Index
Absence of arbitrage principle, I:, I:. See also arbitrage, absence of
ABS/MBS (asset-backed securities/mortgage-backed securities), I:, I:
cash flow of, III:
comparisons to Treasury securities, III:
modeling for, III:
Accounting, II:, II:
Accounting firms, watchdog function of, II:
Accounts receivable turnover ratio, II:
Active-passive decomposition model, III:, III:, III:
Activity ratios, II:, II:
Adapted mesh, one year to maturity, II:
Adjustable rate mortgages (ARMs). See ARMs (adjustable rate mortgages)
Adjustments for changes in net working capital (ANWC), II:
Adverse selection, III:
Affine models, III:
Affine process, basic, I:, I:
Agency ratings, and model risk, II:
Airline stocks, II:, II:, II:, II:
Akaike Information Criterion (AIC), II:, II:
Algorithmic trading, II:
Algorithms, II:, II:, III:
Allied Products Corp., cash flow of, II:
α-stable densities, III:, III:
α-stable distributions
defined, II:
discussion of, III:
fitting techniques for, II:
properties of, II:
simulations for, II:
subordinated representation of, II:
usefulness of, III:
and VaR, II:
variables with, II:
α-stable process, III:
Alternative risk measures
proposed, III:
Amazon.com
cash flows of, II:, II:
American International Group (AIG), stock prices of, III:
Amortization, II:, III:
Analysis
and Barra model, II:
bias in, II:
common-size, II:
crisis-scenario, III:
to determine integration, II:
formulas for quality, II:
fundamental, II:, II:, II:
interpretation of results, III:
mathematical, I:
model-generated, III:
multivariate, II:
statistical, I:, II:
sum-of-the-parts, II:
vertical vs. horizontal common-size, II:
Analytics, aggregate, II:
Anderson, Philip W., III:
Annual percentage rate (APR), II:, II:
Annual standard deviation, vs. volatility, III:
Annuities
balances in deferred, II:
from bonds, I:
cash flows in, II:
future value factor, II:
ordinary, II:
present value factor, II:, II:
valuation of due, II:
valuing deterred, II:
Anticipation, in stochastic integrals, III:
Approximation, quality of, II:
APT (arbitrage pricing theory), I:
Arbitrage
absence of, I:, I:, II:
in continuous time, I:
convertible bond, I:
costless profits, I:
costless trades, I:
defined, I:, I:, I:
in discrete-time, continuous state, I:
and equivalent martingale measures, I:
in multiperiod finite-state setting, I:
in one-period setting, I:
pricing of, I:, I:, II:
profit from, I:
and relative valuation models, I:
and state pricing, I:, I:, I:
test for costless profit, I:
trading strategy with, I:
types of, I:
using, I:
Arbitrage-free, III:, III:
Arbitrage opportunities, I:, I:, I:, I:, I:, I:
Arbitrage pricing theory (APT), I:
application of, I:
development of, II:, II:
factors in, II:
key points on, II:
and portfolio optimization, I:
ARCH (autoregressive conditional heteroskedastic) models
and behavior of errors, II:
defined, I:
in forecasting, II:
reasons for, III:
type of, II:
use of, II:
ARCH/GARCH models
application to VaR, II:
behavior of, II:
discussion of, II:
generalizations of, II:
usefulness of, II:
ARCH/GARCH processes, III:
Area, approximation of, II:, II:
ARIMA (autoregressive integrated moving average) process, II:
ARMA (autoregressive moving average) models
defined, II:
and Hankel matrices, II:
linearity of, II:
and Markov coefficients, II:
multivariate, II:, II:
nonuniqueness of, II:
representations of, II:
and time properties, II:
univariate, II:
ARMA (autoregressive moving average) processes, III:
ARMs (adjustable rate mortgages), III:, III:, III:, III:
Arrays, in MATLAB and VBA, III:, III:, III:
Arrow, Kenneth, II:, II:
Arrow-Debreu price, I:. See also state price
Arrow-Debreu securities, I:, I:
Arthur, Bryan, II:
Artificial intelligence, II:
Asian fixed calls, with finite difference methods, II:
Asian options, pricing, III:
Asset allocation
advanced, I:
building blocks for, I:
modeling of, I:
standard approach to, I:
Asset-backed securities (ABS), I:
Asset-liability management (ALM), II:, III:
Asset management, focus of, I:
Asset prices
codependence of, I:
multiplicative model for, I:, I:
negative, I:, I:
statistical inference of models, I:
Asset pricing, I:, I:, I:, I:, II:
Asset return distributions, skewness of, III:
Asset returns
characteristics of, III:
errors in estimation of, III:
generation of correlated, I:
log-normal distribution applied to, III:
models of, III:
normal distribution of, I:
real-world, III:
simulated vector, I:
Assets
allocation of, I:
on the balance sheet, II:
carry costs, I:
correlation of company, I:
current vs. noncurrent, II:
deliverable, I:
discrete flows of, I:
expressing volatilities of, III:
financing of, II:
funding cost of, I:
future value of, I:, I:
highly correlated, I:
intangible, II:
liquid, II:
management of, II:
market prices of, I:
new fixed, II:
prices of, I:
redundant, I:
representation of, II:
risk-free, I:
risky vs. risk-free, I:
shipping, I:
storage of physical, I:, I:, I:
values of after default events, I:
Asset swaps, I:
Assumptions
about noise, II:
under CAPM, I:
errors in, III:
evaluation of, II:
homoskedasticity vs. heteroskedasticity, II:
importance of, III:
for linear models, II:
for linear regression models, II:
in scenario analysis, II:
simplification of, III:
using inefficient portfolio analysis, I:
violations of, I:
zero mean return, III:
Attribution analysis, II:
AT&T stock, binomial experiment, I:
Audits, of financial statements, II:
Augmented Dickey-Fuller test (ADF), II:, II:, II:, II:
Autocorrelation, II:, II:, II:
Autoregressive conditional duration (ACD) model, II:
Autoregressive conditional heteroskedastic (ARCH) models. See ARCH (autoregressive conditional heteroskedastic) models
Autoregressive integrated moving average (ARIMA) process, II:
Autoregressive models, II:
Autoregressive moving average (ARMA) models. See ARMA (autoregressive moving average) models
AVaR. See average value at risk (AVaR)
Average credit sales per day, calculation of, II:
Average daily volume (ADV), II:
Averages, equally weighted, III:
Average value at risk (AVaR) measure
advantages of, III:
back-testing of, III:
boxplot of fluctuation of, III:
and coherent risk measures, III:
computation of in practice, III:
computing for return distributions, III:
defined, III:
estimation from sample, III:
and ETL, III:
geometrically, III:
graph of, III:
higher-order, III:
historical method for, III:
hybrid method for, III:
minimization formula for, III:
Monte Carlo method for, III:
with the multivariate normal assumption, III:
of order one, III:
for stable distributions, III:
tail probability of, III:
Axiomatic systems, III:
Bachelier, Louis, II:, II:, II:, III:, III:
Back propagation (BP), II:
Back-testing
binomial (Kupiec) approach, III:
conditional testing (Christoffersen), III:
diagnostic, III:
example of, II:
exceedance-based statistical approaches, III:
in-sample vs. out-sample, II:
need for, III:
statistical, III:
strengths/weaknesses of exceedance-based, III:
tests of independence, III:
trading strategies, II:
use of, III:
using normal approximations, III:
of VaRs, III:
Backward induction pricing technique, III:
Bailouts, I:
Balance sheets
common-size, II:, II:
information in, II:
sample, II:, II:
structure of, II:
XYZ, Inc. (example), II:
Balls, drawing from urn, III:, III:, III:
Bandwidth, II:, II:
Bank accounts, and volatility, III:
Bank for International Settlements (BIS), definition of operational risk, III:
Bankruptcy, I:, I:, II:
Banks, use of VaR measures, III:
Barclays Global Risk Model, II:, II:, II:
Barra models
E3, II:, II:, II:
equity, II:
fundamental data in, II:
fundamental factor, II:, II:
risk, II:
use of, II:
Barrier options, II:
Basel II Capital Accord, on operational risk, III:
Basic earning power ratio, II:, II:
Bayes, Thomas, I:, I:
Bayesian analysis
empirical, I:
estimation, I:
hypothesis comparison, I:
in parameter estimation, II:
and probability, I:, I:
steps of decision making in, I:
testing, I:
use of, I:
Bayesian inference, I:, I:, II:
Bayesian Information Criterion (BIC), II:, II:
Bayesian intervals, I:, I:
Bayesian methods, and economic theory, III:
Bayes’ theorem, I:, I:
Behaviors, patterns of, II:, III:
BEKK(1,1,K) model, II:
Beliefs
about long-term volatility, III:
posterior, I:
prior, I:, I:
Bellman’s principle, II:
Benchmarks
choice of, II:
effect of taxes on, II:
fair market, III:
modeling of, II:
portfolio, II:
for risk, II:, III:, III:
risk in, II:
tracking of, II:
for trades, II:, III:
use of, I:, II:
Benchmark spot rate curves, I:
Berkowitz transformation, application of, III:, III:
Bernoulli model, parameter inference in, II:
Bernoulli trials, I:, III:, III:
Bessel function of the third kind, III:
Best bids/best asks, II:
Best practices, I:
Beta function, III:
Betas
beta1963, I:
beta1964, I:
beta1963 vs. beta1964, I:
distribution of, III:
meanings of, I:
in portfolios, II:
pricing model, I:, I:
propositions about, I:
robust estimates of, II:
in SL-CAPM models, I:
two beta trap, I:
Bets, unintended, II:, II:, II:, II:
Better building blocks, I:
Bias
from data, II:
discretization error, III:
estimator, III:
survivorship (look-ahead), II:, II:, II:, II:
Bid-ask bounce, II:
Bid-ask spread
aspects of, III:
average hourly, II:
defined, II:
under market conditions, II:
risk in, III:
Binomial experiment, I:
Black, Fischer, II:, II:
Black and Scholes
assumptions of, I:
Black-Derman-Toy (BDT) model
defined, I:
discussion of, III:
features of, III:
interest rate model, III:
as no arbitrage model, III:
use of, III:
Black-Karasinski (BK) model, III:, III:
binomial lattice, III:
defined, I:
features of, III:
forms of, III:
interest rate trinomial lattice, III:
trinomial lattice, III:
Black-Litterman model
assumptions with, I:
derivation of, I:
discussion of, I:
with investor’s views and market equilibrium, I:
mixed estimation procedure, I:
use of for forecasting returns, I:, II:
use of in parameter estimation, II:
variance of, I:
Black-Scholes formula
for American options, II:
with change of time, III:, III:
and diffusion equations, II:
and Gaussian distribution, II:
and Girsanov’s theorem, I:
statistical concepts for, III:
use of, I:, I:
use of in MATLAB, III:, III:
use of with VBA, III:
and valuation models, I:
Black-Scholes-Merton stock option pricing formula, I:
Black-Scholes model
assumptions of, I:, III:
and calibration, II:
for European options, II:, III:
and hedging, I:
and Merton’s model, I:
for pricing options, I:, I:, I:
usefulness of, I:
use of, I:
volatility in, III:
Black volatility, III:, III:
Bohr, Niels, I:
Bond-price valuation model, III:
Bonds
analytical models for, I:
annuities from, I:
calculating yields on, II:
callable, I:, I:, III:, III:
capped floating rate, valuation of, I:
changes in prices, I:
computing accrued interest and clean price of, I:
convertible, I:, I:
corporate, I:, III:
coupon-paying, III:
default-free, I:
determination of value of, I:
discount, I:
effective duration/convexity of, I:, I:
European convertible, I:
in European-style calls, I:
floating-coupon, I:, I:
floating-rate callable capped, I:
floating valuation, I:
full (dirty) price, I:, I:
futures contracts on, I:
general principles of valuation, I:
inflation-indexed, I:, I:, I:, I:
input information for example, III:
interest rate tree for, I:
loading of specific, II:
modeling prices of, I:
and modified or effective duration, III:
nonpar, I:
option-free, I:, I:
options on, I:, I:, I:
planned amortization class (PAC), III:
plot of convertible functions, I:
prediction of yield spreads, II:
price/discount rate relationship, I:, I:
prices of, I:, I:, I:, II:
prices with effective duration/convexity, III:, III:
pricing for, I:, III:
putable, effective duration of, III:, III:
regression data for spread application, II:
relation to CDSs, I:
risk-free, I:
risk-neutral, III:
risk-neutral/equilibrium models for, III:
security levels of, I:
spreads over time, I:
straight, duration of, III:, III:
time path of, I:
valuation of, I:, I:, I:, II:, III:
valuing of, I:, I:, I:
volatility of, I:
Book value, of companies, II:
Bootstrapping
parametric, II:
of spot rate curve, I:
technique for, II:, II:
usefulness of, III:
use of, I:, III:
Borel functions, III:
Borel measures, III:, III:
Borrowers, III:, III:, III:, III:
Borrowing, I:, I:
Boundary conditions, II:
need for, II:
Box-and-whiskers diagrams, use of, III:
Boxplots, use of, III:
Brennen-Schwartz model, III:
Brown, Robert, III:
Brownian motion, geometric (GBM), I:, III:
Brownian motion (BM)
arithmetic, I:, III:, III:
in binomial models, I:
bounds of, III:
canonical, III:
conditions defining, III:
defined, I:, III:
with drift, III:
early work on, II:
excursion of, III:
fractal properties of, III:, III:
generated by random walk, III:
generating paths for in VBA, III:
geometric, III:, III:, III:
and Girsanov’s theorem, I:, I:
in Ito processes, III:
in Ito’s formula, III:
and the Merton model, I:
one-dimensional standard, III:
paths of, III:, III:, III:
path with deviation zones, III:
process of, I:
properties of, III:, III:, III:
in randomness calculations, III:
and stochastic integrals, III:
time-changed, III:
usefulness of, III:
use of, I:
variants of, III:
Bubbles, discovering, II:
Burmeister-Ibbotson-Roll-Ross (BIRR) model, II:
Burnout effect, III:, III:, III:
Burnout factor
initializing of, III:
Business cycles, I:, I:, II:, II:
Businesses, correlation within sectors, I:
Butterfly’s wings, effect of, II:
Calculus, stochastic, I:
Calendarization, II:, II:
Calibration
of derivatives, I:
effect of, III:
under GIG model, II:
of local volatility, II:
need for, III:
to short forward curve, III:
Callable bonds, I:
Call options
defined, I:
discrepancy measures across maturities of, II:
early exercise of American-style, I:, I:
European, I:, I:, I:, I:, II:, II:
1998 prices of, II:
value of, I:
Calls
American-style, I:, I:
error on value of, II:
European-style, I:, I:, I:
Canonical correlation analysis, I:
Capital asset pricing model (CAPM). See CAPM (capital asset pricing model)
Capital expenditures coverage ratio, II:
Capital gains, taxes on, II:
Caplets, I:, III:
CAPM
multifactor, II:
CAPM (capital asset pricing model). See also Roy CAPM; SL-CAPM
application of, I:
areas of confusion, I:
for assessing operational risk, III:
in asset pricing, II:
defined, I:
and discount factor model, I:
and investor risk, I:
using assumptions under, I:
Caps
defined, I:
value of, I:, III:
valuing of, with floors, I:, I:
Carry, I:, I:
Carry costs, I:, I:, I:, I:, I:, I:. See also net cost of carry
CART (classification and regression trees)
defined, II:
example, input variables for, II:
example, out-of-sample performance, II:
fundamentals of, II:
in stock selection, II:
strengths and weaknesses of, II:
uses of, II:
Cash-and-carry trade, I:, I:, I:
Cash concept, II:
Cash flows
accounting for, III:
analysis of, II:, III:
for bond class, III:
of bonds, I:
cash flow at risk (CFaR), III:
classification of, II:
defined, I:, II:, III:
direct vs. indirect reporting method, II:
discounted, I:
discrete, I:
distribution analysis vs. benchmark, III:
estimation of, I:, II:
expected, I:
factors in, III:, III:
form residential mortgage loans, III:
futures vs. forwards, I:
future value of, II:
influences on, III:
interest coverage ratio of, II:, II:
interim, I:
for loan pool, III:
measurement of, II:, III:
monthly, III:, III:
net free (NFCF), II:, II:
in OAS analysis, I:
perpetual stream of, II:
sources of, II:, II:
in state dependent models, I:
statement of, II:, II:
time patterns of, II:
and time value of money, II:
time value of series of, II:
for total return receivers, I:
for Treasuries, I:, III:
types of in assessing liquidity risk, III:
use of information on, II:
valuation of, II:
vs. free cash flow, II:
Cash flow statements
example of, II:
form of, II:
information from, II:
reformatting of, II:
restructuring of, II:
sample, II:
use of, II:
Cash flow-to-debt ratio, II:
Cash-out refinancing, III:, III:
Cash payments, I:, III:
Categorizations, determining usefulness of, II:
Cauchy, Augustin, II:
Cauchy initial value problem, II:, II:, II:, II:
CAViaR (conditional autoregressive value at risk), II:
CDOs (collateralized debt obligations), I:, I:, III:, III:
CDRs (conditional default rates)
in cash flow calculators, III:
defaults measured by, III:
defined, III:
monthly, III:
projections for, III:
in transition matrices, III:
CDSs (credit default swaps)
basis, I:
bids on, I:
cash basis, I:
discussion of, I:
fixed premiums of, I:
hedging with, I:
illustration of, I:
initial value of, I:
maturity dates, I:
payoff and payment structure of, I:
premium payments, I:, I:
pricing models for, I:
pricing of by static replication, I:
pricing of single-name, I:
quotations for, I:
risk and sensitivities of, I:
spread of, I:
unwinding of, I:
use of, I:, I:, II:
valuation of, I:
volume of market, I:
Central limit theorem
defined, I:, III:, III:
and the law of large numbers, III:
and random number generation, III:
and random variables, II:
Central tendencies, II:, II:, II:
Certainty equivalents, II:, II:
CEV (constant elasticity of variance), III:, III:, III:
Chambers-Mallows-Stuck generator, II:
Change of measures, III:, III:
Change of time methods (CTM)
applications of, III:
discussion of, III:
general theory of, III:
main idea of, III:, III:
in martingale settings, III:
in stochastic differential equation setting, III:
Chaos, defined, II:
Chaos: Making a New Science (Gleick), II:
Characteristic function
vs. probability density function, II:
Characteristic lines, II:, II:, II:, II:
Chebychev inequalities, III:, III:
Chen model, I:
Chi-square distributions, I:, III:
Cholesky factor, I:
Chow test, II:, II:, II:, II:
CID (conditionally independent defaults) models, I:, I:, I:
CIR model, I:, I:, I:
Citigroup, I:, I:, I:
CLA (critical line algorithm), I:
Classes
criteria for, II:
Classical tempered stable (CTS) distribution, II:, II:, II:, II:, III:
Classification, and Bayes’ Theorem, I:
Classification and regression trees (CART). See CART (classification and regression trees)
Classing, procedure for, II:
Clearinghouses, I:
CME Group, I:
CMOs (collateralized mortgage obligations), III:, III:
Coconut markets, I:
Coefficients
binomial, III:, III:
of determination, II:
estimated, II:
Coherent risk measures, III:
and VaR, III:
Coins, fair/unfair, III:, III:
Cointegrated models, II:
Cointegration
analysis of, II:
defined, II:
empirical illustration of, II:
technique of, II:
testing for, II:
test of, II:, II:
use of, II:
Collateralized debt obligations (CDOs), I:, I:, III:, III:
Collateralized mortgage obligations (CMOs), III:, III:
Collinearity, II:
Commodities, I:, I:, I:
Companies. See firms
Comparison principals, II:
Comparisons vs. testing, I:
Complete markets, I:, I:, I:, I:
Complexity, profiting from, II:
Complexity (Waldrop), II:
Complex numbers, II:, II:
Compounding. See also interest
and annual percentage rates, II:
continuous, II:, II:
determining number of periods, II:
discrete vs. continuous, III:
formula for growth rate, II:
more than once per year, II:
and present value, II:
Comprehensive Capital Analysis and Review, I:
Comprehensive Capital Assessment Review, I:
Computational burden, III:
Computers. See also various software applications
increased use of, III:
introduction of into finance, II:
modeling with, I:, II:
random walk generation of, II:
in stochastic programing, III:, III:
Concordance, defined, I:
Conditional autoregressive value at risk (CAViaR), II:
Conditional default rate (CDR). See CDRs (conditional default rates)
Conditionally independent defaults (CID) models, I:, I:, I:
Conditioning/conditions, I:, II:, II:, II:
Confidence, I:, I:, II:, III:
Confidence intervals, II:, III:, III:, III:
Conglomerate discounts, II:
Conseco, debt restructure of, I:
Consistency, notion of, II:
Constant elasticity of variance (CEV), III:, III:, III:
Constant growth dividend discount model, II:
Constraints, portfolio
cardinality, II:
common, III:
commonly used, II:, II:
holding, II:
minimum holding/transaction size, II:
nonnegativity, I:
real world, II:
round lot, II:
setting, I:
turnover, II:
on weights of, I:
Constraint sets, I:, I:, I:
Consumer Price Index (CPI), I:, I:, I:, I:
Consumption, I:, II:, III:
Contagion, I:, I:, I:
Contingent claims
financial instruments as, I:
incomplete markets for, I:
unit, I:
use of analysis, I:
utility maximization in markets, I:
value of, I:
Continuity, formal treatment of, II:
Continuous distribution function (c.d.f.), III:, III:, III:, III:, III:
Continuous distribution function F(a), III:
Continuous time/continuous state, III:
Continuous-time processes, change of measure for, III:
Control flow statements in VBA, III:
Control methods, stochastic, I:
Convenience yields, I:, I:
Convergence analysis, II:
Conversion, I:, I:
Convexity
in callable bonds, III:
defined, I:, III:
effective, III:, III:, III:
measurement of, III:, III:
negative, III:, III:, III:
positive, III:
use of, III:
Convex programming, I:, I:
Cootner, Paul, III:
Copulas
advantages of, III:
defined, III:
mathematics of, III:
usefulness of, III:
visualization of bivariate independence, III:
visualization of Gaussian, III:
Corner solutions, I:
Correlation coefficients
relation to R2, II:
and Theil-Sen regression, II:
use of, III:
Correlation matrices, II:, II:, III:
Correlations
in binomial distribution, I:
computation of, I:
concept of, III:
drawbacks of, III:
between periodic increments, III:
and portfolio risk, I:
robust estimates of, II:
serial, II:
undesirable, I:
use of, II:
Costs, net financing, I:
Cotton prices, model of, III:
Countable additivity, III:
Counterparts, robust, II:
Countries, low- vs. high inflation, I:
Coupon payments, I:, III:
Coupon rates, computing of, III:
Courant-Friedrichs-Lewy (CFL) conditions, II:
Covariance
calculation of between assets, I:
estimators for, I:, I:
matrix, I:, I:, I:
relationship with correlation, I:
reliability of sample estimates, II:
use of, II:
Covariance matrices
decisions for interest rates, III:
eigenvectors/eigenvalues, II:
equally weighted moving average, III:
frequency of observations for, III:
graphic of, II:
residuals of return process of, II:
of RiskMetricsTM Group, III:
statistical methodology for, III:
of ten stock returns, II:
use of, II:, II:
using EWMA in, III:
Coverage ratios, II:
Cox-Ingersoll-Ross (CIR) model, I:, I:, I:, I:, III:, III:
Cox processes, I:, II:
Cox-Ross-Rubenstein model, I:, I:, II:
CPI (Consumer Price Index), I:, I:, I:, I:
CPRs (conditional prepayment rates). See prepayment, conditional
CPR vector, III:. See also prepayment, conditional
Cramer, Harald, II:
Crank-Nicolson schemes, II:, II:, II:, II:
Crank Nicolson-splitting (CN-S) schemes, II:
Crashmetrics, use of, III:, III:
Credible intervals, I:
Credit-adjusted spread trees, I:
Credit crises
of 2007, III:
of 2008, III:
data from and DTS model, I:
in Japan, I:
Credit curing, III:
Credit default swaps (CDSs). See CDSs (credit default swaps)
Credit events
and credit loss, I:
in default swaps, I:, I:
definitions of, I:
descriptions of most used, I:
exchanges/payments in, I:
in MBS turnover, III:
prepayments from, III:
protection against, I:
and simultaneous defaults, I:
Credit hedging, I:
Credit inputs, interaction of, III:
Credit loss
computation of, I:
distribution of, I:
example of distribution of, I:
simulated, I:
steps for simulation of, I:
Credit models, I:, I:, I:
Credit performance, evolution of, III:
Credit ratings
categories of, I:
consumer, I:
disadvantages of, I:
implied, I:
maturity of, I:
reasons for, I:
risks for, II:, II:
use of, I:
Credit risk
common, I:
counterparty, I:
in credit default swaps, I:
defined, I:
distribution of, I:
importance of, III:
measures for, I:
modeling, I:, I:, III:
quantification of, I:
reports on, II:
shipping, I:
and spread duration, I:
vs. cash flow risk, III:
Credit scores, I:, I:, I:, I:
Credit spreads
alternative models of, I:
analysis with stock prices, I:
applications of, I:
decomposition, I:
drivers of, I:
interpretation of, I:
model specification, I:
relationship with stock prices, I:
risk in, II:
use of, I:
Credit support, evaluation of, III:
Credit value at risk (CVaR). See CVaR
Crisis situations, estimating liquidity in, III:
Critical line algorithm (CLA), I:
Cross-trading, II:
Cross-validation, leave-one-out, II:
Crude oil, I:, I:
Cumulation, defined, III:
Cumulative default rate (CDX), III:
Cumulative frequency distributions, II:, II:, II:
formal presentation of, II:
Currency put options, I:
Current ratio, II:
Curve imbalances, II:
Curve options, III:
Curve risk, II:
CUSIPs/ticker symbols, changes in, II:
CVaR (credit value at risk), I:, I:, II:, II:, III:. See also value at risk (VaR)
Daily increments of volatility, III:
Daily log returns, II:
Dark pools, II:, II:
Data. See also operational loss data
absolute, II:
acquisition and processing of, II:
alignment of, II:
amount of, I:
augmentation of, I:
availability of, II:, II:
backfilling of, II:
bias of, II:, II:
bid-ask aggregation techniques for, II:
classification of, II:
collection of, II:, II:
cross-sectional, II:, II:, II:
in forecasting models, II:
frequency of, II:, II:, II:, II:
fundamental, II:
generation of, II:
high-frequency (HFD) (See high-frequency data (HFD))
historical, II:, II:, II:
housing bubble, II:
importing into MATLAB, III:
industry-specific, II:
integrity of, II:
levels and scale of, II:
long-term, III:
in mean-variance, I:
misuse of, II:
on operational loss, III:
from OTC business, II:
patterns in, II:
pooling of, III:
of precision, I:
preliminary analysis of, III:
problems in for operational risk, III:
qualitative vs. quantitative, II:
quality of, II:, II:, II:, II:, II:
reasons for classification of, II:
for relative valuation, II:
restatements of, II:
sampling of, II:, II:
scarcity of, II:, II:, II:
sorting and counting of, II:
standardization of, II:, III:
structure/sample size of, II:
types of, II:
underlying signals, II:
univariate, defined, II:
working with, II:
Databases
Compustat Point-In-Time, II:
Factiva, II:
Institutional Brokers Estimate System (IBES), II:
structured, II:
third-party, II:, II:
Data classes, criteria for, II:
Data generating processes (DGPs), II:, II:, II:, II:, III:
Data periods, length of, III:
Data series, effect of large number of, II:
Data sets, training/test, II:
Data snooping, II:, II:, II:, II:, II:
Datini, Francesco, II:
Davis-Lo infectious defaults model, I:
Days payables outstanding (DPO), calculation of, II:
Days sales outstanding (DSO), calculation of, II:
DCF (discounted cash flow) models, II:, II:
DDM (dividend discount models). See dividend discount models (DDM)
Debt
long-term, in financial statements, II:
models of risky, I:
restructuring of, I:
risky, I:
Debt-to-assets ratio, II:
Debt-to-equity ratio, II:
Decomposition models
active/passive, III:
Default correlation, I:
contagion, I:
cyclical, I:, I:
linear, I:
measures of, I:
tools for modeling, I:
Default intensity, III:
Default models, I:, I:
Default probabilities
adjustments in real time, I:
between companies, I:
cyclical rise and fall, I:, I:
defined, I:
effect of business cycle on, I:
effect of rating outlooks on, I:
empirical approach to, I:
five-year (Bank of America and Citigroup), I:, I:
merits of approaches to, I:
Merton’s approach to, I:
probability of, II:, II:, II:
and survival, I:
and survival probability, I:
term structure of, I:
time span of, I:
vs. ratings and credit scores, I:
for Washington Mutual, I:, I:
of Washington Mutual, I:, I:
Defaults
annual rates of, I:
and Bernoulli distributions, III:
calculation of monthly, III:
clustering of, I:
contagion, I:
copulas for times, I:
correlation of between companies, I:
cost of, I:, I:
dollar amounts of, III:
effect of, I:, III:
event vs. liquidation, I:
factors influencing, III:
first passage model of, I:
historical database of, I:
intensity of, I:, I:
looping, I:
measures of, III:
in Merton approach, I:
Moody’s definition of, I:
predictability of, I:
and prepayments, III:, III:
process, relationship to recovery rate, I:
pseudo intensities, I:
rates of cumulative/conditional, III:
recovery after, I:
risk of, I:
simulation of times, I:, I:
threshold of, I:
times simulation of, I:
triggers for, I:
variables in, I:
Default swaps
assumptions about, I:
and credit events, I:
digital, I:
discussion of, I:
market relationship with cash market, I:
and restructuring, I:
value of spread, I:
Default times, I:
Definite covariance matrix, II:
Deflators, I:, I:
Degrees, in ordinary differential equations, II:
Degrees of freedom (DOF)
across assets and time, II:
in chi-square distribution, III:
defined, II:
for Dow Jones Industrial Average (DJIA), II:, II:
prior distribution for, I:
range of, I:
for S&P 500 index stock returns, II:, II:
Delinquency measures, III:
Delivery date, I:
Delta, I:, I:, I:
Delta-gamma approximation, I:, III:
Delta hedging, I:, I:, I:, I:
Delta profile, I:
Densities
beta, III:
Burr, III:
closed-form solutions for, III:
exponential, III:, III:
gamma, III:
Pareto, III:
posterior, I:
two-point lognormal, III:
Density curves, I:
Density functions
asymmetric, III:
of beta distribution, III:
chi-square distributions, III:
common means, different variances, III:
computing probabilities from, III:
discussion of, III:
of F-distribution, III:
histogram of, III:
of log-normal distribution, III:
and normal distribution, II:
and probability, III:
rectangular distributions, III:
requirements of, III:
symmetric, III:
of t-distribution, III:
Dependence, I:, II:
Depreciation, II:
accumulated, II:
expense vs. book value, II:
expense vs. carrying value, II:
in financial statements, II:
on income statements, II:
methods of allocation, II:
Derivatives
construction of, II:
described, II:
embedded, I:
energy, I:
exotic, I:, I:
of functions, defined, II:
and incomplete markets, I:
interest rate, III:
nonlinearity of, III:
OTC, I:
pricing of, I:, III:
pricing of financial, III:
relationship with integrals, II:
for shipping assets, I:, I:, I:
use of instruments, I:
valuation and hedging of, I:
vanilla, I:
Derman, Emanuel, II:
Descriptors, II:, II:, II:
Determinants, II:
Deterministic methods
usefulness of, II:
Diagonal VEC model (DVEC), II:
Dice, and probability, III:, III:, III:, III:
Dickey-Fuller statistic, II:
Dickey-Fuller tests, II:
Difference, notation of, I:
Differential equations
classification of, II:
defined, I:, II:, II:
first-order system of, II:
general solutions to, II:
linear, II:
linear ordinary, II:
partial (PDE), II:, II:
stochastic, II:
systems of ordinary, II:
usefulness of, II:
Diffusion, III:, III:
Diffusion invariance principle, I:
Dimensionality, curse of, II:, III:
Dirac measures, III:
Directional measures, II:, II:
Dirichlet boundary conditions, II:
Dirichlet distribution, I:, I:
Discounted cash flow (DCF) models, II:, II:
Discount factors, I:, I:, I:, II:
Discount function
calculation of, III:
defined, III:
discussion of, III:
forward rates from, III:
graph of, III:
for on-the-run Treasuries, III:
Discounting, defined, II:
Discount rates, I:, I:, I:, II:
Discovery heuristics, II:
Discrepancies, importance of small, II:
Discrete law, III:
Discrete maximum principle, II:
Discretization, I:, II:, II:
Disentangling, II:
complexities of, II:
predictive power of, II:
return revelation of, II:
usefulness of, II:, II:
Dispersion measures, III:, III:, III:
Dispersion parameters, III:
Distress events, I:
Distributional measures, II:
Distribution analysis, cash flow, III:
Distribution function, III:, III:
Distributions
application of hypergeometric, III:
beliefs about, I:
Bernoulli, III:, III:
beta, I:, III:
binomial, I:, III:, III:, III:
Burr, III:
categories for extreme values, II:
common loss, III:
commonly used, III:
conditional, III:
conditional posterior, I:, I:, I:
conjugate prior, I:
continuous probability, III:
discrete, III:
discrete cumulative, III:
discrete uniform, III:, III:, III:
empirical, II:, III:, III:
exponential, III:
finite-dimensional, II:
of Fréchet, Gumbel and Weibull, III:
gamma, III:, III:
Gaussian, III:
Gumbel, III:, III:
heavy-tailed, I:, II:, III:, III:
hypergeometric, III:, III:
indicating location of, III:
infinitely divisible, III:, III:
informative prior, I:
inverted Wishart, I:
light- vs. heavy-tailed, III:
lognormal, III:, III:, III:
mixture loss, III:
for modeling applications, III:
multinomial, III:, III:
non-Gaussian, III:
noninformative prior, I:
normal (See normal distributions)
parametric, III:
Poisson, I:, III:, III:, III:
Poisson probability, III:
posterior, I:, I:, I:, I:, I:, I:
power-law, III:
predictive, I:
prior, I:, I:, I:
proposal, I:
representation of stable and CTS, II:
spherical, II:
stable, III:, III:, III:, III: (See also α-stable distributions)
subexponential, III:
tails of, III:, III:
tempered stable, III:, III:
testing applied to truncated, III:
Diversification, II:
achieving, I:
and cap weighting, I:
and credit default swaps, I:
example of, I:
international, II:
Markowitz’s work on, II:
Diversification effect, III:
Diversification indicators, I:
Dividend discount models (DDM)
applied to electric utilities, II:
applied to stocks, II:
basic, II:
constant growth, II:, II:
defined, II:
finite life general, II:
free cash flow model, II:
intuition behind, II:
multiphase, II:
non-constant growth, II:
predictive power of, II:
in the real world, II:
stochastic, II:, II:
Dividend payout ratio, II:, II:
Dividends
expected growth in, II:
forecasting of, II:
measurement of, II:, II:
per share, II:
reasons for not paying, II:
required rate of return, II:
and stock prices, II:
Dividend yield, II:, II:
Documentation
of model risk, II:, II:
Dothan model, I:, I:
Dow Jones Global Titans 500 (DJGTI), II:, II:
Dow Jones Industrial Average (DJIA)
in comparison of risk models, II:
components of, II:
fitted stable tail index for, II:
frequency distribution in, II:
performance (January 2004 to June 2011), II:
relative frequencies, II:
stocks by share price, II:
Drawing without replacement, III:
Drawing with replacement, III:, III:, III:
Drift
effects of, III:
of interest rates, I:
in randomness calculations, III:
in random walks, I:, I:
time increments of, I:
of time series, I:
as variable, III:
DTS (duration times spread), I:, I:, I:
Duffie-Singleton model, I:
Dupire’s formula, II:, II:
DuPont system, II:, II:
Duration
calculations of real yield and inflation, I:
computing of, I:
defined, I:, III:
effective, III:, III:
effective/option adjusted, III:
empirical, of common stock, II:, II:
estimation of, II:
measurement of, III:, III:
models of, II:
modified vs. effective, III:
Duration/convexity, effective, I:, I:
Duration times spread (DTS). See DTS (duration times spread)
Durbin-Watson test, III:
Dynamical systems
equilibrium solution of, II:
study of, II:
Dynamic conditional correlation (DCC) model, II:
Dynamic term structures, III:, III:, III:
Early exercise, I:, I:. See calls, American-style; options
Earnings before interest, taxes, depreciation and amortization (EBITDA), II:
Earnings before interest and taxes (EBIT), II:, II:, II:
Earnings growth factor, II:
Earnings per share (EPS), II:, II:, II:
Earnings revisions factor, II:, II:
EBITDA/EV factor
correlations with, II:
examples of, II:, II:, II:, II:
in models, II:, II:
use of, II:
Econometrics
financial, II:, II:, II:
modeling of, II:, II:
Economic cycles, I:, II:
Economic intuition, II:
Economic laws, changes in, II:
Economy
states of, I:, II:, III:
term structures in certain, III:
time periods of, II:
Economy as an Evolving Complex System, The (Anderson, Arrow, & Pines), II:
Educated guesses, use of, I:
EE (explicit Euler) scheme, II:, II:
Effective annual rate (EAR), interest, II:
Efficiency
in estimation, III:
Efficient frontier, I:, I:, I:
Efficient market theory, II:, III:
Eggs, rotten, I:
Eigenvalues, II:, II:, II:, II:
Einstein, Albert, II:
Elements, defined, III:
Embedding problem, and change of time method, III:
Emerging markets, transaction costs in, III:
EM (expectation maximization) algorithm, II:, II:
Empirical rule, III:, III:
Endogenous parameterization, III:
Energy
cargoes of, I:
commodity price models, I:
forward curves of, I:
power plants and refineries, I:
storage of, I:, I:
Engle-Granger cointegration test, II:, II:, II:
Entropy, III:
EPS (earnings per share), II:, II:, II:
Equally weighted moving average, III:, III:, III:
Equal to earnings before interest and taxes (EBIT), II:, II:, II:
Equal-variance assumption, I:, I:
Equations
difference, homogenous vs. nonhomogeneous, II:
difference vs. differential, II:
diffusion, II:, II:
error-correction, II:, II:
homogeneous linear difference, II:, II:
homogenous difference, II:, II:, II:, II:
linear, II:
linear difference, systems of, II:
matrix characteristics of, II:
no arbitrage, III:, III:
nonhomogeneous difference, II:, II:, II:
stochastic, III:
Equilibrium
and absolute valuation models, I:
defined, II:
dimensions of, III:
in dynamic term structure models, III:
expectations for, II:
expected returns from, II:
modeling of, III:, III:
in supply and demand, III:
Equilibrium models
use of, III:
Equilibrium term structure models, III:
Equities, I:
investing in, II:
Equity
on the balance sheet, II:
changes in homeowner, III:
in homes, III:
as option on assets, I:
shareholders’, II:
Equity markets, II:
Equity multipliers, II:
Equity risk factor models, II:
Equivalent probability measures, I:, III:
Ergodicity, defined, II:
Erlang distribution, III:
Errors. See also estimation error; standard errors
absolute percentages of, II:, II:
estimates of, II:
in financial models, II:
a posteriori estimates, II:
sources of, II:
terms for, II:
in variables problem, II:
Esscher transform, III:, III:
Estimates/estimation
confidence in, I:
consensus, II:
equations for, I:
in EVT, III:
factor models in, II:
with GARCH models, II:
in-house from firms, II:
maximum likelihood, II:
methodology for, II:
and PCA, II:
posterior, I:
posterior point, I:
processes for, I:, II:
properties of for EWMA, III:
robust, I:
techniques of, II:
use of, II:
Estimation errors
accumulation of, II:
in the Black-Litterman model, I:
covariance matrix of, III:
effect of, I:
pessimism in, III:
in portfolio optimization, II:, III:
sensitivity to, I:
and uncertainty sets, III:
Estimation risk, I:
minimizing, III:
Estimators
bias in, III:
efficiency in, III:
equally weighted average, III:
factor-based, I:
terms used to describe, II:
unbiased, III:
variance, II:
ETL (expected tail loss), III:
Euler approximation, II:, II:, II:
Euler constant, III:
Euler schemes, explicit/implicit, II:
Europe
common currency for, II:
risk factors of, II:
European call options
Black-Scholes formula for, III:
computed by different methods, III:, III:
explicit option pricing formula, III:
pricing by simulation in VBA, III:
pricing in Black-Scholes setting, III:
simulation of pricing, III:, III:
and term structure models, III:
European Central Bank, I:
Events
defined, III:, III:, III:
effects of macroeconomic, II:
extreme, III:, III:, III:
identification of, II:
mutually exclusive, III:
in probability, III:
rare, III:
rare vs. normal, I:
tail, III:, III:, III:
three-δ, III:
EVT (extreme value theory). See extreme value theory (EVT)
EWMA (exponentially weighted moving averages), III:
Exceedance observations, III:
Exceedances, of VaR, III:, III:
Excel
accessing VBA in, III:
add-ins for, I:, III:
data series correlation in, I:
determining corresponding probabilities in, III:
Excel Link, III:
Excel Solver, II:
interactions with MATLAB, III:
macros in, III:, III:
notations in, III:
random number generation in, III:
random walks with, I:, I:, I:, I:
@xRISK in, II:
syntax for functions in, III:
Exchange-rate intervention, study on, III:
Exercise prices, I:, I:, I:
Expectation maximization (EM) algorithm, II:, II:
Expectations, conditional, I:, II:, III:
Expectations hypothesis, III:, III:
Expected shortfall (ES), I:, III:. See also average value at risk (AVaR)
Expected tail loss (ETL), III:, III:, III:, III:, III:
Expected value (EV), I:
Expenses, noncash, II:
Experiments, possibility of, II:
Explicit costs, defined, III:
Explicit Euler (EE) scheme, II:, II:
Exponential density function, III:
Exponential distribution, III:
applications in finance, III:
Exponentially weighted moving averages (EWMA)
discussion of, III:
forecasting model of, III:
properties of the estimates, III:
standard errors for, III:
statistical methodology in, III:
usefulness of, III:
volatility estimates for, III:
Exposures
calculation of, II:
correlation between, II:
distribution of, II:, II:, II:
management of, II:
monitoring of portfolio, II:
name-specific, II:
Extrema, characterization of local, I:
Extremal random variables, III:
Extreme value distributions, generalized, III:
Extreme value theory (EVT), II:, III:, III:
defined, III:
for IID processes, III:
in IID sequences, III:
role of in modeling, II:
Factor analysis
application of, II:
based on information coefficients, II:
defined, II:, II:
discussion of, II:
importance of, II:
vs. principal component analysis, II:
Factor-based strategies
vs. risk models, II:
Factor-based trading, II:
model construction for, II:
performance evaluation of, II:
Factor exposures, II:, II:
Factorials, computing of, III:
Factorization, defined, II:
Factor mimicking portfolio (FMP), II:
Factor model estimation, II:, II:
alternative approaches and extensions, II:
applied to bond returns, II:
computational procedure for, II:
fixed N, II:
large N, II:
Factor models
in the Black-Litterman framework, I:
commonly used, II:
considerations in, II:
cross-sectional, II:
defined, II:
fixed income, II:
in forecasting, II:
linear, II:, II:
normal, II:
predictive, II:
static/dynamic, II:, II:
in statistical methodology, II:
strict, II:
types of, II:
usefulness of, II:, II:
use of, I:, II:, II:, II:, II:
Factor portfolios, II:
Factor premiums, cross-sectional methods for evaluation of, II:
Factor returns, II:, II:
calculation of, II:
Factor risk models, II:, II:
Factors
adjustment of, II:
analysis of data of, II:
categories of, II:
choice of, II:
defined, II:, II:
desirable properties of, II:
development of, II:
estimation of types of, II:
graph of, II:
known, II:
K systematic, II:
latent, II:, II:
loadings of, II:, II:, II:, II:, II:, II:
market, II:
orthogonalization of, II:
relationship to time series, II:
sorting of, II:
sources for, II:
statistical, II:
summary of well-known, II:
transformations applied to, II:
use of multiple, II:
Failures, probability of, II:
Fair equilibrium, between multiple accounts, II:
Fair value
determination of, III:
Fair value, assessment of, II:
Fama, Eugene, II:, II:
Fama-French three-factor model, II:, II:
Fama-MacBeth regression, II:, II:, II:, II:, II:, II:
Fannie Mae/Freddie Mac, writedowns of, III:
Fast Fourier transform algorithm, II:
Fat tails
of asset return distributions, III:
in chaotic systems, II:
class , III:
comparison between risk models, II:
effects of, II:
importance of, II:
properties of, III:
in Student’s t distribution, II:
Favorable selection, III:
F-distribution, III:
Federal Reserve
effects of on inflation risk premium, I:
study by Cleveland Bank, III:
timing of interventions of, III:
Feynman-Kac formulas, II:
FFAs (freight forward agreements), I:
Filtered probability spaces, I:, I:
Filtration, II:, III:, III:, III:
Finance, three major revolutions in, III:
Finance companies, captive, I:
Finance theory
development of, II:
effect of computers on, II:
in the nineteenth century, II:, II:
in the 1960s, II:
in the 1970s, II:
stochastic laws in, III:
in the twentieth century, II:
Financial assets, price distribution of, III:
Financial crisis (2008), III:
Financial date, pro forma, II:
Financial distress, defined, I:
Financial institutions, model risk of, II:
Financial leverage ratios, II:, II:
Financial modelers, mistakes of, II:
Financial planning, III:, III:, III:
Financial ratios, II:, II:
Financial statements
assumptions used in creating, II:
data in, II:
information in, II:, II:
pro forma, II:
time statements for, II:
usefulness of, II:
use of, II:, II:
Financial time series, I:, I:, II:, II:
Financial variables, modeling of, III:
Find, in MATLAB, III:
Finite difference methods, II:, II:, II:, II:, II:, III:
Finite element methods, II:, II:, II:
Finite element space, II:
Finite life general DDM, II:
Finite states, assumption of, I:
Firms
assessment of, II:
and capital structure, II:
characteristics of, II:, II:, II:
clientele of, II:
comparable, II:, II:
geographic location of, II:
history vs. future prospects, II:
phases of, II:
retained earnings of, II:
valuation of, II:, II:
value of, II:, II:
vs. characteristics of group, II:
First boundary problem, II:, II:
First Interstate Bancorp, I:
analysis of credit spreads, I:
debt ratings of, I:
First passage models (FPMs), I:, I:
Fischer-Tippett theorem, III:
Fisher, Ronald, I:
Fisherian, defined, I:
Fisher’s information matrix, I:
Fisher’s law, II:
Fixed-asset turnover ratio, II:
Fixed-charge coverage ratio, II:
Flesaker-Hughston (FH) model, III:
Flows, discrete, I:
FMP (factor mimicking portfolio), II:
Footnotes, in financial statements, II:
Ford Motor Company, I:, I:
Forecastability, II:
Forecastability, concept of, II:
Forecast encompassing
defined, II:
Forecasts
of bid-ask spreads, II:
comparisons of, II:
contingency tables, II:
development of, II:
directional, II:
effect on future of, II:
errors in, II:
evaluation of, II:, III:
machine-learning approach to, II:
measures of, II:, II:
need for, II:
in neural networks, II:
one-step ahead, II:
parametric bootstraps for, II:
response to macroeconomic shocks, II:
usefulness of, II:
use of models for, II:
of volatility, III:
Foreclosures, III:, III:
Forward contracts
advantages of, I:
buying assets of, I:
defined, I:, I:
equivalence to futures prices, I:
hedging with, I:, I:
as OTC instruments, I:
prepaid, I:
price paths of, I:
short vs. long, I:, I:
valuing of, I:
vs. futures, I:, I:
vs. options, I:
Forward curves
graph of, I:
modeling of, I:, I:, I:
normal vs. inverted, I:
of physical commodities, I:
Forward freight agreements (FFAs), I:, I:, I:
Forward measure, use of, I:
Forward rates
calculation of, I:, III:
defined, I:
from discount function, III:
implied, III:
models of, III:
from spot yields, III:
of term structure, III:
Fourier integrals, II:
Fourier methods, I:
Fourier transform, III:
FPMs (first passage models), I:, I:
Fractals, II:, III:, III:
Franklin Tempelton Investment Funds, II:, II:, II:
Fréchet distribution, II:, III:, III:, III:, III:, III:
Fréchet-Hoeffding copulas, I:, I:
Freddie Mac, II:, II:, III:
Free cash flow (FCF), II:
analysis of, II:
calculation of, II:, II:
defined, II:, II:
expected for XYZ, Inc., II:
financial adjustments to, II:
statement of, direct method, II:, II:
statement of, indirect method, II:, II:
vs. cash flow, II:
Freedman-Diaconis rule, II:, II:, II:
Frequencies
accumulating, II:
distributions of, II:, II:
empirical cumulative, II:
formal presentation of, II:
Frequentist, I:, I:
Frictions, costs of, II:
Friedman, Milton, I:
Frontiers, true, estimated and actual efficient, I:
F_SCORE, use of, II:
F-test, II:, II:, II:, II:, II:
FTSE 100, volatility in, III:
Fuel costs, I:, I:. See also energy
Full disclosure, defined, II:
Functional, defined, I:
Functional-coefficient autoregressive (FAR) model, II:
Functions
affine, I:
Archimedean, I:, I:, I:
Bessel, of the third kind, II:
beta, II:
characteristic, II:, II:
choosing and calibrating of, I:
Clayton, Frank, Gumbel, and Product, I:
continuous, II:, II:, II:, II:
continuous/discontinuous, II:
convex, I:, I:, I:, I:
convex quadratic, I:, I:
copula, I:, I:, I:
for default times, I:
defined, I:, I:
density, I:
with derivatives, II:
elementary, III:
elliptical, I:
empirical distribution, III:
factorial, II:
gamma, II:, II:, III:
gradients of, I:
Heaviside, II:
hypergeometric, III:, III:
indicator, II:, II:, II:
likelihood function, I:, I:, I:, I:, I:, I:
measurable, III:, III:, III:
minimization and maximization of values, I:, I:
monotonically increasing, II:, II:
nonconvex quadratic, I:
nondecreasing, III:, III:
normal density, III:
optimization of, I:
parameters of copulas, I:
properties of quasi-convex, I:
quasi-concave, I:, I:
right-continuous, III:, III:
surface of linear, I:
with two local maxima, I:
usefulness of, I:
utility, I:, I:, I:
Fund management, art of, I:
Fund separation theorems, I:
Futures
Eurodollar, I:
hedging with, I:
market for housing, II:
prices of, and interest rates, I:
telescoping positions of, I:
theoretical, I:
valuing of, I:
vs. forward contracts, I:
Futures contracts
defined, I:
determining price of, I:
pricing model for, I:
theoretical price of, I:
vs. forward contracts, I:, I:
Futures options, defined, I:
Future value, II:
determining of money, II:
Galerkin methods, principle of, II:
Gamma, I:, I:
Gamma process, III:
Gamma profile, I:
Gapping effect, I:
GARCH (generalized autoregressive conditional heteroskedastic) models
asymmetric, II:
exponential (EGARCH), II:
extensions of, III:
factor models, II:
GARCH-M (GARCH in mean), II:
Markov-switching, I:
time aggregation in, II:
type of, II:
usefulness of, III:
use of, I:, I:, II:, II:, III:
and volatility, I:
weights in, II:
GARCH (1,1) model
Bayesian estimation of, I:
defined, II:
results from, II:, II:
skewness of, III:
strengths of, III:
Student’s t, I:
use of, I:, III:
GARCH (1,1) process, I:
Garman-Kohlhagen system, I:, I:
Gaussian density, III:
Gaussian model, III:
Gaussian processes, III:, III:
Gaussian variables, and Brownian motion, III:
Gauss-Markov theorem, II:
GBM (geometric Brownian motion), I:, I:
GDP (gross domestic product), I:, I:, II:, II:
General inverse Gaussian (GIG) distribution, II:
Generalized autoregressive conditional heteroskedastic (GARCH) models. See GARCH (generalized autoregressive conditional heteroskedastic) models
Generalized central limit theorem, III:, III:
Generalized extreme value (GEV) distribution, II:, III:, III:
Generalized inverse Gaussian distribution, use of, II:
Generalized least squares (GLS), I:, II:
Generalized tempered stable (GTS) processes, III:
Generally accepted accounting principles (GAAP), II:, II:, II:
Geometric mean reversion (GMR) model, I:
computation of, I:
Gibbs sampler, I:, I:, I:
GIG models, calibration of, II:
Gini index of dissimilarity (Gini measure), III:
Ginnie Mae/Fannie Mae/Freddie Mac, actions of, III:
Girsanov’s theorem
and Black-Scholes option pricing formula, I:
with Brownian motion, III:
and equivalent martingale measures, I:
use of, I:, III:
Glivenko-Cantelli theorem, III:, III:, III:, III:
Global Economy Workshop, Santa Fe Institute, II:
Global Industry Classification Standard (GICS®), II:, II:
Global minimum variance (GMV) portfolios, I:
GMR (geometric mean reversion) model, I:
GMV (global minimum variance) portfolios, I:, I:
GNP, growth rate of (1947–1991), II:, II:
Gradient methods, use of, II:
Granger causality, II:
Graphs, in MATLAB, III:
Greeks, the, I:
beta and omega, I:
delta, I:
gamma, I:
rho, I:
theta, I:, I:
use of, I:, II:, III:
vega, I:
Greenspan, Alan, I:
Growth, I:, II:, II:, II:
Gumbel distribution, III:, III:, III:
Hamilton-Jacobi equations, II:
Hankel matrices, II:
Hansen-Jagannathan bound, I:, I:
Harrison, Michael, II:
Hazard, defined, III:
Hazard (failure) rate, calculation of, III:
Heat diffusion equation, II:
Heath-Jarrow-Morton framework, I:, I:
Heavy tails, III:, III:
Hedge funds, and probit regression model, II:
Hedge ratios, I:, I:
Hedges
importance of, I:
improvement using DTS, I:
in the Merton context, I:
rebalancing of, I:
risk-free, I:
Hedge test, I:, I:
Hedging
costs of, I:, II:
and credit default swaps, I:
determining, I:
with forward contracts, I:, I:
of fuel costs, I:
with futures, I:
gamma, I:
portfolio-level, I:
of positions, II:
ratio for, II:
with swaps, I:
transaction-level, I:
usefulness of, I:
use of, I:
using macroeconomic indices, I:
Hessian matrix, I:, I:, I:, III:
Heston model, I:, I:, I:, II:
with change of time, III:
Heteroskedasticity, II:, II:, II:, II:
HFD (high-frequency data). See high-frequency data (HFD)
Higham’s projection algorithm, II:
High-dimensional problems, II:
High-frequency data (HFD)
and bid-ask bounce, II:
defined, II:
generalizations to, II:
Level I, II:, II:, II:
Level II, II:
properties of, II:, II:
recording of, II:
time intervals of, II:
use of, II:, II:
volume of, II:
Hilbert spaces, II:
Hill estimator, II:, III:
Historical method
drawbacks of, III:
weighting of data in, III:
Hit rate, calculation of, II:
HJM framework, I:
HJM methodology, I:
Holding period return, I:
Ho-Lee model
continuous variant for, I:
defined, I:
in history, I:
interest rate lattice, III:
as short rate model, III:
for short rates, III:
as single factor model, III:
Home equity prepayment (HEP) curve, III:, III:
Homeowners, refinancing behavior of, III:
Home prices, I:, II:, II:, III:
Homoskedasticity, II:, II:
Horizon prices, III:
Housing, II:, III:
Howard algorithm (policy iteration algorithm), II:, II:
Hull-White (HW) models
binomial lattice, III:
for calibration, II:
defined, I:
interest rate lattice, III:
and short rates, III:
for short rates, III:
trinomial lattice, III:, III:
usefulness of, I:
use of, III:, III:
valuing zero-coupon bond calls with, I:
Hume, David, I:
Hurst, Harold, II:
Hypercubes, use of, III:
IBM stock, log returns of, II:
Ignorance, prior, I:
Implementation risk, II:
Implementation shortfall approach, III:
Implicit costs, III:
Implicit Euler (IE) scheme, II:, II:
Implied forward rates, III:
Impurity, measures of, II:
Income, defined for public corporation, II:
Income statements
common-size, II:, II:
defined, II:
in financial statements, II:
sample, II:, II:
structure of, II:
XYZ Inc. (example), II:
Income taxes. See taxes
Independence, I:, II:, III:, III:
Independence function, in VaR models, III:
Independently and identically distributed (IDD) concept, I:, I:, II:, III:, III:, III:
Indexes
characteristics of efficient, I:
defined, II:
of dissimilarity, III:
equity, I:, II:, II:
tail, II:, II:, III:
tracking of, II:, II:
use of weighted market cap, I:
value weighted, I:
volatility, III:, III:
Index returns, scenarios of, II:, II:
Indifference curves, I:, I:, I:
Industries, characteristics of, II:, II:
Inference, I:, I:
Inflation
effect on after-tax real returns, I:
and GDP growth, I:
indexing for, I:
in regression analysis, II:
risk of, II:
risk premiums for, I:
seasonal factors in, I:
shifts in, I:
volatility of, I:
Information
anticipation of, III:
from arrays in MATLAB, III:
completeness of, I:
contained in high volatility stocks, III:
and filtration, III:
found in data, II:
and information propagation, II:
insufficient, III:
integration of, II:
overload of, II:
prior in Bayesian analysis, I:, I:
propagation of, I:
structures of, I:, II:
unstructured vs. semistructured, II:
Information coefficients (ICs), II:, II:, II:, II:, II:
Information ratios
defined, II:, II:, II:, II:
determining, II:
for portfolio sorts, II:
use of, II:
Information sets, II:
Information structures
defined, II:
Information technology, role of, II:
Ingersoll models, I:, I:
Initial conditions, fixing of, II:
Initial margins, I:
Initial value problems, II:
Inner quartile range (IQR), II:
Innovations, II:
Insurance, credit, I:
Integrals, II:, II:. See also stochastic integrals
Integrated series, and trends, II:
Integration, stochastic, III:, III:, III:
Intelligence, general, II:
Intensity-based frameworks, and the Poisson process, I:
Interarrival time, III:, III:
Intercepts, treatment of, II:
Interest
accumulated, II:, II:
annual vs. quarterly compounding, II:
compound, II:, II:
computing accrued, and clean price, I:
coverage ratio, II:
defined, II:
determining unknown rates, II:
effective annual rate (EAR), II:
mortgage, II:
simple vs. compound, II:
terms of, II:
from TIPS, I:
Interest rate models
binomial, III:, III:
classes of, III:
confusions about, III:
importance of, III:
properties of lattices, III:
realistic, arbitrage-free, III:
risk-neutral/arbitrage-free, III:
Interest rate paths, III:, III:, III:
Interest rate risk, III:
Interest rates
absolute vs. relative changes in, III:
approaches in determining future, III:
binomial model of, III:
binomial trees, I:, I:, I:, I:, I:, I:, III:
borrowing vs. lending, I:
calculation of, II:
calibration of, I:
caps/caplets of, III:
caps on, I:
categories of term structure, III:
computing sensitivities, III:
continuous, I:, I:
derivatives of, III:
determination of appropriate, I:
distribution of, III:
dynamic of process, I:
effect of, I:
effect of shocks, III:
effect on putable bonds, III:
future course of, III:, III:
and futures prices, I:
importance of models, III:
jumps of, III:
jumpy and continuous, III:
long vs. short, III:
market spot/forward, I:
mean reversion of, III:
modeling of, I:, I:, I:, I:, I:, III:
multiple, II:
negative, III:
nominal, II:
and option prices, I:
and prepayment risk, III:
risk-free, I:
shocks/shifts to, III:
short-rate, I:, III:
simulation of, III:
stochastic, I:, I:
structures of, III:, III:
use of for control, I:
volatility of, III:, III:
Intermarket relations, no-arbitrage, I:
Internal consistency rule, in OAS analysis, I:
Internal rate of return (IRR), II:
in MBSs, III:
International Monetary Fund
Global Stability Report, I:
International Swap and Derivatives Association (ISDA). See ISDA
Interpolated spread (I-spread), I:
Interrate relationship, arbitrage-free, III:
Intertemporal dependence, and risk, III:
Intertrade duration, II:, II:
Intertrade intervals, II:
Intervals, credible, I:
Interval scales, data on, II:
Intrinsic value, I:, I:, I:, II:
Invariance property, III:
Inventory, II:, II:
Inverse Gaussian process, III:
Investment, goals of, II:
Investment management, III:
Investment processes
activities of integrated, II:
evaluation of results of, II:
model creation, II:
monitoring of performance, II:
quantitative, II:, II:
quantitative equity, II:, II:, II:
research, II:
sell-structured, II:
steps for equity investment, II:
testing of, II:
Investment risk measures, III:
Investments, I:, II:, II:
Investment strategies, II:, II:
Investment styles, quantamental, II:, II:
Investors
behavior of, II:, II:
comfort with risk, I:
completeness of information of, I:
focus of, I:, II:
fundamental vs. quantitative, II:, II:, II:, II:
goals/objectives of, II:, II:, III:
individual accounts of, II:
monotonic preferences of, I:
number of stocks considered, II:
preferences of, I:, I:, II:, II:, II:
prior beliefs of, II:
real-world, II:
risk aversion of, II:, II:
SL-CAPM assumptions about, I:
sophistication of, II:
in uncertain markets, II:
views of, I:
Invisible hand, notion of, II:
ISDA (International Swap and Derivatives Association)
Credit Derivative Definitions (1999), I:, I:
Master Agreement, I:
organized auctions, I:
supplement definition, I:
I-spread (interpolated spread), I:
Ito, Kiyosi, II:
Ito definition, III:
Ito integrals, I:, III:, III:, III:
Ito isometry, III:
Ito processes
defined, I:
generic univariate, I:
and Girsanov’s theorem, I:
under HJM methodology, I:
properties of, III:
and smooth maps, III:
Ito’s formula, I:, III:
Ito’s lemma
defined, I:
discussion of, I:
in estimation, I:
and the Heston model, I:
James-Stein shrinkage estimator, I:
Japan, credit crisis in, I:
Jarrow-Turnbull model, I:
Jarrow-Yu propensity model, I:
Jeffreys’ prior, I:, I:, I:
Jensen’s inequality, I:, III:
Jevons, Stanley, II:
Johansen-Juselius cointegration tests, II:, II:
Joint jumps/defaults, I:
Joint survival probability, I:
Jordan diagonal blocks, II:
Jorion shrinkage estimator, I:, I:
Jump-diffusion, III:, III:
Jumps
default, I:
diffusions, I:
downward, I:
idiosyncratic, I:
incorporation of, I:
in interest rates, III:
joint, I:
processes of, III:
pure processes, III:, III:
size of, III:
Kalotay-Williams-Fabozzi (KWF) model, III:, III:, III:
Kamakura Corporation, I:, I:, I:, I:
Kappa, I:
Karush-Kuhn-Tucker conditions (KKT conditions), I:
Kendall’s tau, I:, I:
Kernel regression, II:, II:, II:
Kernels, II:, II:, II:
Kernel smoothers, II:
Keynes, John Maynard, II:
Key rate durations (KRD), II:, III:, III:
Key rates, II:, III:
Kim-Rachev (KR) process, III:
KKT conditions (Karush-Kuhn-Tucker conditions), I:, I:, I:
KoBoL distribution, III:
Kolmogorov extension theorem, III:
Kolmogorov-Smirnov (KS) test, II:, III:, III:
Kolomogorov equation, use of, III:
Kreps, David, II:
Krispy Kreme Doughnuts, II:, II:
Kronecker product, I:, I:
Kuiper test, III:
Kurtosis, I:, III: