
Optimal value, 207
Optimization, 201. See also
Multiperiod stochastic
optimization; Scenario
algorithm, 660
application, 660–661
models. See Myopic one-period
optimization models
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