Index
Angelo Corelli
(Maastricht School of Management, The Netherlands)
Understanding Financial Risk Management, Third Edition
ISBN: 978-1-83753-253-7, eISBN: 978-1-83753-250-6
Publication date: 27 May 2024
This content is currently only available as a PDF
Citation
Corelli, A. (2024), "Index", Understanding Financial Risk Management, Third Edition, Emerald Publishing Limited, Leeds, pp. 569-578. https://doi.org/10.1108/978-1-83753-250-620243024
Publisher
:Emerald Publishing Limited
Copyright © 2024 Angelo Corelli
INDEX
Absolute risk aversion (ARA)
, 10
Acceptance
, 21
Active acceptance
, 21
Advanced approach
, 488
Advanced IRR hedging
, 494
duration vectors
, 496–499
hedging with fixed income derivatives
, 499–502
M-absolute and M-squared models
, 494–496
Advanced Measurement Approaches (AMAs)
, 360, 366
Adverse selection
, 37
Aggregation
, 18
Alternative risk transfer (ART)
, 507, 514
insurance derivatives
, 519–522
market
, 514–516
primary contracts
, 516–519
Alternative standardized approach
, 366
Altman z score model
, 260–262
Analytic approximations
, 201–203
Annualized variance
, 380
Anti-money laundering (AML)
, 531
Arbitrage
, 23–25, 130
trading
, 131
Arbitrage pricing theory (ATP)
, 62
Arbitrageurs
, 130–131
Arithmetic returns
, 175
Arrow-Pratt coefficient
, 10
Arrow–Pratt relative risk aversion coefficient
, 324
Assessments
, 351
Asset-backed securities (ABS)
, 462
Assets
, 14, 341
return volatility
, 375
swaps
, 450–454
Asymptotic normality
, 71
Autocorrelation of financial returns
, 89–93
Autoregressive conditional heteroscedasticity model (ARCH model)
, 85–89
Autoregressive model
, 86
Available amount of stable funding (ASF)
, 328
Average rate of trading
, 315
Backtesting
, 112, 203–206, 406–408
Bands
, 238
Bank for International Settlement (BIS)
, 286
Bank of America
, 144
Bank risk
, 550–552
Banking sector
, 550
areas of future improvements
, 556–558
bank risk and business models
, 550–552
risk management systems
, 552–556
Banks
, 173, 251
Basel Accord
, 113
Basel Committee
, 329–330, 444
Basel II Accord
, 195
Basel II Approach
, 362–367
Basel III framework
, 330
Basic indicator approach (BIA)
, 364
Basis point value method (BPV method)
, 239
Basis risk
, 237
Bayesian probability models
, 114
BEKK model
, 425–426
Bernoulli utility functions
, 10
Bernoulli variable
, 29, 103–104
Bid–ask spreads
, 302, 305
Big data
, 525, 529–532
Binomial distribution
, 102–106, 406–407
Binomial trees
, 154–158, 165, 478
Bitcoin
, 536
derivatives on
, 536–539
hedging techniques
, 536–538
impact on markets and investments
, 538–539
Bivariate survival function
, 396
Black model
, 145
Black-76 model
, 142
Black/Scholes framework
, 25
Black–Scholes pricing formula
, 263
Black–Scholes–Merton model (BSM model)
, 65–66, 127, 153, 158–162
Blockchain
, 526
Bonds
, 12–13
prices
, 212–217
Bootstrapped historical simulation method
, 511
Bootstrapping
, 229
Bottom-up approach
, 360
Breakeven asset swap spread
, 454
Brownian motion
, 28–33, 236, 513
Business models
, 550–552
Business risk
, 1, 11, 15
Butterfly shifts
, 221
Calendar effects
, 95
Calibration
, 273
Call option
, 131
Callable bonds
, 377–380
Capital
, 444
relief
, 467–468
requirement
, 361
Capital asset pricing model (CAPM)
, 25, 40, 52, 60–63
model assumptions
, 52–55
SML
, 55–60
Capital market line (CML)
, 49–50
Caps
, 141–143
Captives
, 515
Cash CDO
, 464
Catastrophe reinsurance swaps
, 520
Central bank
, 308
Central limit theorem
, 29
Certainty equivalent of lottery
, 9
Chain rule
, 57
Chance nodes
, 114
Characteristic function of random variable
, 110
Chebyshev’s inequality
, 180
Chicago Board of Trade (CBOT)
, 289
Chicago Board Options Exchange (CBOE)
, 536
Chicago Mercantile Exchange (CME)
, 289
Chief executive officers (CEOs)
, 342
Chief information officer (CIO)
, 353
Cholesky composition
, 206
Cholesky decomposition
, 189
Citigroup
, 144
Classic risk management
, 340
Classic theory
, 17
Classical MC simulation method
, 513
Classical portfolio problem
, 4
Classical random walk
, 29
Clayton copula
, 392
Coefficient of lower tail dependence
, 396
Collateral
, 331
Collateralization
, 463
Collateralized debt obligations (CDOs)
, 439, 463–467
Commercial banks
, 238–239
Committee of Sponsoring Organizations (COSO)
, 339, 341
ERM
, 344–346
Commodity Exchange (COMEX)
, 289
Commodity futures
, 290–294
Commodity markets
, 285
commodity types and classification
, 286–288
risk for traders and investors
, 288–289
Commodity options
, 294–298
Commodity prices
, 287
Commodity risk
, 285
commodity markets
, 285–289
hedging
, 290–298
Commodity seller
, 295
Company
, 17
Competitive bidding
, 36
Compliance risk
, 344
Component VaR
, 197–198
Compound interest
, 212
Compounding frequencies for interest rates
, 226
Concavity of utility function
, 5
Concentration of funding
, 331
Concentration reports
, 553
Conditional correlation
, 83–85
Conditional covariance
, 82–83
Conditional default probability
, 273
Conditional dependence
, 81
financial comovements
, 82–85
time series analysis
, 85–95
Conditional expected value
, 178
Conditional heteroscedasticity
, 86
Conditional risk analysis
multivariate return distributions
, 424–426
VaR
, 420–424
Conditional VaR (CVaR)
, 411, 419, 422–424
Consistency
, 71
Constant absolute risk aversion (CARA)
, 15
Constant conditional correlation (CCC)
, 426
Constant relative risk aversion (CRRA)
, 15
Consumption-based capital asset pricing model (CCAPM)
, 60
Continuous auction market
, 302
Continuous compounding
, 212
Contractual maturity mismatch
, 330
Control activities
, 346
Conversion factors (CF)
, 256
Convexity adjustment for interest rate derivatives
, 501–502
Convexity hedging
, 240–244
Cooling degree day (CDD)
, 519
Copula functions
, 389–390
application to risk management
, 396–399
basic properties
, 390–393
measures of dependence
, 393–396
Cornish–Fisher approximation
, 320, 412, 423, 510
Corporate (managerial) appetite for risk
, 349
Corporate governance
, 543–544
management fails
, 544–547
postcrisis perspectives
, 549–550
remuneration and incentive systems
, 547–549
Corporate Governance Committee (CGC)
, 544
Corporate stockholders
, 17
Corporate value dilution
, 342
Correction factor
, 181
Correlation
, 40, 63–73, 206, 393
Correlation coefficient
, 44
Correlogram
, 91
Cost of hedging
, 167–170, 480–483
Counterparties
, 251
Counterparty credit risk, CDS spreads with
, 458–460
Coupon bond value
, 272
Covariance
, 66–69
Covariance matrix
, 187
of financial returns
, 72
Cox, Ingersoll and Ross model (CIR model)
, 232
Cramer–Rao lower bound
, 71
Credit analysis
, 259
Credit crunch
, 440
Credit default swaps (CDS)
, 441, 454–457
Credit derivatives
, 450
asset swaps
, 450–454
CDS spreads with counterparty credit risk
, 458–460
credit default swaps
, 454–457
Credit event
, 455
Credit rating agencies (CRAs)
, 442
Credit ratings
, 259–262
Credit risk
, 11–13, 18, 251, 552
credit ratings
, 259–262
default probabilities
, 252–255
loss
, 255–259
reduced-form models
, 271–277
structural models
, 262–271
Credit risk hedging
, 475, 483
CVA
, 487–491
modeling exposure
, 483–487
Monte Carlo methods
, 491–494
Credit score
, 13
Credit value adjustment (CVA)
, 487–491
CreditMetrics™ model
, 269–271
CreditRisk+™
, 275–277
Critical rate
, 223
Critical value
, 186–187, 196
Cross hedge
, 499
Cross-currency asset swap
, 452
Crypto tokens
, 538
Crypto traders
, 535
Cryptocurrencies
, 527, 535
Cumulative distribution
, 98, 101
Cumulative distribution function (c. d. f.)
, 511
Cumulative positions
, 238
Currency forward
, 369
Currency risk
, 11, 367
foreign exchange derivatives
, 369–373
risk hedging in FX markets
, 373–375
types
, 367–369
Currency swap
, 373
Current exposure (CE)
, 256
Current exposure method (CEM)
, 256, 489
Customer assets
, 341
Data
, 350
analysis
, 350
errors
, 431
filtering
, 429–432
protection
, 533
visualization
, 351
Database Italiano delle Perdite Operative (DIPO)
, 360
Debt financing
, 18
Decision nodes
, 114
Decision trees
, 113–116
Decomposition
, 196–199
Dedication
, 244
Default probability (DP)
, 12, 252–255, 492
Delta hedge
, 163
Delta hedging
, 163–165, 476–478
Delta neutral
, 163
Delta of derivative
, 163
Delta of payer swaption
, 146
Delta-neutral
, 476
Delta-normal approach
, 201
Delta–gamma approach
, 202, 509
Delta–gamma minimization method
, 510
Delta–gamma-Johnson method
, 510
Depth
, 309
Derivative securities
, 127
Derivatives arbitrage
, 24
Diagonal VEC model (DVEC model)
, 425
Diamond–Dybvig model
, 322–325
Digital finance
, 525
derivatives on bitcoin
, 536–539
Fintech revolution
, 526–535
Digital payments
, 532
Digitalization
, 528
Direct costs
, 17
Direct implied volatility estimate (DIVE)
, 66
Dispersion
, 7
Distance to default (DD)
, 263, 265
Distributions
, 97–98
binomial distribution
, 102–106
Pareto distribution
, 98–102
Poisson distribution
, 106–112
of stock price fluctuations
, 95
Diversification
, 11, 18, 40
Documentation
, 469
Dollar duration
, 241
Downside risk
, 178
measures
, 200
Dual trigger contracts
, 518
Duffie–Singleton model
, 273–274
Dupire’s model
, 377
Duration
, 240–244
of callable bond
, 379
vectors
, 496–499
Duration Vector Models (DVM)
, 496
Durbin–Watson test
, 92
Econometric models
, 66, 97
Economic risk
, 367–368
Economic theories of consumption
, 6
Economies of scale
, 36
Effective convexity
, 244
Effective duration
, 240, 242
Efficiency
, 71
Efficient frontier
, 45–46
Efficient market hypothesis (EMH)
, 6, 25–28
Elasticity
, 305
Employee/supplier assets
, 341
Energy derivatives
, 559–562
Enron
, 546
Enterprise risk
, 339
building and enhancing capabilities
, 347–352
COSO ERM
, 344–346
ERM framework
, 343–344
fundamentals
, 340–346
identification and assessment
, 340–343
implementation and models
, 354–355
management
, 352–354
practical implementation
, 352–355
process view
, 347–350
technological capabilities
, 350–352
Entrepreneurial risk management (ERM)
, 339
framework
, 343–344
Environmental risk
, 342
Equal weighting of observations
, 184
Equilibrium
, 307
gross return
, 312
Equity
, 18
Estimation methods
, 86
Euler’s theorem
, 197
on homogeneous functions
, 189–190
European Financial Stability Facility (EFSF)
, 446
European Union (EU)
, 445
Event identification
, 345
Event risk category
, 358
Excel statistical functions
, 111–112
Exception monitoring
, 351
Exchange rate risk management
, 357
Exchange-traded insurance derivatives (ET insurance derivatives)
, 519
Expected cash inflows (ECI)
, 327
Expected cash outflows (ECO)
, 327
Expected default frequency (EDF)
, 266
Expected exposure (EE)
, 12, 488
Expected losses (EL)
, 363
Expected return on the stock
, 25
Expected shortfall (ES)
, 178, 409–411, 419–422
Expected value of lottery
, 7
Explanatory simulation
, 117
Exponential smoothing
, 85
Exposure-at-default (EaD)
, 256
Exposure-at-recovery (EaR)
, 258
External consultants
, 20
Extreme value theory (EVT)
, 389, 399
data application
, 403–404
extreme VaR
, 404–406
theoretical background
, 399–403
Extreme VaR
, 404–406
Factor analysis
, 193
Factor mapping for VaR
, 193–194, 209–210
Fair strike
, 381
Fama–French model
, 62
Fannie Mae (FMA)
, 449
Fat tails
, 95
Financial Accounting Standards Board
, 553
Financial and reporting risks
, 344
Financial assets
, 341
Financial comovements
, 82
conditional correlation
, 83–85
conditional covariance
, 82–83
Financial crisis
, 439
credit derivatives
, 450–460
in Europe
, 444–448
impact on financial industry
, 448–450
lack of regulatory framework
, 440–444
and regulation
, 440–450
securitization
, 461–469
Financial deregulation
, 441
Financial derivatives
, 127, 130
interest rate derivatives
, 139–147
options and futures
, 128–138
Financial fraud
, 531
Financial instability
, 37
Financial institutions
, 18, 211
Financial instruments
, 1
Financial investors
, 45
Financial markets
, 1, 39
CAPM
, 52–63
MPT
, 40–51
Financial returns
, 95
Financial risk
, 1, 15–16
banking sector
, 550–558
challenges for research
, 558–565
corporate governance
, 544–550
management
, 543
Financial Stability Board
, 442
Financial volatility
, 63
Fintech
, 525
big data
, 529–532
revolution
, 526–535
and risk management
, 532–535
First difference
, 90
First passage models
, 266–268
First-order conditions
, 73
Fixed income futures
, 217–222
Fixed trigger
, 518
Flat volatility approach
, 143
Floorlet
, 141
Floors
, 141–143
Foreign currencies
, 13
Foreign exchange derivatives
, 369–373
Foreign exchange risk
, 13, 552
Forward
, 134–137
contracts
, 127, 136, 290–294
points
, 371
price of asset
, 135
Foucault model
, 306
Frank copula
, 392
Fraud risk
, 14
Frèchet distribution form
, 400
Freddie Mac (FMC)
, 449
Free-market rule
, 441
Funding liquidity
, 308–314
Funding risk
, 13
Futures
, 127–138
market
, 539
price
, 320
price of commodity
, 308
value
, 212
FX forward
, 370
G20
, 442
Gamma distribution
, 101
Gamma hedging
, 165–167, 478–480
Gamma swaps
, 383
Gap analysis
, 238
Gap method
, 554
Gaussian (normal) distribution
, 41
Gaussian copula model
, 269, 391–392
Gaussian estimator
, 89
Gaussian likelihood
, 89
Gaussian multi-factor model
, 234–235
Generalized autoregressive conditional heteroscedasticity model (GARCH model)
, 85–89
GARCH (p, q) modeling
, 424–426
for variance estimation
, 185
Generalized Brownian motion
, 31
Generalized extreme value (GEV)
, 390, 401
Generalized Pareto distribution (GPD)
, 403
Generalized Wiener process
, 31
Geometric Brownian motion
, 32
Geometric returns
, 176, 186–187
Global Association of Risk Professionals (GARP)
, 18
Global Operational Loss Database (GOLD)
, 360
Globalization of financial markets
, 357
Grace period
, 486
Gramm–Leach–Bliley Act
, 442
Greeks of swaptions
, 146
Gross income
, 364
Gross return
, 312
Group captives
, 517
Gumbel copula
, 392
Gumbel distribution
, 400
Hazard rate
, 271
Heating degree day (HDD)
, 519
Hedge ratio
, 225
Hedged assets
, 326
Hedgers
, 128–129, 217
Hedging
, 18
advanced IRR hedging
, 494–502
credit risk hedging
, 483–494
with fixed income derivatives
, 499–502
market risk hedging
, 476–483
techniques
, 158, 475, 536–538
Heterogeneous ARCH process (HARCH process)
, 433
Heterogeneous volatility
, 433–435
Heteroscedasticity
, 86
High minus low (HML)
, 62
High-frequency data
, 429
high-frequency trading
, 429–433
intraday risk analysis
, 433–435
High-frequency trading
, 429
basic stylized facts
, 432–433
data filtering
, 429–432
High-quality assets (HQAs)
, 325
Hill estimator of tail index
, 404
Historical assessment
, 359
Historical data
, 113
Historical simulation approach
, 184–185, 240, 511–513
Historical volatility
, 63
Holding periods
, 310
Ho–Lee model
, 233
Hot wallets
, 535
Hotline management
, 351
Hull–White model
, 233
Illicit financial flows
, 531
Illiquidity
, 306
Immunization
, 220–226, 244
Implied forward rate
, 140
Implied volatility
, 65, 375–377
Incentive systems
, 547–549
Incremental VaR
, 198
Indirect costs
, 17
Information and communication
, 346
Inside value at risk
, 195
VaR features
, 195–203
VaR testing
, 203–207
Insurance
, 22, 37
contracts
, 519
derivatives
, 519–522
Interbank risk
, 543, 558–559
Interest rate cap (IRC)
, 141
Interest rate floor (IRF)
, 141
Interest rate risk (IRR)
, 11, 211, 552
duration and convexity hedging
, 240–244
dynamics of
, 212–226
management
, 236
measurement techniques
, 238–240
short rate models
, 226–236
sources and identification
, 236–238
Interest rate swaps (IRSs)
, 127, 139–141
Interest rates
, 12
caps and floors
, 141–143
derivatives
, 139
interest rate swaps
, 139–141
swaptions
, 144–147
Internal control process
, 362
Internal data processing
, 366
Internal environment
, 345
Internal rate of return (IRR)
, 214
International Monetary Fund (IMF)
, 287, 442
Intraday effects
, 95
Intraday risk analysis
, 433
heterogeneous volatility
, 433–435
Intuition assessment
, 359
Inverse functions
, 391
Investment banks
, 442
Investors
, 4, 6, 39, 306
Itô process
, 31
Ito’s lemma
, 123–125
January effect
, 27–28, 95
Jarrow–Turnbull model
, 271–273
Jensen’s inequality
, 9
Joint probability density function
, 69
JP Morgan Chase
, 144
Kendall’s tau
, 394–395
KMV-Merton approach
, 262–266
Kupiec’s test
, 204–205
Lagged value
, 89
Lagrangian function
, 46
Lagrangian multipliers
, 46–47
Latent variable models
, 397
Learning
, 22
Legal risk
, 358
Lehman Brothers (LB)
, 441
Leverage
, 50, 238
Likelihood function
, 69–71, 108
Likelihood ratio
, 407
test
, 204
Limit law
, 400
Limit order
, 303
Linear correlation
, 389, 393
Linear utility
, 14
Liquidity
, 305, 468
black holes
, 313–314
CAPM
, 337–338
Liquidity coverage ratio (LCR)
, 325–328
Liquidity models
, 314
Diamond–Dybvig model
, 322–325
theoretical models
, 314–318
traceable models
, 318–322
Liquidity risk
, 11, 13, 301, 552
liquidity models
, 314–325
market prices
, 302–314
and regulation
, 325–332
Liquidity-adjusted VaR (LVaR)
, 314, 319
Log-likelihood
, 89, 105, 108
function
, 70–71
London Inter Bank Offered Rate (LIBOR)
, 139
Loss
, 255–259
frequency
, 363
function
, 492
severity
, 363
Loss given default (LGD)
, 488
Losses and profits (L/P)
, 175
Lower tail dependence coefficient
, 396
M-absolute models
, 494–496
m-dimensional copula
, 390
M-squared models
, 494–496
Macaulay duration
, 240, 242
Macro hedge
, 500
Maintenance margin
, 304
Managed CDOs
, 467
Managers
, 17
Mapping
, 193, 209
to regulation
, 350
Margin Agreements (MAs)
, 486
Marginal scrubbing error
, 431
Marginal VaR
, 196–197
Market clearing condition
, 311
Market efficiency
, 36
Market failures
, 36
types of
, 36–37
Market inefficiencies
, 36
Market liquidity
, 308–314
risk
, 14
Market microstructure
, 302–306
Market portfolio
, 52–53
Market prices
, 302
funding vs. market liquidity
, 308–314
market microstructure
, 302–306
price formation
, 306–308
of risk
, 150–152
Market risk
, 11, 18, 173
metrics
, 174–178
overview
, 174–176
quantile metrics and VaR
, 176–179
VaR calculation methods
, 184–189
VaR rationale and definition
, 180–182
Market risk hedging
, 476
cost of hedging
, 480–483
delta hedging
, 476–478
gamma and Vega hedging
, 478–480
Marking to market
, 137, 293
Markov chain
, 282
Markov process
, 28
for transition matrices
, 282–283
Mass function of binomial distribution
, 104
Matching
, 244
Maturity model
, 355
Maximum likelihood estimation (MLE)
, 69
Maximum likelihood estimator
for binomial distribution
, 105
for time-independent probability
, 282
Maximum likelihood methods
, 69–73
Mean of binomial distribution
, 105
Mean reversion effect
, 28
Mean-excess function (MEF)
, 403
Measurement techniques
, 238–240
Merton latent variable model
, 397
Metrics
, 330–332
Miners
, 527
Minimization problem
, 316
Minimum transfer amount
, 486
Minimum variance portfolio (MVP)
, 45
Mispricing
, 27
Modern portfolio theory (MPT)
, 40
optimal portfolios of risky assets
, 45–48
optimal portfolios with risk-free asset
, 48–51
risk/return trade off
, 40–44
Modified Delta-VaR
, 508–510
Modified duration
, 240, 242
Modified MC and scenario analysis
, 513–514
Monitoring tools
, 330–332
Monte Carlo kernel
, 397
Monte Carlo methods
, 491–494
Monte Carlo simulation (MC simulation)
, 117, 187–189, 507
of copulas
, 399
Moral hazard
, 37
Mortgages
, 440
Multi-factor models
, 234–236
Multidimensional approach
, 14
Multiperiod model
, 60
Multiple peril products
, 517
Multivariate GARCH (MGARCH)
, 419
Multivariate return distributions
, 424
GARCH (p, q) modeling
, 424–426
Mutual funds
, 441
n-copula
, 391
n-dimensional copula
, 390
n-dimensional covariance matrix
, 82
Nationally Recognized Statistical Rating Organization (NRSRO)
, 443
Natural monopoly
, 36
Negative externalities
, 36
Net cash outflows (NCO)
, 325
Net liquidity demand (NLD) indicator
, 309
Net present values (NPVs)
, 115
Net return
, 312
Net Stable Funding Ratio (NSFR)
, 328–330
Net working capital
, 19
Netting agreement
, 484
New York Mercantile Exchange (NYMEX)
, 289
Newton–Rapson method
, 460
No-arbitrage models
, 233
Nonlinearity
, 94, 202
Nonnormal percentile
, 320
Nonparallel shifts
, 220
Normal distribution
, 98
Normality
, 173
Null hypothesis
, 92, 204–205, 408
Objective-setting
, 345
Obligations
, 251
One-factor copula model
, 398
One-period return on security
, 60
Operational risk
, 11, 14, 18, 344, 358
Basel II Approach
, 362–367
identification and assessment
, 358–361
treatment and control
, 361–362
Operational Riskdata eXchange (ORX)
, 360
Optimal asset value
, 312
Optimal bid price
, 307
Optimal contract
, 324
Optimal portfolios
with risk-free asset
, 48–51
of risky assets
, 45–48
Optimal trading model
, 314
Optimization approach
, 374
Option contracts
, 294
Option pricing
, 153
binomial trees
, 154–158
BSM model
, 158–162
models
, 154–162
theory
, 202
Option spreads
, 295
Option structure
, 131–133
Option value
, 376
Optionality
, 238
Options
, 127–138
Order statistic
, 409
Order-driven markets
, 306
Ordinary least squares (OLS)
, 86
Organization for Economic Cooperation and Development (OECD)
, 544
Organizational assets
, 341
Over-the-counter markets (OTC markets)
, 127, 288
Par yield
, 216
Parallel shifts
, 220
Parametric method
, 185–187
Pareto distribution
, 98–102
Passive acceptance
, 21
Past stock price
, 25
Path-dependent simulation
, 485
Payoffs
to bondholders at time
, 263
equation
, 456
of forward contract
, 134, 290
at maturity
, 380
Payout
, 131–133
Peak over threshold method (POT method)
, 402
Permanent impact
, 316
Physical assets
, 341
Piecewise constant random function
, 29
Poisson distribution
, 106–112
Poisson process
, 494
Portfolio hedging
, 163
cost of hedging
, 167–170
delta hedging
, 163–165
gamma and Vega hedging
, 165–167
Portfolio optimization in Excel
, 51
Portfolio return
, 49
Portfolio value
, 43
Portfolio weights
, 49
Positive and negative outcomes
, 3–4
Positive externality
, 36
Postcrisis perspectives
, 549–550
Potential future exposure (PFE)
, 256
Power law (PL)
, 437
for intraday data
, 437–438
Premium
, 52
Present value
, 457
of bond in discrete compounding
, 216
Preventive controls
, 362
Prices
, 63
cycle
, 287
drop
, 316
dynamics
, 315
formation
, 302, 306–308
tree
, 157
Primary contracts
, 516–519
Principal component analysis of term structure
, 248–249
Probabilistic approaches
, 112
decision trees
, 113–116
scenario analysis
, 112–113
simulations
, 116–118
Probability
and consequences
, 3
mass function
, 106
Probability density function (p. d. f.)
, 40, 102, 511
Probability of default (PD)
, 456, 488
Process risk
, 342, 358
Product copula
, 391
Profit/loss data (P/L data)
, 174
Proportion of failures test (POF test)
, 204–205, 407
Public economic policies
, 6
Public goods
, 36
Put option
, 131
Put-call parity formula
, 373
Quantile metrics
, 176–179
Quantile of return distribution
, 423
Quasi-Monte Carlo methods (QMC methods)
, 513
Random error component
, 25
Random walk theory of financial assets
, 6
Randomness
, 2–5
Rating agencies
, 259
Rational expectations theory
, 5–6
Rationality
, 5–10
Real options
, 127
Recovery rate (RR)
, 12, 255
Reduced-form models
, 271
(see also Structural models)
CreditRisk+™
, 275–277
Duffie–Singleton model
, 273–274
Jarrow–Turnbull model
, 271–273
Reference entity
, 455
Regression formula
, 58
Regret operator
, 201
Reinsurers
, 520
Relative liquidity-adjusted total risk
, 321
Relative risk aversion (RRA)
, 14
Remargin period
, 486
Remuneration system
, 543, 547–549
Replication argument
, 381
Reputational risk
, 358
Required amount of stable funding (RSF)
, 328
Resiliency
, 309
Response management
, 351
Return of equity (ROE)
, 468
Return on assets (ROA)
, 19
Risk
, 1, 4, 39, 357
acceptance
, 349
arbitrage
, 24
assessment
, 20, 345
avoidance
, 22, 349
in corporations and financial institutions
, 15–18
currency risk
, 367–375
dashboards
, 351
factor
, 320
hedging in FX markets
, 373–375
identification, measurement and mitigation
, 19–21
impact
, 20
likelihood
, 20
management
, 15–22
measure
, 410
mitigation
, 22, 362
operational risk
, 358–367
or threat
, 3
premium
, 8, 22, 52, 54
priority
, 21
process
, 16
randomness and uncertainty
, 2–5
rationality and risk aversion
, 5–10
reduction
, 349
repository
, 350
response
, 345
response strategies
, 21–22
scoring
, 351
sharing
, 349
theory of markets
, 22–33
for traders and investors
, 288–289
transfer
, 362
types
, 10–15
volatility risk
, 375–383
Risk aversion
, 5–10
relationship
, 9
Risk management
, 97, 532–535
systems
, 552–556
Risk mapping
to objectives
, 350
to policies
, 350
Risk-Adjusted Return on Capital (RAROC)
, 386–387
Risk-averse investors
, 50
Risk-neutral probability
, 155–156
Risk-purchasing groups
, 515
Risk-retention groups
, 515
Risk–return trade-off
, 39–44
Rolling yield
, 537
Sampling of Brownian Motion paths in Excel
, 32–33
Sarbanes–Oxley Act (2002)
, 546
Scaling laws
, 94, 433
Scenario analysis
, 112–113, 366
Scorecards
, 359, 361
Securitization
, 439, 461, 551
advantages and disadvantages
, 467–469
CDOs
, 463–467
structure and participants
, 461–463
Security market line (SML)
, 52, 55–60
Semistrong-form version of EMH
, 26
Semivariance operator
, 201
Sensitivity of portfolio
, 201
Sensitivity-based risk measures
, 200
Shape of utility function
, 8
Short rate models
, 226
multi-factor models
, 234–236
single-factor models
, 230–234
term structure of interest rates
, 226–229
Significance level
, 179
Simple interest
, 212
Simulations
, 116–118, 240
Single-factor models
, 230–234
Sister captives
, 517
Skewing
, 95
Small firm effect
, 28
Small minus big (SMB)
, 62
Soft storage wallets
, 535
Sovereign risk dynamics
, 562–565
Spearman’s rho
, 394–395
Special purpose vehicle (SPV)
, 446, 472–473
Specialized analytics
, 351
Specific risk
, 11
Speculation
, 129
Speculators
, 129–130, 217
Spot rates
, 219
Spot volatility approach
, 143
Spot–forward parity
, 136
Stabilization of rates
, 238
Stable funding
, 328–329
Stablecoins
, 538
Standard deviation
, 40, 56
Standard duration
, 495
Standard error of estimation
, 64
Standard normal distribution
, 78–79
Standardized approach
, 364, 488
Static risk management processes
, 340
Static simulations
, 240
Statistical analysis
, 97
distributions
, 98–112
probabilistic approaches
, 112–118
Steady state distribution function
, 30
Stocks
, 4, 12, 55
prices
, 158
Stop-loss order
, 303
Strategic risks
, 344
Stress testing
, 206–207
Strike
, 131
Strong-form version of theory
, 26
Structural models
, 262
(see also Reduced-form models)
CreditMetrics™ model
, 269–271
first passage models
, 266–268
KMV-Merton approach
, 262–266
Student-t factor model
, 492
Student’s t-copula
, 391–392
Stylized facts
, 93–95
Subadditivity
, 409, 420
Subprime mortgages
, 461
Sum of square deviation from mean
, 64
Super cycles
, 287
Survival function
, 253
of Pareto variable
, 98
Survival probability
, 272
Swaps
, 294–298
cash flows
, 140
payments
, 453
Swaptions
, 144–147
Synthetic CDO
, 464
System integration
, 351–352
Systematic risk
, 10, 52
Tail
, 98
dependence of copulas
, 395
index
, 433
Tangency point
, 49
Temporary impact
, 315
Term structure of interest rates
, 226–229
Tether
, 538
Theoretical models
, 314–318
Theory of markets
, 22–33
Three-factor model
, 61
Threshold
, 486
Tick frequencies
, 430
“Tick” loss target function
, 413
Tightness
, 309
Time horizon
, 179, 514
Time series
, 81
analysis
, 85
ARCH/GARCH models
, 85–89
autocorrelation of financial returns
, 89–93
stylized facts
, 93–95
Time Until First Failure test (TUFF test)
, 204, 407
Top-down approach
, 360
Total cost of trading
, 316
Total portfolio VaR
, 197
Traceable models
, 318–322
Traders in market
, 128–131
Trading
path
, 318
strategy
, 315
Trans-European Automated Real-time Gross Settlement Express Transfer System
, 445
Transaction cost calculations
, 318
Transaction risk
, 367
Transfer risk
, 22
Transition matrix
, 269
Transition periods
, 508
Transition thresholds
, 271
Translation risk
, 367
Transparency
, 305, 545
Transparent financial reporting
, 21
Trial and error approach
, 215
Twice differentiable payoff function
, 381
Twist shift
, 221
12-point Gauss–Hermite integration
, 512
Uncertainty
, 2–5, 339
Utility functions
common forms of
, 14–15
of investor
, 4
Value at Risk (VaR)
, 12, 195, 256, 314, 406, 419, 507, 554
advances
, 507–514
analysis
, 173, 176–179
analytic approximations
, 201–203
backtesting
, 406–408
calculation methods
, 184–189
choice of parameters for
, 183
conditional VaR
, 411–413
decomposition
, 196–199
expected shortfall
, 409–411
features
, 195–203
historical simulation approach
, 184–185
limitations
, 199–201
Monte Carlo simulation
, 187–189
parametric method
, 185–187
for portfolios of derivatives
, 416–417
rationale and definition
, 180–182
testing
, 203–207
Value tokens
, 538
Variable trigger
, 518
Variance decomposition of returns
, 59
Variance of portfolio
, 43
Variance swaps
, 380–383
Vasicek model
, 230, 232
Vector of optimal weights
, 47
Vega hedging
, 147, 165–167, 478–480
Vigilance
, 21
Volatility
, 40, 63–73
strategy with strangles
, 138
surface
, 376
types
, 63–66
Volatility risk
, 11, 357, 375
callable bonds
, 377–380
implied volatility
, 375–377
variance swaps
, 380–383
Volume, velocity, variability or veracity
, 529–530
Weak-form efficiency
, 25
Weekend effects
, 95
Weibull distribution
, 401
Weighted spread
, 322
Weighting factor
, 185
Worst-case scenario (WCS)
, 514
Yield curve
, 223, 226
risk
, 200, 237
Yield shifts
, 220–226
Yield to call
, 377–378
Yield to maturity (YTM)
, 214
Yield to worst
, 377
Yields
, 212–217
Zero-coupon bond price
, 235
Zero-coupon rate
, 495
Zero-volatility spread
, 454
Zipf’s law
, 437
- Prelims
- Chapter 1: Risk: An Overview
- Chapter 2: Financial Markets and Volatility
- Chapter 3: Conditional Dependence and Time Series
- Chapter 4: Statistical Analysis
- Chapter 5: Financial Derivatives
- Chapter 6: Option Pricing and Risk Modeling
- Chapter 7: Market Risk
- Chapter 8: Inside Value at Risk
- Chapter 9: Interest Rate Risk
- Chapter 10: Credit Risk
- Chapter 11: Commodity Risk
- Chapter 12: Liquidity Risk
- Chapter 13: Enterprise Risk
- Chapter 14: Other Risks
- Chapter 15: Beyond Normality and Correlation
- Chapter 16: Conditional Risk Analysis
- Chapter 17: High-frequency Data
- Chapter 18: Financial Crisis and Securitization
- Chapter 19: Hedging Techniques
- Chapter 20: Advanced Topics
- Chapter 21: Digital Finance and Risk
- Chapter 22: The Future of Financial Risk Management
- Index