Glossary

Symbols

(functional) excess risk, 39
0-1 loss, 29.1.2

A

absence of arbitrage, 0b.1.3
absolute score, 19.9, 19.9
abstract Bayes theorem, 19.14.3
accounting signals, 13.5
accrued interest, 0a.2.1
accuracy
    binary classification, 29.4
action, 24.2
    Bayesian, 24.2.2
    minimax, 24.2.3
activation function, 39.4.1
activity time, 1.8.2
actual cash-flow, 0a.2.3
actual exchange rate, 0a.2.3
actual value, 0a.2.3
adapted basis, 15.1.3
adapted variable
    partition, 19.14.3
adaptive execution algorithm, 10.3.2
additive, 19.12.2
admissible, 37.2.1
algebraic multiplicity, 15.5.4
algebraic Riccati equation, 15.6.6
allocation policy, 6.5
almost everywhere
    function equality, 17.3.1
alpha, 7.3.1
    binary classification, 29.1
alternative beta, 9c
alternative hypothesis, 41.1
analysis of variance, 28.1.10
ancestor, 30.2.4
angle, 15.3.1
    canonical, 22.3.2
    covariance, 22.3.2
    expectation, 22.3.1
anti-monotonic
    function, 16.5.3
arbitrage pricing theory, 0c.3.1
architecture, 39.4.1
area under curve (AUC), 29.1.4
arithmetic Brownian motion with drift, 36.1.3
Arrow-Debreu securities, 0c.1.2
Arrow-Pratt absolute risk aversion function, 7.5.1
ask size, 1.8.1
assets, 6.7.1
at the money, 1.4.2
    foreign exchange market, 1.4.4
augmented view variables, 31.5.3
autocorrelation
    function, 34.1
autocovariance
    function, 34.1
autoencoder, 30.1
autoregressive conditional duration, 2.6.2
autoregressive fractionally integrated moving average, 2.4
autoregressive moving average process
    autoregressive
        univariate (AR), ??, ??
    integrated
        multivariate (VARIMA), relationships-varma-vma-var
        univariate (ARIMA), ??
    moving average
        univariate (MA), ??, ??
    multivariate (VARMA), 34.3.2
    univariate (ARMA), 34.3.1
autoregressive of order one, 34.2
auxiliary measure, 19.10

B

Bachelier, 0e.3.1
backpropagation, 18.2.3, 39.4.1
backward cash-flow-adjusted value, 0a.1.5
backward/forward exponential weighted moving average, 3.10.6
bag of words, 30.2.3
bagging, 40.4.1
balance sheet, 6.7.1
balanced, 40.1
bandpass filter, 34.5.3
bandwidth, 3.1.2
    kernel density estimate, 3.2.3
bandwidth matrix, 3.1.2
base case, 31.6.1
base distribution, 31.1.1
base measure, 19.10
basis, 12.4.3, 15.1.2
    canonical, 15.1
    orthonormal, 15.3.2
basis denominator, 12.4.3
basis instruments, 0c.1.1
Bayes classifier, 29.2.3
Bayes error
    expected error, 38.1.2
    frequentist approach, 38.4.2
    frequentist prediction, 38.3.2
Bayes risk, 24.3.1
Bayes theorem, 19.3.2
Bayesian networks, 30.2.6
benchmark, 12.5.1
best ask, 1.8.1
best bid, 1.8.1
best prediction, 15.3.3
beta
    binary classification, 29.1
beta conditions
    projection coefficients, 15.3.2
    projection equation, 15.3.2
beta distortion index, 7.8.2
beta-adjusted excess return, 12.5.2
bets, 8b.4
between-cluster/group variance, 28.1.10
Bhattacharyya coefficient, 40.4.4
bias, 38.1.2
    binary classification, 29.1
bias reduction, 39
bid size, 1.8.1
bid-ask spread, 10.1
bilateral value adjustment, 6.2
binary classification, 29.1.5
binary classifier, 29.1.4
binary partition encoder, 19.9
binning, 1.8.3
binomial inverse theorem, 15.7.4
binomial tree, 2.1.2
bins, 1.8.3, 25.2
bins width, 25.2
Black-Merton-Scholes model, 0e.3.2
Bochner’s theorem, 17.6.1
bond yield, 5.3.2
bootstrap aggregating, 40.4.1
Borel sets, 19.14.1
boundedness, 31.1.7
breadth, 9c.5.2, 39.4.1
breakdown point, 3.7.2
Brier scoring rule, 29.3.1
Brownian motion, 2.1.1
Buhlmann pricing equation, 0b.5
    expectation, 0b.5
Buhlmann principle, 0d.2.4
butterfly, 0c.1.2, 1.4.4

C

calendar signal, 13.5
calibrate, 0e
call option, 1.4.1
canonical correlation matrix, 23.3.1
canonical parameters, 19.10
capital asset pricing model, 0c.2
capital gain, 0a.1.6
cardinality, 17.1.2
cardinality constraint, 18.4
carry signal, 13.1
CART, 39.3.1
cash-flow function, 5.1
cash-flow-adjusted value, 0a.1.5
categorical distributions, 19.9
categories, 19.9
Cauchy distribution, 19.6.2
Cauchy-Schwarz inequality, 15.3.1
causal, 34.5.3
center of the bin, 25.2
central tendency, 22.5.1
    affine equivariant, 22.4.1, 22.4.2
certainty-equivalent, 7.5
certainty-equivalent principle, 0d.2.2
chain rule, 30.2.6
    gradient, 16.1.2
    matrix-variate, 16.1.3
    multivariate, 16.1.2
    univariate, 16.1.1
change of variable formula
    multivariate, 16.4.3
    univariate, 16.4.1
characteristic equation, 15.5.1
characteristic function
    multivariate, 19.1.3
    univariate, 19.1.2
characteristic matrix, 9c.4
characteristic polynomial, 15.5.1
characteristic portfolio, 9c.2
characteristic portfolios, 9c.4
Chebyshev’s inequality, 22.2.7
chi-squared distribution, 19.5.1
child, 30.2.4
child orders, 10
Cholesky decomposition, 15.6.5
Cholesky root
    lower triangular, 15.6.5
    upper triangular, 15.6.5
CIR, 36.2.2
claims, 1.6
classes, 19.9
classical-equivalent, 37.2.1
classification
    multinomial classification, 29.2
classification and regression trees, 39.3.1
Classification trees
    splitting criterion, 29.3.9
classification trees, 29.3.9
clean price, 0a.2.1, 0a.2.1
clique, 30.2.4
clique factorization, 30.2.5
clustering, 30.1.2
co-monotonic
    function, 16.5.3
    variables, 20.2.4
co-monotonic additivity, 7.2
coarseness level, 25.2
codes, 30.1
coherent satisfaction measure, 7.9.1
    coherent probability measure, 7.9.1
    worst case expectation representation, 7.9.1
cointegrated, 33.1
cointegrated space, 2.8.1
cointegration signal, 13.3.3
cointegration vector, 2.8.1
    multivariate process, 33.1
collateral, 6.8.1
commonalities, 26.4.5
comparable instruments, 0e
complete, 0c.1.1
complete metric space, 17.3.1
compound distribution, 19.3.4
compound Poisson process, 36.1.4
compounded rate of return
    (instantaneous) compounded rate of return, 12.4.6
    average compounded rate of return, 12.4.6
compounded return, 12.4.1
Comprehensive Capital Analysis and Review, 6.6
concave down function
    univariate, 16.6.1
concave function
    multivariate, 16.6.2
    univariate, 16.6.1
concave up function
    univariate, 16.6.1
concavity, 7.2
condition number, 3.5.2
conditional cdf, 19.3.1
conditional covariance, 19.3.3
conditional distribution of variable, 19.3.1
conditional excess distribution, 7.6.2
conditional expectation, 19.3.3
    with respect to the events set, 19.14.3
conditional independence, 30.2, 40.1
conditional pdf, 19.3.1
conditional principal component analysis, 26.6.16
conditional principal directions, 26.6.16
conditional principal variances, 26.6.16
conditional probability, 19.3.1
    with respect to the events set, 19.14.3
conditional statistical feature, 19.3.3
conditional value at risk, 7.8.2
conditioning-marginalization, 31.1.3
cone, 18.3.1
confusion matrix, 29.1
conic programming, 18.3.1
conjugate distribution, 37.2.3
consistency with weak dominance, 7.2
consistent with q-th order dominance, 7.2
constancy, 7.2
constant proportion portfolio insurance, 9d.4.1
constraint set, 18.1
contingency table, 29.2.1
continuous-state distributions, 2.1
control variable, 27.1.3
convex function
    multivariate, 16.6.2
    univariate, 16.6.1
convex programming, 18.3
convex set, 18.3
convexity, 5.3.2, 5.3.2
    effective key-rates, 5.3.2
    risky investment, 9d.6
    satisfaction/risk measures, 7.2
convolution, 17.3.4
    cyclic, 17.3.4
    discrete, 17.3.4
    periodic, 17.3.4
coordinate descent, 18.4.7
copula, 20.2.2, 20.2.2
copula-marginal combination, 20.4.2
copula-marginal distributions, 20.4.2
copula-marginal separation, 20.4.1
copula-pdf, 20.2.3
Cornish-Fisher approximation, 7.6.2
Cornish-Fisher expansion, 7.6.2
correlation, 23.3
correlation function, 23.3
correlation matrix, 23.3
cost of equity, 0e.2.1
cost of trading, 9d.6
counterparty credit risk, 6.2
coupon, 1.10.2
coupon bond, 1.3.1
CoVaR, 6.6.1
covariance matrix, 22.2.1
    cross-covariance, 22.2.1
covariance principle, 0b.5
covariant, 21.1.1
covariates, 27.1
Cramer-Lundberg ruin model, 6.7.5
credit ratings, 1.5.3
credit structural model, 459
credit value adjustment , 6.2
critical point, 18.2.1
cross the spread, 10.1
cross-autocovariance
    function, 34.1
cross-entropy, 27.5.1
cross-sectional, 9c, 9c
cross-sectional linear factor model, 26.5
cross-sectional sample median of default probabilities, 1.5.3
cumulant , 4.7.1
cumulative cash-flow, 0a.1.3
cumulative distribution function
    multivariate, 19.1.3
    univariate, 19.1.2
cumulative link, 19.9.2
cumulative monetary amount, 1.8.1
cumulative number of migrations, 1.5.3
cumulative P&L, 1.9
cumulative signed volume, 1.8.1
cumulative trade sign, 1.8.1
cumulative volume, 1.8.1
currency carry trade, 5.2.2
curvature, 1.3.5
curve/surface signals, 13.5
cutoff classifier, 29.1.4

D

data, 37.1
debt, 6.7.1
debt value adjustment, 6.2
decay, 1.3.5
decision function
    admissible, 24.3.3
    deterministic, 24.3
    randomized , 24.3
decision problem
    data-driven, 24.3
    no-data, 24.2
decision region
    binary classification, 29.2.3
decision regions
    multinomial classification, 29.2
decoder, 30.1
decreasing function, 16.5.1
    entrywise, 16.5.2
    matrix-valued, 16.5.2
    strictly, 16.5.1
degree of reversal, 9c.2.3
delta, 1.4.4
delta p, 29.4
delta rule, 39.4.1
dependent variables, 26.1, 27.1
depth, 39.4.1
derivative
    directional, 16.1.2
    first, 16.1.1
    higher order, 16.1.1
    partial, 16.1.2
    second, 16.1.1
    total, 16.1.2
    univariate, 16.1.1
descendant, 30.2.4
design of experiments, 27.1.3
determinant, 15.2.3
deviation
    expectile, 22.5.2
    maximum, 22.5.2
    mean absolute, 22.5.2
    median absolute, 22.5.2
    subquantile, 22.5.2
differentiable function
    multivariate, 16.1.2
    univariate, 16.1.1
dimension, 15.1.2
Dirac delta, 17.3.2
direct sum, 15.1.3
directed graph, 30.2.4
dirty price, 0a.2.1
discount, 1.10.2
discount factor, 0a.2.3
discount function, 5.1
discounted cash-flow, 0e.2.1
discounted cash-flow adjusted value, 0d.3.1
discounted payoff, 0d.2
discrete-state distributions, 2.1
discrete-state random walk, 2.1.2
discretized pdf, 25.2
discriminant
    linear regression, 28.3.5
    regression, 28.3.4
discriminant classification, 29.3.5
discriminant model, 27.2.2, 27.2.2
discriminant next-step model, 2.7.6
discriminant variables, 19.9
dispersion, 22.5.1
    affine equivariant, 22.4.1
    modal, 22.4.1
distance, 15.4.2
    absolute, 15.4.2
    covariance, 22.3.2
    Euclidean, 15.3.1
    expectation, 22.3.1
    identity of indiscernibles, 15.4.2
    Lp, 22.6.2
    Mahalanobis, 15.4.2
    p, 15.4.2
    subadditivity, 15.4.2
    symmetry, 15.4.2
    triangle inequality, 15.4.2
distance matrix, 29.2.1
distance to default, 2.3.4
distorted cdf
    satisfaction indices/risk measures, 7.8.1
distorted pdf
    satisfaction indices/risk measures, 7.8.1
distortion function, 7.8.1
distortion principle, 0d.2.3
distortion satisfaction measure, 7.8.1
distribution function, 19.14.1
distributional view, 31.1.3
divergence, 15.4.3
    Bregman, 15.4.3
    difference, 15.4.3
    extended f, 15.4.3
    identity of indiscernibles, 15.4.3
    separable, 15.4.3
diversification distribution, 8b.4
diversity, 40.4.4
dividend-adjusted value, 1.1
    stocks, 0a.1.5
divisors, 19.12.3
dollar duration, 6.1.3
dollar-neutral constraint, 9c.2.2
domain
    circle, 17.1.1
    continuous, 17.1.1
    cyclic group, 17.1.1
    discrete, 17.1.1
    frequency, 17.4
    time, 17.4
    torus, 17.1.1
dominant-residual LFM, 26.1.2
dot product, 15.3
drawdown, 12.6
    maximum (absolute) drawdown, 12.6
    maximum percentage drawdown, 12.6
    percentage drawdown, 12.6
dual Legendre, 21.1.3
dually flat, 21.1.3
duration, 5.3.2
    effective key rates, 5.3.2
DV01, 6.1.3
dynamic allocation, 9c
dynamic conditional correlation, 3.9.3
dynamic linear factor model, 32.2
dynamic models, 32
dynamic principal component, 32.6
dynamic regression model, 32.4

E

e-affine coordinates, 21.1.2
e-flat, 21.1.2
e-geodesic, 21.1.2
EBITDA, 6.7.2
economic capital, 7.12
economic net income, 6.7.2
edges, 30.2.4
effective delta, 5.3.3
effective duration
    effective, 5.3.2
effective number of bets, 8b.4
effective number of scenarios, 3.1.4
effective rank, 31.1.6
effective rho, 5.3.3
    key-rates, 5.3.3
effective volga, 5.3.3
efficient market hypothesis, 2.1
eigenfunction, 17.5.2
eigenvalue, 15.5.1
    linear transformation, 15.5.1
eigenvector, 15.5.1
    linear transformation, 15.5.1
elastic net, 18.4.7, 40.2.2
    constrained generalized elastic net, 18.4.7
elicitability
    satisfaction measures, 7.2
ellipsoid, 22.2.4
    expectation-covariance, 22.2.4
    location-dispersion, 22.4.2
ellipsoid test for invariance, 35.1
elliptical distribution, 19.7.1
EM algorithm
    population, 37.4.6
encoder, 30.1
enterprise value, 0e.2.2
equal in distribution
    multivariate, 19.1.3
    univariate, 19.1.2
equilibrium performance model
    Black-Litterman, 14.11
equilibrium returns
    Black-Litterman, 14.7
equity, 6.7.1
equity book value, 6.7.1
equivalent optimization problem, 18.5.1
ergodic (in mean), 33.1
Erlang process, 36.1.4
error, 38.1.2
    multivariate, 22.5.3
    multivariate mean absolute, 22.5.3
    multivariate mean squared, 22.5.3
    posterior error, 38.1.3
    univariate, 22.5.1
    univariate mean squared, 22.5.1
error correction, 34.2.7
error prediction matrix, 26.2.6
Esscher principle, 0d.2.4
estimable, 7.2
estimate, 38.1.1
estimation, 27.3
estimation model, 3.4
    Bayesian estimation, 37.2.1
estimation risk, 24.3.4
estimation set, 40.1
    point prediction, 38.3.1
    predictive distribution, 38.4.1
estimation uncertainty, 37.2.1
estimator, 38.1.1
European-style derivatives, 1.4
evidence, 30.2
    maximum likelihood, 37.1
evidence lower bound, 37.4.5
ex-dividend date, 0a.1.2
exotic beta, 9c
expectation
    function, 34.1
    multivariate, 22.2.1
    univariate, 22.1.1
expectation rule, 19.8.3
expectation-maximization, 37.1.3
    expectation step, 37.1.3
    maximization step step, 37.1.3
expected drawdown, 7.3.1
expected overperformance, 7.3.1
expected shortfall, 7.8.2
expected utility, 7.5
expected value of the process variance (EVPV), 28.1.10
expectile, 19.1.2
expectile-VaR, 7.9.2
expiry, 1.4
explanatory variables, 27.1
exponential decay probabilities, 3.1.1
exponential family distribution, 19.10
exponential kernel, 3.1.2
exponential of the entropy, 3.1.4
exponential operator, 16.3.1
exponential principle, 0d.2.2
exponential tilting, 31.1.5
exponentially weighted moving average, 3.2.4
exponentially weighted moving correlation, 3.2.4
exponentially weighted moving covariance, 3.2.4
exponentially weighted moving quantile, 3.2.4
exponentially weighted moving standard deviation, 3.2.4
exposure, 6.1.3
    portfolio P&L, 9c.2
    risky investment, 9d.6
exposure at default, 1.5.2
extrema
    local, 18.1
    relative, 18.1
extreme value theory, 7.6.2

F

f-divergence, 21.1.4
F-measure
    binary classification, 29.4
F1 score
    binary classification, 29.4
face value, 1.3.1
factor analysis, 3.5.6
    confirmatory, 26.4
    equamax, 26.4.4
    exploratory, 26.4
    orthomax, 26.4.4
    parsimax, 26.4.4
    quartimax, 26.4.4
    varimax , 26.4.4
factor analysis matrix, 3.5.6
factor loadings, 26.1
factor premia, 9c.4.2
factor premium, 9c.1
factor-analysis linear factor model, 26.4.1
factor-replicating portfolios
    arbitrage pricing theory, 0c.3.1
factors, 9c, 27.1
    linear factor model, 26.1
fair value, 0a.1.2
fallout, 29.1
false negative
    accuracy, 29.1
    probability, 29.1
    rate, 29.1
false positive
    accuracy, 29.1
    probability, 29.1
    rate, 29.1
feature engineering, 28.1
feature map
    canonical, 17.7.2
    Mercer, 17.7.2
Feller condition, 36.5.1
filter, 34.5
    backward shift
        polynomial, 15.8.2
    linear time invariant , 34.5.3
filtering, 27.3
filtration, 33.4
    adapted process, 33.4
        (fully-recombining) binomial tree, 33.4t
        (fully-recombining) tree, 33.4t
        martingale, 33.4
    Radon-Nikodym process
        martingale, finite-discrete-time-stoch-process-sec
financial instrument, 0a.1.1
finite difference
    backward first order, 16.2.1, 16.2.2
    central first order, 16.2.1, 16.2.2
    central second order, 16.2.1, 16.2.2
    forward first order, 16.2.1, 16.2.2
first in, 8b.1.1
first order criterion, 18.2.1
first order differential, 16.1.2
    matrix-variate, 16.1.3
Fisher consistent, 3.7.1
Fisher discriminant analysis (FDA), 29.1.8
Fisher information distance, 21.1.4
Fisher’s linear discriminant, 29.1.8
flexible probabilities, 3
    estimation, 19.8
forecast, 26.1
    point, 27.2
    probabilistic, 27.2
forecasting
    inference, 27.3
        multi-period, 32.1
foreign exchange function, 5.1
foreign exchange rate, 1.2.1
forward, 1.2.2
forward cash-flow-adjusted value, 0a.1.5
forward exchange rate, 1.2.1
forward rate, 1.10.2
forward swap, 1.3.1
forward variance swap rate, 1.4.6
Fourier transform, 17.4
    convolution theorem, 34.179
    discrete (DFT), 17.4.5
    discrete time (DTFT), 17.4.3
    Fourier series, 17.4.4
    integral, 17.4.2
    inverse, 17.4
fractional Brownian motion, 36.4
Frechet derivative, 17.8.2
    second order, 17.8.3
Frechet-Hoeffding bounds, 23.1.1
frequency response function, 34.5.3
frequentist risk, 24.3.1
full-investment, 9c.2.2
fully constrained LFM, 26.6.17
function space, 17.2.1
    addition, 17.2.1
    scalar multiplication, 17.2.1
functional, 17.8
functional derivative, 39.5
fundamental accounting equation, 6.7.1
fundamental law of active management, 9c.5.2
fundamental linear factor model, 26.5
fundamental signals, 13.5
fundamental theorem of asset pricing, 0b.2.2
    martingale pricing formula, 0c.4.3
fundamental theorem of calculus
    first, 16.4.2
    second, 16.4.2
funding risk, 6.2
funding value adjustment, 6.2

G

gamma distribution, 19.5.2
Gateaux derivative, 17.8.1
Gaussian kernel, 3.1.2, 3.2.3
Gaussian process, 19.4.2
generalized autoregressive conditional heteroscedastic, 2.6.1
generalized excess return, 12.5.2
generalized linear models (GLM), 28.3.6
generalized linear return, 12.4.3
generalized method of moments
    iterated GMM, 3.5.5
generalized method of moments with flexible probabilities (GMMFP) estimate, 3.6.2
    minimization, 3.6.3
generalized negative entropy, 27.5.1
generalized Pareto distribution, 7.6.2
generalized weight, 12.4.4
generative model, 27.2.2
generative next-step model, 2.7.6
generator
    Markov chain, 36.3.1
    matrix, 15.2.3
generic position, 0e.1.3
geometric Brownian motion, 5.1.1
geometric multiplicity, 15.5.4
Gibbs distribution, 30.2.5
Gini coefficient, 29.1.4
Giny impurity, 29.3.3
glasso, 3.5.5
    Tikhonov, 40.2.3
Glivenko-Cantelli theorem, 3.2.1
global minimum variance portfolio, 9a.3
Gordon growth model, 0e.2.1
grade, 20.1
grades, 20.2.1
gradient, 16.1.2
    matrix-variate, 16.1.3
    vector-valued function, 16.1.2
gradient descent, 18.2.3
    stochastic, 18.2.3
Gram matrix, 15.6.1
Gram-Schmidt process
    backward, 15.6.5
    forward, 15.6.5
Gramian, 15.6.1
grand mean, 3.5.1
graph, 30.2.4
graphical lasso, 3.5.5
Greeks, 5.3
gross exposure, 6.1.3
group
    general linear, 15.2.3
    orthogonal, 15.3.4
    special orthogonal, 15.3.4
    unitary, 15.3.4
growth stocks, 13.2.1