Index

Akaike information criterion (AIC), 84, 90

Altman z-score, 297, 300, 306, 307

analysis of variance (ANOVA), 355

Archimedean copulas, 15

ARCH model. See autoregressive conditionally heteroskedastic model

Arrow–Pratt risk aversion index, 158, 161, 164, 194

asset allocation. See also portfolio optimization

and regime switching, 78–79

and state of the world, 95

asset classes, 181

asset/liability management (ALM), 167–182. See also portfolio optimization

asset returns. See also bond returns; stock returns

in credit risk models, 299, 300, 301–302

i.i.n.d., 73, 80, 82

and mean absolute deviation, 221

multiple-asset models for, 85–87

multivariate normal distribution of, 242

predicting, 78

real-world dynamics of, 73–74

and securities class actions, 383, 387, 390, 391, 394, 395

single-asset models for, 79–82

three-state estimation for, 84–85

and transaction costs, 212, 230–231

two-state estimation for, 82–84

assets

value of, 7, 10, 312

variance/covariance of, 364

volatility of, 301, 306

asymmetric vector GARCH model, 368, 369, 370

asymptotic single factor structural default model, 7

autoregressive conditionally heteroskedastic (ARCH) model, 78, 364–366

available capital, defined, 223

average value at risk (AVaR), 15

banking stability index, 12

bankruptcy

counterparty, 30

and credit contagion, 26

global increase in, 312

and loss cascade, 9

predicting, 300, 305–306

and systemic risk, 6

banks

capital calculating by, 298

charge-off rates for, 275

and counterparty credit risk, 22–41

and credit risk modeling, 274, 280, 291–292, 310

estimating efficiency of, 47–57

interdependence of, 8, 15, 17–20

risk correlations for, 279

and securities class actions, 373, 391

transaction costs applied by, 235

Basel Committee on Banking Supervision (BCBS)

counterparty credit risk measures under, 25, 27, 28, 29, 30

credit portfolio monitoring under, 313

and credit rating, 304, 305

default under, 315

risk measures under, 12

and stress testing, 273, 274, 280, 281, 293

Bayes information criterion, 90

bear markets, 78, 85, 87

Benter, Bill, 201, 202

bilateral netting, 29–30

Black–Scholes–Merton option pricing model, 73, 316

Black–Scholes option pricing model, 7

bond returns

indices for, 283, 284

vs. stock returns, 182, 188–192

Branch-and-Fix Coordination (BFC-MS), 137

brokers

and transaction costs, 212, 218, 220

VPIN applications for, 361

Buffett, Warren, 201, 202

bulk volume classification (BVC), 341, 342, 343–344, 357, 361

bull markets, 86–87

buy-and-hold strategies

and stochastic programming, 171–172

and transaction costs, 213, 215, 218

CAMEL-based risk management, 312–313

capital

allocating, 303

available vs. invested, 223, 231

economic, 29, 31, 34, 42

equity, 373

regulatory, 277, 280, 282, 291

working, 383

capital adequacy assessment process, 280, 315

capital asset pricing model (CAPM)

in collateral considerations, 25

and portfolio optimization, 158

and risk-return payoffs, 75

and Sharpe ratio, 251

and transaction costs, 217

capital gains taxes, 212

capital growth theory, 194

CCAR. See Comprehensive Capital Analysis and Review program

CDF threshold in VPIN, 339, 340–342, 344, 345, 347, 356, 358, 360, 361

CEO turnover, 374

certainty equivalent method, 160, 206

Cholesky factorization, 57

class actions (CAs). See also securities class actions

prediction methodology, 376–378, 394

risk of, 373

settlements of, 372

Clayton copula, 15

coherence, in risk measurement, 277

collateral

concentrations of, 35, 36

and counterparty credit risk, 25, 26, 28, 34, 39

decline in value of, 312

for nonperforming loans, 46

Commodity Futures Trading Commission (CFTC), 338

Comprehensive Capital Analysis and Review (CCAR) program, 273, 274, 277, 292

concave piecewise linear cost functions, 227–229

concentration risk, 35–36

conditional value at risk (CoVaR or CVaR)

in asset/liability management, 177

in copula models, 16

in energy sector examples, 133, 134, 143–146

in portfolio rebalancing, 220

in risk modeling, 12, 15, 100–103, 105

in stress test example, 117–121

worst-case, 108

constant correlation model, 367–368, 369

contagion index, 14, 17

continuous time modeling, 169

convex piecewise linear cost functions, 225–227

copula function, 15–20, 26

counterparty close-out, 40–41

counterparty credit exposure (CCE), 24, 35

counterparty credit risk (CCR)

and close-out, 40–41

and collateral, 39

and concentrations, 35–36

concept of risk in, 41–43

definition of, 26

function of, 22–25, 27

limits on, 38–39

metrics for, 34–35

and model validation, 39–40

supervisory requirements for, 25–34

and wrong-way risk, 38

covariance

in ARCH-type modeling, 364–368

in CCR measurement, 22

empirical analysis, 368–370

credit approval, 315

credit contagion, 26

credit default models, 8. See also credit risk models

credit default swaps (CDSs), 23–26, 312

credit limits, and stress testing, 281

CreditMetrics, 274, 281, 293, 297, 299–300, 303, 304

CreditPortfolioView (CPV), 297, 299, 300, 304

credit rating

classes of, 317, 330

and counterparty credit risk, 23, 24

internal vs. external, 313

migration matrix, 285

as ordinal, 318

pros/cons of, 303–305

credit rating agencies (CRAs), 296–298, 313, 314

credit rating models/systems

attributes in, 315–316

credit risk role in, 313–314

development process for, 316–317

empirical analysis of, 325–330

functions of, 315

MCDA approach to, 317–325

credit risk

defined, 312, 315

predictors of, 316

credit risk management

factors influencing, 312

integrated approach to, 331

MCDA methodology in, 314, 330–331

systems for, 312–313

credit risk models

accounting-based, 297, 300–301, 305–307, 309

function of, 296, 310, 312

MCDA approach to, 319–320

ratings-based, 296–300, 303–305, 309, 313–314

structural, 297, 301–302, 307–308, 309, 314, 331

credit risk stress testing (ST)

conceptual issues in, 276–277

defined, 277

example, 281–291

function of, 277–279, 281

purpose of, 273–276

supervisory requirements for, 280–281

credit scoring, 313, 315–323, 330, 378

credit valuation adjustment (CVA), 23, 24, 34, 36–38

cross-product netting rules, 30

crowded trades, 35

cumulative mortality rate (CMR), 23

current exposure (CE), 22, 34

current exposure (CEM) method, 32

data envelopment analysis (DEA), 47, 48, 49, 55

data mining, 324

debt. See also asset/liability management

mutual, among banks, 8, 20

and securities class action risk, 392

state-guaranteed, 13

in systemic risk modeling, 7–8

debt valuation adjustment (DVA), 24, 37

decision models. See also specific models

asset/liability, 167, 169

criteria for, 98

in energy sector, 126–128, 132–137

multistage, 139, 147

and portfolio optimization, 99, 122

risk quantification in, 99–106

robustness concern in, 323–324

stress testing for, 110–122

worst-case analysis in, 107–110

default

and counterparty close-out, 40–41

and counterparty credit risk, 22, 24, 26

point of, 308, 315

probability of (see probability of default)

relative ranking of, 303

structural models for, 7–10, 301–392

systemic, 25

trigger of, 297

default risk (DR), 283–289, 314. See also probability of default (PD)

derivatives. See also specific derivative instruments

and counterparty credit risk, 27, 34

and CVA, 36

in energy sector example, 137

inherent risk in, 312

over-the-counter (OTC), 20, 31, 38

deviation functions in risk quantification, 99, 100–101, 102–103

directional input distance functions, 51

directional output distance function, 47, 48, 51, 65

directional technology distance function, 48

disintermediation, 312

distance to default (DD), 297, 301–302, 307, 308

distress barrier in systemic risk modeling, 7–10

distress dependency matrix, 11

diversification

and credit risk stress testing, 279

and estimated portfolio weights, 264

and extreme scenarios, 167

international, 79

and noninstitutional investors, 214

and transaction costs, 217, 218

Dow Jones Industrial Average (DJIA), 184, 337

dynamic portfolio theory, 194–199

economic capital (EC)

in CCR measurement, 29, 31, 34

and credit risk stress testing, 277–278, 291

estimating, 274, 280

stylized representation of, 42

efficiency estimating

calculations for, 47–57

Japanese banking application, 57–67

efficient frontier. See also portfolio weights

and Sharpe ratio, 251, 261

statistical properties of, 242–245, 247, 267

energy sector

case studies, 137–147

risk aversion strategies for, 132–137

risk modeling for, 126–127

spot/forward pricing in, 128–132, 137

stochastic processes for, 128

equity capital, 373

equity to total assets (E/TA) ratio

and credit rating, 326, 328

and default probability, 297, 306

and distress barrier, 7

and securities class actions, 382, 392

estimated default frequency (EDF), 300, 308

Europe

credit ratings in, 314, 325–331

pension system in, 182–184

securities class actions in, 375

European Monetary System (EMS), 77

event horizon parameter (VPIN), 341, 342, 345, 347, 357–359, 361

exchange rates, and regime switching, 76–77

expected exposure (EE), 28, 29, 30–32, 39

expected log, in ALM modeling, 169

expected loss (EL), 277, 291, 315

expected negative exposure, 25

expected positive exposure (EPE), 22–23, 28–33

expected return

errors in, 242–243

and estimated portfolio weights, 267

and transaction costs, 217, 219, 232

expected shortfall. See also conditional value at risk

in decision modeling, 105

in energy sector example, 130, 133–136

in pension fund example, 192

expected utility, 133, 164, 251–255

exposure-at-default (EAD), 23, 27–32, 280, 281, 315

false positive rate (FPR)

optimization of, 348–353, 354, 357

in VPIN prediction, 340, 341, 345–346, 360, 361

financial/banking sector

and securities class actions, 373, 374, 375

systemic risk in, 4, 5

financial system

and credit risk stress testing, 280–281

systemic risk in, 6

financial time series modeling, 364–365

first-order stochastic dominance (FSD), 103–104, 108–109, 130, 133, 135–137

first-to-default time, 26

Fitch, 296, 297, 313

fixed-mix ALM models, 171–174

Flash Crash of 2010, 337–339, 342

foreign exchange rates, and regime switching, 76–77

futures contracts

in energy sector, 127

and Flash Crash, 338

and VPIN, 339, 340

gain and loss equivalent method, 160, 161, 206–207

GARCH model

covariance specifications for, 364, 367–370

in energy sector risk modeling, 130, 147

and regime switching, 78, 88

Gaussian Mixture Model (GMM), 91–92, 94

global financial crisis (GFC)

and credit risk management, 273, 274, 296, 297, 303, 304, 312, 313, 314

effects of, 3–4, 27, 43

and foreign exchange volatility, 77

and securities class actions, 374

stress testing example, 116–122

goodwill, and securities class actions, 383, 391–392, 395

gross domestic product (GDP), and default risk, 289, 300, 304

Gumbel copula, 15

Hausch, Donald, 160, 161

heteroskedasticity, in asset return statistics, 73, 81, 82, 88

high-frequency trading (HFT), 338, 344

historicism

in risk measurement, 41–43

and securities class actions, 385, 392

and uncertainty, 276

home bias, in asset allocation, 79

housing bubble (US), 3

human behavior, and economic prediction, 276

IBM OSL stochastic programming code, 187

independently and identically normally distributed (i.i.n.d.) asset returns, 73, 80, 82

index tracking, 218–219

industrial sector, securities class actions in, 374–375, 391, 394

inflation

and default risk, 289

and interest rates, 76

InnoALM pension fund, 184–194

Innovest, 185, 193

insurance

asset/liability management in, 175–176

average value at risk in, 15

and counterparty default, 24

premium calculation, 14

interest rates

and credit risk, 33, 300, 304

and historical analysis, 43

and regime switching, 75–76

internal model method (IMM), in CCR

measurement, 27, 28, 29, 30, 31–32

International Capital Asset Pricing Model, 79

International Organization of Securities Commissions (IOSCO), 27

invested capital, 223, 231

Kallberg and Ziemba method, 207–208

Kelly capital growth approach, 194–199, 202

Kernel Search, 221

Keynes, John Maynard, 201, 202

KMV credit risk model, 297, 300, 301–302, 307

kurtosis, in asset return statistics, 79, 81, 82, 88

Lee-Ready trade classification algorithm, 343

leptokurtosis, in asset return statistics, 73, 78, 81

leverage

and class actions, 383, 385, 392, 395

in credit rating, 316, 326, 328, 331

and estimated default frequency, 300

and systemic risk, 6, 7

leverage effect, 367

linear cost functions, 224–229

liquidity

and class actions, 383, 385, 389, 390, 394

and counterparty credit risk, 34, 39

in credit rating, 316

and market volatility, 338–339

and portfolio optimization, 167

and stress testing, 280

and systemic failure, 5

litigation. See class actions; securities class actions

loans

identifying distressed, 307

nonperforming (see nonperforming loans)

pricing of, 313, 315

logistic regression (LR), 330, 331

loss

expected, 277, 291, 315

in systematic risk measurement, 13–14

unexpected, 277, 281, 291

loss cascades, 9, 14, 20

loss-given-default (LGD), 23, 32, 280, 315

LP computability, 213–214, 221, 222

Luenberger productivity indicator, 50

MADS. See Mesh Adaptive Direct Search algorithm

majority voting (MV), 378, 393, 394, 395

market capitalization, in credit rating, 326–328, 330, 331

market risk, measuring, 23, 33, 36

markets (financial)

and credit risk models, 304, 305, 306, 307

decision modeling for (examples), 113–114, 116–122

Flash Crash effect on, 337–339

states of, 75, 78, 79–84, 87, 93–94

transaction costs in, 215, 234–237

volatility in, 338, 340, 342, 345, 361, 372

Markov regime switching. See regime switching models

Markowitz model

and portfolio optimization, 155–156, 242

standard deviation in, 221

worst-case analysis for, 107–108

maximum intermediate return (MIR), as volatility measure, 340, 345

maximum safety portfolio, 235

MCDA. See multicriteria decision aid methodology

mean absolute deviation (MAD), 221, 222

mean-risk efficiency, 105–106

mean-variance analysis, 164, 168, 169, 217

Merton credit risk model, 297, 301, 306, 307

Mesh Adaptive Direct Search (MADS) algorithm, 348–350

MHDIS. See multi-group hierarchical discrimination

modeling. See also specific models

analyzing uncertainty in, 353–360

for class action prediction, 375–394

for counterparty credit risk, 27–32, 39–40

for credit risk assessment (see credit rating models/systems; credit risk models)

for decision making (see decision models)

for financial time series, 364–365

regime switching (see regime switching models)

scenario generation for, 128–130, 147

monetary policy, and interest rates, 75–76

Monte Carlo simulation

in credit risk models, 299–300

in default calculation, 7

Moody's

and credit risk models, 296, 297, 299, 300, 303

Default Risk Service, 283, 285

MSVARlib, 82

multicriteria decision aid (MCDA) methodology, 314, 317–325, 377, 389

empirical analysis, 325–330

multi-group hierarchical discrimination (MHDIS), 377, 387–390, 393–395

multistage models

in asset/liability management, 164, 169, 170, 173, 175, 178, 194

stochastic solution for, 139, 147

in stress testing, 100, 112, 122

netting

and counterparty credit risk, 30–33

legal enforceability of, 36

reporting of, 35

Nikkei Financial Quest, 57

NOMAD. See Nonlinear Mesh Adaptive Direct Search

nominal price of the bar (in VPIN), 342, 343

Nonlinear Mesh Adaptive Direct Search (NOMAD), 340, 348, 349–350, 351–352, 359

nonperforming loans (NPLs)

and bank efficiency, 49–50

banks’ acceptance of, 46

estimating costs of, 47, 65

in Japanese banking example, 59–66

shadow prices of, 48–49

normal copula, 15

OCC/BOG-FRB Bulletin 2011–2012, 277

OSIRIS Database of Bureau van Dijk, 379, 382

output analysis, 106–107, 122

output distance function, 47–48

over-the-counter (OTC) derivatives, 28, 30, 31, 38

peak exposure, 23, 31, 38

pension funds, ALM model for, 182–194

polynomial chaos expansion (PCE), 355, 356

portfolio optimization

and decision models, 99, 122

diversification in (see diversification)

dynamic portfolio theory in, 194–199

estimation errors in, 242–243

and great investors, 201–205

mean estimates in, 163–167

parameter estimation in, 242–243

pension fund model in, 182–194

and regime switching models, 93

risk quantification in, 100, 221

robustness in, 106

static portfolio theory in, 155–163

stochastic programming approach in, 167–182

transaction costs in (see transaction costs)

portfolio rebalancing

and capital gains taxes, 212

and transaction costs, 214, 215, 217, 220–221

portfolio weights

empirical tests of, 255–266, 267

for expected utility portfolios, 251–255

for maximum Sharpe ratio portfolios, 250–251, 261, 267

notation for, 245–247

parameters for, 242–245, 267

for tangency portfolios, 247–250, 256–260

potential exposure (PE), 22, 23, 35

potential future exposure (PFE), 28, 38

prediction. See also modeling

of asset returns, 78

feedback effect in, 276

of securities class actions, 373, 374, 375, 376

premium calculation (insurance), 14, 364

principal component analysis (PCA), 129

probability of default (PD)

in accounting risk models, 306

in counterparty credit risk measurement, 23, 27

in credit rating, 313, 315, 317, 318

and regulatory requirements, 280

in structural risk models, 297, 301, 307

and systemic risk, 10–11

and wrong-way risk, 38

probability of informed trading (PIN), 342

productivity, and class actions, 383, 391

profitability

as credit rating factor, 326–328, 331

and securities class actions, 383, 390, 391, 394

profit risk, 133–137

case studies, 137–147

proportional cost with minimum charge (PCMC), 229, 234, 235, 237

pure fixed cost (PFC), 224, 225, 234–236

pure proportional cost (PPC), 224, 225, 234–236

quadratic form, in efficiency calculations, 48, 49, 55, 57, 65

quantiles, in systemic risk measurement, 14–15

quantitative easing, 43

quantitative stability analysis

mean-risk efficiency in, 105

and portfolio optimization, 122

stress testing in, 107

quote stuffing, 338

recession. See also global financial crisis 2008–09, 3

and credit risk stress tests, 280

regime switching models

and asset allocation, 78–79

assumptions of, 87

in energy sector models, 129

and exchange rates, 76–77

function of, 74–75

implementing, 89–95

and interest rates, 75–76

intuitive attractions of, 87–89

multiple-asset, 85–87

single-asset, 79–82

and stock returns, 77–78

three-state, 84–85

two-state, 82–84

regularization principle, 324

regulatory capital (RC), 277, 280, 282, 291

relative prices, 65

repo transactions, 27, 30, 36

risk. See also specific types

of class action litigation, 373

defined, 168

in energy sector, 127

extreme, 304

individual vs. interrelated factors, 15

quantification of, 6, 99–106

vs. uncertainty, 41–43

risk aggregation, 277–278, 293

risk appetite

in portfolio weight calculations, 246, 251–253, 259–265, 267

and stress testing, 279

risk aversion

absolute, 158, 161, 231

energy sector examples, 132–137

estimating, 206–208

measuring, 161–162

and risk/probability premiums, 159

RiskCalc, 297, 300

risk models, formulating, 6, 99–106. See also specific models

risk premia, 364

risk-return trade-offs, 75, 95

risk tolerance

of banks, 33–34

equation, 158

and stress testing, 279

robustness. See also stress testing

of companies facing SCAs, 391, 394

and MCDA, 323–325

robust stochastic dominance, 108–110

Rubinstein risk aversion measure, 161, 162

Russell-Yasuda Kasai stochastic programming model, 171, 175–182

sample average approximation (SAA), 106

S&P. See Standard & Poor's

Sarbanes-Oxley (SOX) Act, 372, 394

second-order stochastic dominance (SSD)

in decision modeling, 103–104, 109–110

energy sector example, 133, 136–137

in expected utility analysis, 164

securities

number in portfolio, 217

transaction costs for, 212, 215

Securities Class Action Clearinghouse, 379

securities class actions (SCAs)

empirical analysis, 378–394

factors in, 373–374

frequency of, 372

legal framework for, 375

prediction methodology, 376–378, 394

by sector, 380

targets of, 383, 390–392, 394

securities financing transactions (SFTs)

and counterparty credit risk, 28, 30, 36

and wrong-way risk, 38

securities fraud, 372

semi mean-absolute deviation (semi-MAD), 214, 217, 218, 221–222, 223, 234–236, 237

shadow prices

calculations for, 53–54

of nonperforming loans, 48–49, 65

Sharpe ratio

and great investors, 201–202

in portfolio weight estimations, 246, 250–251, 261, 267

Shepard output distance functions, 47–48, 55

Shiller, Robert, 81, 82

Siemens InnoALM pension fund, 182–194

Simons, Jim, 201, 202

simulation

in ALM modeling, 169

Monte Carlo, 7, 299–300

single-asset Markov regime switching models, 79–82

skewness

in asset return statistics, 79, 81, 82

in portfolio weight distributions, 267

slippage, 199

Sobol senstivity indices, 356, 357, 358

special purpose entities (SPEs), and credit risk, 35

stagflation, 291

standardized method (SM), in CCR measurement, 27, 32

Standard & Poor's (S&P), 296, 297, 298, 299, 303, 314

Standard & Poor's (S&P) 500, 337, 338

static portfolio theory, 155–163

statistical learning, 324

Stein's lemma, 242, 246

stochastic control, in ALM modeling, 169, 170

stochastic dominance (SD)

in energy sector example, 133, 135–136

in risk quantification, 103–104

worst-case, 108–110

stochastic programming (SP)

advantages of, 167–170

applications for, 170–171

code for, 187

in energy sector modeling, 128, 137–141, 147

and fixed-mix models, 171–174

in pension fund model, 186

Russell-Yasuda Kasai model for, 175–182

stock returns

vs. bond returns, 182, 188–192

and exchange rates, 77

and regime switching, 77–78

and risk, 183–184

and securities class actions, 373, 375

stress testing (ST)

and concentration management, 35–36

via contamination, 111–122

in credit risk modeling (see credit risk stress testing)

effect on outcomes, 42

function of, 110

and risk quantification, 100, 106–107

support vector machines (SVMs), 313, 377, 393, 394

support window parameter, in VPIN, 341, 342, 344, 357, 358, 359, 361

systematic risk

in credit risk assessment, 313

defined, 4

systemic risk

copula models for, 15–20

defined, 4–5

for interdependent banks, 17, 19–20

measuring, 10–15, 20

modeling, 7–10

tangency portfolios, 243, 247–250, 256–260

Thorp, Ed, 201, 202, 204

tick rule, 343

Tobin's separation theorem, 156

too big to fail, 12

too interconnected to fail, 12

trading. See also volume synchronized probability

of informed trading (VPIN)

buys vs. sells in, 343

in energy sector, 127

high-frequency, 338

and risk exposure, 23–24, 27, 31, 35, 36, 39

transaction costs in (see transaction costs)

transaction costs

in ALM modeling, 199–201

fixed vs. variable, 214, 217–218, 223–224

function of, 212

literature on, 215–221

in portfolio optimization models, 223, 230–234

in real-life portfolio optimization, 234–237

step-increasing, 220

structure of, 223–229

translog functional form, 48, 49, 55

uncertainty

decision making under, 98

defined, 276

in energy sector, 126, 128, 142

as market condition, 75

vs. risk, 41–43

Uncertainty Quantification Toolkit (UQT), 341

uncertainty quantification (UQ), 353–360, 361

unexpected loss (UL), 277, 281, 291

United States

credit ratings agencies in, 314

equity vs. bond returns in, 189

monetary policy in, 76, 77

securities class actions in, 375, 379

stock market in, 81–82

UQTK, 355–356

US Federal Reserve System (FRS)

Board of Governors (BOG), 25

CCAR program, 273, 274, 277, 292

policy regimes of, 77

US Office of the Comptroller of the Currency (OCC), 25

US Securities and Exchange Commission (SEC), 338

Utilités Additives Discriminantes (UTADIS), 376, 387, 388, 389, 390, 392–395

utility function

in class action modeling, 376, 377

in decision models, 103–104, 122

in energy sector examples, 133, 138

estimating, 206–207

in portfolio selection, 245–246

in static portfolio theory, 156, 158–162, 194

validation sample, 317

value at risk (VaR)

in asset/liability management, 177

in asset return prediction, 94

and coherence, 277

and credit risk models, 297, 299, 300, 303, 304

and credit risk stress testing, 281

in CVA measurement, 37–38

in energy sector example, 133

in portfolio optimization, 220

in risk functions, 100

in securities financing transactions, 28

in systemic models, 12, 14

for top 200 banks, 275

worst-case, 108

variable neighborhood seach (VNS), 350–353, 354

variance

in CCR measurement, 22

modeling of, 366

vector GARCH model, 368, 369, 370

volatility

in bear markets, 79

and credit rating, 283, 285

and default rate, 289, 301, 306

of energy prices, 137

of exchange rates, 76, 77

and high-frequency trading, 338

and market risk measurement, 23

modeling, 364–366

and securities class actions, 372

time-varying, 73, 85

of US bonds, 191

of US stocks, 192

during VPIN events, 340, 342, 345

volume synchronized probability of informed trading (VPIN)

computational cost of, 346–347

defined, 339–340

FPR optimization in, 348–353, 354, 361

introduction of, 338, 342

parameters for, 340–341, 342–346, 358–360, 361

uncertainty quantification in, 353–360

VPIN event, 339–340, 344–346

worst-case analysis, 107–110

wrong-way risk (WWR), 34, 38

Yasuda Fire and Marine Insurance Company (Yasuda Kasai), 171, 175–182

z-score, 297, 300, 306, 307