Index
Angelo Corelli
(Associate Professor of Finance, Center of Excellence for Research in Finance and Accounting, American University in Dubai, UAE)
Understanding Financial Risk Management, Second Edition
ISBN: 978-1-78973-794-3, eISBN: 978-1-78973-791-2
Publication date: 28 October 2019
This content is currently only available as a PDF
Citation
Corelli, A. (2019), "Index", Understanding Financial Risk Management, Second Edition, Emerald Publishing Limited, Leeds, pp. 543-556. https://doi.org/10.1108/978-1-78973-791-220192001
Publisher
:Emerald Publishing Limited
Copyright © 2019 Emerald Publishing Limited
INDEX
Absolute Risk Aversion (ARA)
, 15
Accounting
, 10, 58, 123, 349, 455
Accrued interest
, 431, 433, 436
Active acceptance of risk
, 22
Actuarial price
, 5
Advanced IRR hedging
, 475
duration vectors
, 477–480
hedging with fixed income derivatives
, 480–482
M-Absolute and M-Squared models
, 475–477
Adverse selection
, 38
Aggregation
, 19, 530
All-or-nothing
, 333
Alternative risk transfer (ART)
, 489
insurance derivatives
, 501–504
market
, 496–498
primary contracts
, 498–501
Altman z-score model
, 307–308
American Accounting Association (AAA)
, 374
American Institute of Certified Public Accountants (AICPA)
, 374
American option
analytic approximation to prices
, 249–251
binomial tree
, 198–202, 209, 458
early exercise
, 403
future options compared to spot options
, 262
Monte Carlo simulation and
, 231–233
non-standard
, 82
option on dividend paying stock
, 209, 458
option on non-dividend paying stock
, 191
put-call relationship
, 191
Amortizing period
, 420
Amount of stable funding (ASF)
, 358
Analytic approximations
, 247–249
to prices
, 249–251
Analytical tools
, 95
Approximation methods
, 65
Arbitrage opportunity
, 175
Arbitrage Pricing Theory
, 62
Arbitrage theory
, 23–25
Arbitrage trading
, 175
Arbitrageurs
, 172, 174
Arithmetic returns
, 219–220, 230
Arrow-Pratt coefficient of absolute risk aversion
, 10
Ask price
, 166, 335, 337, 339–341, 351, 507
Asked price
, 364
Assessments
, 381
Asset return volatility
, 406
Asset swaps
, 430–434
Asset-Backed Securities (ABS)
, 443
Asymmetry of information
, 37
Asymptotic normality
, 70
ATP estimation
, 62
Autocorrelation (see also Correlation)
, 79
absence of
, 91
coefficient of time series
, 88
of financial returns
, 87–91
of returns
, 91
of squared returns
, 92
Autoregressive conditional heteroscedasticity model (ARCH model)
, 83–87
ARCH variance
, 66
Average rate of trading
, 345
Average strike call
, 486
Average strike put
, 486
Axiomatic approach
, 245
Back testing
, 109, 123, 140–142, 249
Backward induction
, 112
Backward PDE
, 407
Balance sheet
, 19–20
Bank funding structure
, 523
Bank liquidity management
, 531
Bank of America
, 188
Bank regulation
, 530
Bank risk
, 522–524
Banking sector
, 515, 522
areas of future improvements
, 528–531
bank risk and business models
, 522–524
risk management systems
, 524
Banks
, 448
Banks business model
, 523
Basel Accord
, 2, 110, 224
Basel committee
, 530–531
Basel II approach
, 393–396
Basel III framework
, 359
Basic Indicator Approach (BIA)
, 393–394
Basic stylized facts
, 506–508
Basis Point Value method (BPV method)
, 285–286
Basis risk
, 283
hedging and
, 283
Basket option
, 348, 533–534
Bayesian probability models
, 111
BEKK model
, 160
Bermudan-style options
, 534
Bermudan-style receiver swaption
, 433
Bernoulli default variables
, 473
Bernoulli utility functions
, 10
Bernoulli variable
, 29–30, 100–101
Beta
, 246
of asset
, 54
risk measure
, 55
Bid-ask spread
, 166–167, 173, 332, 335–336
bouncing of prices
, 167
Big data
and risk
, 538–539
vendors
, 504
Binary random vector
, 131
Binomial distribution
, 100–103, 140–141, 249
characteristic function of
, 107
Binomial mass function
, 106
Binomial model in discrete time
, 172
Binomial trees
, 198–202, 209, 458
Bivariate normal distribution
, 33, 125
Bivariate survival function of random vector
, 130
Black holes, liquidity
, 343–344
Black Model
, 187–189
Black-76 model
, 186
Black–Scholes model
, 26
continuous dividend version
, 206
option pricing model
, 194
pricing formula
, 309
theoretical option value
, 205
Black–Scholes–Merton model (BSM model)
, 64–65, 171–172, 197, 202–207, 311, 403
in continuous time
, 172
Bloomberg
, 164, 504
Bond
embedded
, 407
price
, 12, 258–263, 300, 436
pricing formula
, 262
yields
, 12
Bootstrapped historical simulation method
, 493
Bootstrapping method
, 273
Bottom tranche
, 444
Bottom-up approach
, 390, 473
Boundary conditions
, 204
Brent’s method
, 434
Brownian motion
, 29, 282, 495
basic properties
, 30–31
sampling of Brownian motion paths in excel
, 33
Business
models
, 522–524
risk
, 1, 16
Butterfly shifts
, 268
Buying on margin
, 333
Calendar effects
, 92
Call options
, 175
Callable asset swaps
, 433
Callable bonds
, 407–410
Cap rate
, 186
Capital asset pricing model (CAPM) (see also Option pricing models)
, 26, 51, 59
assumptions
, 51–55
ATP estimation
, 62
implication
, 60
SML
, 55–59
three factor model
, 61
Capital market line (CML)
, 49, 52
Capital relief
, 449
Caplet interest rate
, 186
Caplets
, 185–186
CAPM-based asset pricing model
, 366
Caps
, 185–188
Captives
, 497–499
Cascade process
, 450
Cash ratio
, 20
Cash settlement
, 435
Cash-flow
, 527
CDOs
, 448
mapping
, 246
statement
, 19
Cat Swap
before
, 502
after
, 503
Catastrophe reinsurance swaps
, 502
Cauchy–Schwarz inequality
, 47
Central limit theorem
, 30
Centralized continuous auction market
, 333
CEO
, 382–384
compensation
, 520
facing challenges
, 372
remuneration
, 519
risk aspect
, 383
separation
, 521
Certainty equivalent of lottery
, 10
Chain rule
, 57
Chance nodes
, 111, 113
Characteristic function
for binomial distribution
, 107
of random variable
, 107
Chebyshev’s inequality
, 224
Chicago Board of Trade (CBOT)
, 502
Chicago Mercantile Exchange (CME)
, 502
Cholesky decomposition
, 233
Cholesky matrix
, 253
Christoffersen’s framework
, 142, 251
Citigroup
, 188
Classic risk management
, 370
Classic theory
, 18
Classical Monte Carlo simulation method
, 495
Classical random walk
, 29
Clayton copula
, 126–127
Clearing house
, 181, 518
Clustered volatility
, 91
Clustering of exceptions
, 142
Coefficient of lower tail dependence
, 130
Coefficient of upper tail dependence
, 129–130
Coherent measures
, 123
Collateralization
, 444
Collateralized bond obligations (CBO)
, 444
Collateralized Debt Obligation (CDO)
, 132, 425, 444–448
Collateralized loan obligation (CLO)
, 444
Collateralized mortgage obligations (CMO)
, 444
Combination option trading strategy
, 182
Commodity price
, 11, 217, 533–534
Commodity swaps
, 183
Commodity-linked investments
, 532
Communication
, 376
Compliance risk
, 374
Compound interest
, 258
Compounding frequencies for interest rates
, 272
Concave function
, 64
utility function
, 8–9
Conditional Autoregressive VaR
, 147, 158
Conditional covariance
, 80–81
Conditional coverage model
, 142, 251
Conditional dependence
, 79
Conditional expected value
, 222
Conditional heteroscedasticity
, 84
Conditional loss (CL)
, 222
Conditional risk analysis (see also Statistical analysis)
, 153
multivariate return distributions
, 158–161
VaR
, 154–158
Conditional VaR (CVaR)
, 145–147, 156–158
Confirmation
, 91
Consistency
, 70
Constant Absolute Risk Aversion (CARA)
, 15
Constant Conditional Correlation Model (CCC Model)
, 160
Constant interest rate
, 272
Constant Relative Risk Aversion (CRRA)
, 15
Consumption-based capital asset pricing model (CCAPM)
, 59–60
Continuous auction market
, 332
Continuous compounding
, 258
Continuous liquidity-adjusted net return
, 350
Continuous n-variate distribution function
, 125
Continuous variable
, 180
Control activities
, 376
Convenience yield
, 338
Conversion factor
, 302–303
Convertible bond
, 311
Convexity
, 289
adjustment for interest rate derivatives
, 483
hedging
, 286–290
of risk surface
, 143
Cooling degree day (CDD)
, 502
Copula functions
, 123
application to risk management
, 130–133
basic properties
, 124–127
Copula Clayton Frank
, 127
Copula Gauss student
, 126
measures of dependence
, 127–130
Cornish-Fisher approximation
, 146, 151, 157
Cornish-Fisher expansion
, 492
Corporate governance
management failures
, 516–519
post-crisis perspectives
, 522
remuneration and incentive systems
, 519–521
role in financial risk management
, 516
Corporate Governance Committee (CGC)
, 516
Corporate stockholders
, 17
Corporations, risk in
, 16–19
Correction factor
, 225
Correlation
, 62, 66–69, 123
coefficient
, 44
coefficient
, 67–68
Correlation effects
, 19
Correlogram
, 88–89
Cosandey’s model
, 351
COSO
, 371
ERM
, 374–377
framework
, 383
Cost of hedging
, 212–214, 460–463
Counterparty
, 13–14, 131, 302, 305, 465
Coupon
, 264
bond
, 260
fixed
, 183
zero-coupon
, 274–275, 289
Coupon-paying bond
, 274
Covariance
, 44, 66–69
Covariance matrix
, 80
of financial returns
, 72
Cox, Ingersoll, and Ross model (CIR model)
, 278, 281
Cramer–Rao lower bound
, 70
Credit conversion factors (CF)
, 302
Credit Crunch
, 420
Credit default spread
, 438
Credit Default Swaps (CDS)
, 435–438
market
, 300
spreads with counterparty credit risk
, 438–440
Credit derivatives
, 430
asset swaps
, 430–434
Credit event
, 298, 301, 308, 310, 435, 439
Credit exposure
, 302
Credit management
, 539
Credit quality
, 450
report
, 525
Credit Rating Agencies (CRA)
, 422, 424
Credit ratings
, 305–308, 423
Credit risk (see also Interest rate risk (IRR))
, 12–13, 19, 130–131, 297–298, 469, 529
credit ratings
, 305–308
default probabilities
, 298–301
LgD
, 302–305
management
, 297, 430, 524, 529
Markov process for transition matrices
, 332–329
reduced-form models
, 317–324
structural models
, 308–317
Credit risk hedging (see also Market risk hedging)
, 463
CVA
, 467–472
modeling exposure
, 463–467
Monte Carlo methods
, 472–475
Credit score
, 13
Credit spread
, 217, 305, 316–317, 343, 431, 436, 469, 471–472, 535–536
Credit swaps
, 183
Credit value adjustment (CVA)
, 467–472
Credit VaR measurement
, 317
CreditMetrics
, 132
CreditMetrics™ model
, 315–317
CreditRisk+™ model
, 321–324
Critical rate
, 269
Critical value
, 231, 242
Cross-currency asset swap
, 433
Crude Oil Swap
, 533–534
Cumulative density function
, 492
Cumulative distribution
, 99, 132
Cumulative distribution function (c.d.f.)
, 494
Cumulative normal distribution
, 65
Currency forwards
, 399–400, 402, 405, 414
Currency option pricing model
, 403
Currency risk
, 13, 397
FX derivatives
, 399–403
risk hedging in FX markets
, 404–405
types
, 397–399
Currency swaps
, 183, 399–400, 403, 414
Current exposure (CE)
, 302
Current exposure method (CEM)
, 302, 470
Current ratio
, 20
Curvature
, 267–268, 289, 476–477, 480
Cutting-edge treasuries
, 384
Data
analysis
, 381
errors
, 165, 505
filtering
, 163–166, 504–506
visualization
, 381
Day count conventions
, 183
Day order
, 333
Debt
on asset ratio
, 20
on equity ratio
, 20
market
, 362
value at time
, 320
Decision nodes
, 111, 113
Decision trees
, 110–113
Decision-making process
, 382
Default correlation
, 321–322, 440
Default probability (DP)
, 12, 298–301, 473
density
, 437
Default risk
, 432, 435–436, 451, 455
Delivery
, 264, 395
Delivery price
, 179, 401
Delta
, 212, 461
approach
, 491
approximation
, 471, 491
of call option
, 458
delta-gamma-minimization method
, 492
for European receiver swaptions
, 191
hedging
, 207–210, 456–458
of payer swaption
, 190
standard delta-normal approach
, 150
vector of value
, 248
Delta-gamma-Monte Carlo methods
, 491
Delta-neutral portfolio
, 456–459
Delta-neutrality
, 210, 457
delVaR approach
, 245
Depth
, 339–340
Derivative
derivatives arbitrage
, 25
securities
, 171
Diagonal VEC model (DVEC model)
, 160
Diamond-Dybvig model
, 352–355
Diffusion process
, 309
Digitalization
, 537
Big data and risk
, 538–539
Fintech, impact of
, 538
Direct costs
, 17
Direct Implied Volatility Estimate (DIVE)
, 65
Direct-jump simulation
, 465
Discount bond
, 292
Discount rates
, 469
Discrete-time estimator
, 332
Discrete-time Markov chain model
, 332
Discrete-time transition matrix
, 329
Dispersion
, 7
Distance to default (DD)
, 309
Distributions
, 95–96
binomial
, 100–103
Pareto
, 96–100
Poisson
, 103–109
Diversification
, 11, 40
effect
, 45
of income
, 524
Dividend
BSM model
, 202
continuous dividend rate
, 206
discounting and
, 6
dividend-paying stocks
, 181
Put-Call parity formula for American options
, 191
storage costs vs.
, 180
yield
, 180, 292
Documentation
, 450
Dollar duration
, 287
Down-and-out option
, 311
Downside risk
, 222
Drift rate
, 32
Drift term
, 32
Duffie-Singleton model
, 320–321
Dupire’s model
, 407
Duration
, 286–290
vectors
, 477–480
Duration vector models (DVM)
, 477
Durbin–Watson test
, 89
Dynamic Conditional Correlation (DCC)
, 161
Dynamic hedging
, 343, 529
Dynamics of interest rates
, 258
Econometric models
, 66, 95
Economic risk
, 404
Economic theories of consumption
, 6
Economies of scale
, 37
Effective ERM
, 380
Efficiency
, 70
Efficient frontier for portfolio or risky assets
, 45
Efficient Market Hypothesis (EMH)
, 6, 25–29
information subsets
, 28
Electronic trading
, 91
Embedded options
, 285, 289, 387
Empirical research
, 421
Energy derivatives
, 532–535
Energy prices
, 532–533
Enterprise risk
, 369
building and enhancing
, 377
COSO ERM
, 374–377
ERM framework
, 373–374
identification and assessment
, 370–373
implementation and models
, 385–386
improving process view
, 377–380
practical implementation
, 382
role of management
, 382–385
technological capabilities
, 380–382
Entrepreneurial risk management (ERM)
, 369, 373–374, 384
Equilibrium
, 337
Equilibrium model
, 276, 279
Equity
, 362
index
, 534
swaps
, 183
tranche (see Bottom tranche)
Equivalent Martingale measure
, 276
Error
, 505
sequence of econometric model
, 84
Estimation methods
, 84
Euler’s theorem
, 243
on homogeneous functions
, 234
Europe, crisis in
, 424–428
European Financial Stability Facility (EFSF)
, 426
European Investment Bank (EIB)
, 427
European option
binomial trees
, 202
Black-Scholes model on non-dividend-paying stock
, 191
dividend-paying stock
, 206
non-dividend-paying stock
, 191
put-call parity
, 191, 403
European receiver swaptions, Delta for
, 191
Event identification
, 375
Ex-dividend date
, 202
Excel statistical functions
, 108–109
Exception monitoring
, 381
Exchange options
, 188
Exchange rate risk management
, 387
Exchange-traded insurance derivatives (ET insurance derivatives)
, 501
Expected cash inflows (ECI)
, 357
Expected cash outflows (ECO)
, 357
Expected default frequency (EDF)
, 311
Expected exposure (EE)
, 13, 468
Expected future
bond price
, 483
cash flows
, 184
returns
, 229
spot value
, 263
Expected losses (EL)
, 298, 393
Expected return
, 32
of portfolio
, 43, 48
on stock
, 26
Expected shortfall (ES)
, 143–145, 153–156, 222
Expected tail loss (ETL)
, 222
Expected value
of lottery
, 7
of utility
, 8
Expiration date
, 179, 219, 424
Explanatory simulation
, 114
Exponential smoothing
, 80, 83
Exponentially weighted moving average (EWMA)
, 145, 156
compared with GARCH
, 117
Exposure at default (EAD)
, 302, 470
Exposure at recovery (EaR)
, 304–305
Exposure-at-default (EaD)
, 302
Extended Vasicek model
, 279
External rating
, 530
Externalities
, 37
Extreme value theory (EVT) (see also Modern portfolio theory (MPT))
, 123, 131, 133
data application
, 137–138
extreme VaR
, 138–140
theoretical background
, 134–137
Factor analysis
, 238, 255
Factor loading
, 296
Factor mapping for VaR
, 238–239, 255–256
Factor models
, 472
Fama–French model
, 62
Fannie Mae (FME)
, 429
Fat tails
, 92
Fat-tailed distribution
, 167
Federal Housing Finance Agency (FHFA)
, 429
FICO score
, 421
Financial Accounting Standards Board (FASB)
, 526
Financial arbitrage
, 23–24
Financial crisis
, 419, 515, 519–521, 530
credit derivatives
, 430–440
in Europe
, 424–428
impact on financial industry
, 428–430
lack in regulatory framework
, 420–424
model of SPVs
, 453–454
Newton–Raphson method
, 441
and regulation
, 420
Financial deregulation
, 421
Financial derivatives (see also Interest rate derivatives)
, 171–172, 218, 257
options and futures
, 172–183
Financial Executives International (FEI)
, 374
Financial instability
, 38
Financial institutions
, 18, 360
risk in
, 16–19
Financial instruments
, 1
Financial intermediary
, 453
Financial investors
, 44, 387
Financial markets
, 1, 25, 39, 163
CAPM
, 51–62
MPT
, 40–51
Financial ratios
, 449
Financial returns
, 41, 92
autocorrelation of
, 87–91
covariance matrix of
, 72
Financial risk (see also Market risk)
, 1, 4, 10–11, 16, 374
management
, 2
managers
, 1
Financial risk management
, 515, 538
banking sector
, 522–531
challenges for research
, 531
corporate governance role
, 516–522
digitalization and risk management
, 537–539
energy derivatives
, 532–535
interbank risk
, 515–516
interbank risk
, 531–532
sovereign risk dynamics
, 535–537
Financial service institutions
, 448
Financial Stability Board (FSB)
, 422
Financial time series analysis
, 83
Financial volatility
, 63
Fintech, impact of
, 538
First passage models
, 312–315
Fixed Income Arbitrage
, 24–25
Fixed income derivatives, hedging with
, 480–482
Fixed income futures
, 263–266
Fixed trigger
, 500
Flat volatility approach
, 188
Floating rate bond with face value, value of
, 185
Floorlets
, 185–186
Floors
, 185–188
FOC
, 60
Foreign exchange (FX)
, 387–388
derivatives
, 399–403
risk
, 13
risk hedging in markets
, 404–405
risk management
, 527
Forward contract
, 171, 177, 480
delivery
, 177–179
foreign exchange (FX)
, 178, 398, 401
payoff of
, 178–179, 483
replication
, 179
settlement process
, 181
stocks
, 180
valuing
, 180
Forward exchange rate
, 401
Forward price
, 178–179, 263
cut-off value and
, 412
for investment asset
, 179
and spot price
, 264, 400
Forward swap
, 190
Forwards
, 177–183
Foucault model
, 336
Frank copula
, 126–127
Fraud Risk
, 14
Fréchet distribution form
, 134–135
Frechet Weibull distribution
, 136
Freddie Mac (FMC)
, 429
Fully parametric ARCH method
, 145, 157
Fundamental financial analysis
, 19
Funding
, 524
liabilities
, 361
liquidity
, 338–342
risk
, 14
Funds
, 25
Futures contract
delivery
, 338
forward contract vs.
, 181
and interest rates
, 266
macro hedge with
, 482
portfolio
, 412
positions in oil
, 173
price options
, 186
Futures options
, 172
forwards and futures
, 177–183
market regulation of
, 530
option structure and payout
, 175–177
traders in market
, 172–175
volatility strategy with strangles
, 182
G20
, 422
Gamma
approximation
, 471
distribution
, 98
hedging
, 210–212, 458–460
of portfolio
, 150
of swaption
, 191
Gamma neutral portfolio
, 212, 214, 460, 463
Gap analysis
, 284–286
GARCH (1,1) specification of variance
, 145, 157
GARCH specifications
, 81, 83
GARCH variance
, 66
GARCH(p,q) modeling
, 159–161
Gaussian copula
, 125–126, 316
Gaussian distribution
, 41
Gaussian estimator
, 87
Gaussian factor model
, 472
Gaussian likelihood
, 87
Gaussian multi-factor model
, 280–281
Generalized autoregressive conditional heteroscedasticity model (GARCH model)
, 83–87
Generalized Brownian motion
, 32
Generalized extreme value distribution (GEV distribution)
, 134–135
Generalized Pareto Distribution (GPD)
, 99, 137
Generalized Wiener process
, 32, 120
Geometric Brownian motion
, 32
Geometric returns
, 220, 231
Global factors
, 536
Global financial crisis
, 515
Globalization of financial markets
, 387
Goldman Sachs Commodity Index (GSCI)
, 533
Government-sponsored enterprises (GSE)
, 429
Gramm-Leach-Bliley act
, 422
Greek letters
, 197–198
Gross income
, 394
Gumbel copula
, 126–127
Gumbel distribution
, 134, 136
Hazard rate
, 318
Heating degree day (HDD)
, 502
Heavy tail
, 96
Hedge/hedging (see also Advanced IRR hedging; Credit risk hedging)
, 18, 455
advanced IRR hedging
, 475–482
convexity
, 286–290
convexity adjustment for interest rate derivatives
, 483
cost of
, 212–214, 460–463
credit risk hedging
, 463–475
delta
, 207–210, 456–458
dynamic
, 343, 529
in energy markets
, 535
with fixed income derivatives
, 480–482
IRR
, 455–456
market risk hedging
, 456–463
ratio
, 271
strategy
, 402
Hedgers
, 172–173
Heston model
, 534
Heterogeneous ARCH process (HARCH process)
, 167–168, 508
Heterogeneous volatility
, 167–169, 508–510
Heteroscedasticity
, 84
High Book-to-Value ratio stocks
, 61
High minus low book-to-value stocks (HML book-to-value stocks)
, 61
High quality assets (HQA)
, 355–357
High short-period low volatility
, 64
High-frequency data
, 163
datasets
, 164
high-frequency trading
, 163
intraday risk analysis
, 167–169
High-frequency trading
, 163, 504
basic stylized facts
, 166–167, 506–508
data filtering
, 163–166, 504–506
heterogeneous volatility
, 508–510
Hill estimator of tail index
, 138
Hill graph
, 138
Historical simulation approach
, 228–229
Historical volatility
, 63
Ho-Lee model
, 279
Homogeneous of degree
, 234
Hotlines management
, 381–382
Hull-White model
, 279
Human error
, 164
Illiquidity
, 336
Immunization
, 267–272, 290
Implied volatility (see also Volatility smile patterns)
, 63–65, 406–407
In-sample VaR estimation
, 139
Incentive systems
, 517, 519–521, 528
Income statement
, 19
Incremental VaR (IVaR)
, 244
Index
, 54, 502
credit
, 439
equity
, 534
funds
, 54
Hill estimator of tail
, 138
market
, 3, 406, 526
spotting
, 25
stock
, 54
tail
, 124, 138–139, 167, 507
temperature
, 503
variance
, 55
weigh stocks
, 62
Indirect costs
, 17
Indirect modeling of correlation
, 82
Infinite order ARCH model
, 160
Information
, 336, 376
Inhomogeneous time series
, 164, 505
Initial margin
, 333–334, 365
Instantaneous forward rate
, 276, 280, 475–476, 478, 480
Institute of Internal Auditors (IIA)
, 374
Institute of Management Accountants (IMA)
, 374
Insurable risk-management functions
, 384
Insurance
, 38
derivatives
, 501–504
risk
, 22
Interbank market
, 531
Interbank risk
, 515–516, 531–532
Interest rate cap (IRC)
, 185
Interest rate derivatives
, 183
caps and floors
, 185–188
IRSs
, 183–185
swaptions
, 188–191
Interest rate floor (IRF)
, 185
Interest rate management procedures
, 526
Interest rate risk (IRR) (see also Credit risk)
, 12, 257–258, 260, 455–456
bond prices and yields
, 258–263
compounding frequencies for interest rates
, 272
duration and convexity hedging
, 286–290
dynamics of interest rates
, 258
fixed income futures
, 263–266
management
, 282
measurement techniques
, 284–286
principal component analysis of term structure
, 295–296
short rate models
, 272–282
sources and identification
, 282–284
yield shifts and immunization
, 267–272
Interest rate swaps (IRS)
, 171, 183–185, 482
Internal control process
, 391–392
Internal Model Method (IMM)
, 302
Internal rate of return (IRR)
, 260
Internal rating schemes of banks
, 525
International Monetary Fund (IMF)
, 422
Interpolation methods
, 164
Intraday effects
, 92
Intraday risk analysis
, 167
heterogeneous volatility
, 167–169
Intrinsic value
, 202
Inverse functions
, 125
Investment banks
, 422
Investment grade
, 13, 306
rate
, 449
sovereign bonds
, 447
Investment returns
, 42
Investors
, 336–337, 450
Itô’s lemma
, 120–122, 310
Itô’s process
, 32
January effect
, 28, 92
Jarrow-Turnbull model
, 317–320
Jensen’s inequality
, 9–10, 64
Joint probability density function
, 69
JP Morgan Chase
, 188
Jump process
, 310, 474
Kendall’s tau
, 128–129
KMV model
, 132
KMV-Merton approach
, 308–312
Kupiec’s test
, 141–142, 250
Kurtosis
, 92, 166
Lagged value
, 87
Lagrangian function
, 46
Lagrangian multipliers
, 46–47
Least squares estimates
, 90
Least squares regression
, 167, 508
Lehman Brothers (LB)
, 428
Leverage
, 50, 284
of company
, 16
Levy processes
, 535
Likelihood function
, 69–71
Likelihood ratio
, 250
test
, 141
Limit law
, 134
Limit order
, 333, 336–337, 352
Linear approximation
, 150
Linear correlation
, 123, 127–128, 153
Linear model
, 109, 150, 286
Linear utility
, 15
Linearity
, 218
Liquidity
, 340, 450
black holes
, 343–344
CAPM
, 366–367
Diamond-Dybvig model
, 352–355
LCR
, 355–357
market prices
, 332–342
models
, 344
monitoring tools
, 359–362
NSFR
, 358–359
risk and regulation
, 355
risk
, 14, 331–332
theoretical models
, 344–348
traceable models
, 348–352
Liquidity Adequacy Requirements (LAR)
, 360
Liquidity coverage ratio (LCR)
, 355–357
Liquidity-adjusted VaR (LVaR)
, 344, 349
Loans
, 525
Log function
, 70
Log likelihood
, 87
function
, 70–71, 97
Lognormal property
, 407
Lognormal VaR
, 231
London Inter Bank Offered Rate (LIBOR)
, 183, 187
curve
, 280
market models
, 282
London International Financial Futures and Options Exchange (LIFFE)
, 163, 504
London Stock Exchange
, 24
Long call
, 176
Long hedge
, 486
Long position
, 174–178, 180–181, 208, 212, 263–264, 431, 435, 445, 456
Long put
, 177
Long-period high volatility
, 64
“Long-run” unconditional variance
, 86
Long-term debt on total debt
, 20
Loss function
, 473
Loss given default (LgD)
, 302–305, 468
Lower tail dependence, coefficient of
, 130
M-absolute model
, 475–477
m-dimensional copula
, 124
M-squared model
, 475–477
Macaulay duration
, 287
Macroeconomic effects
, 532
Maintenance margin
, 334, 365
Managed CDOs
, 448
Management failures
, 516–519
Mapping
, 165, 238, 255
Margin
, 181
account
, 333–334
buying on
, 333
gross
, 16
initial
, 333–334
maintenance
, 334, 365
minimum
, 333
net
, 16
operating
, 424
profit
, 16
Margin agreements (MA)
, 466
Marginal scrubbing error
, 164, 505
Marginal VaR (MVaR)
, 242–243
Market
clearing condition
, 341
completeness
, 448
efficiency
, 37
failure types
, 37–38
inefficiencies
, 37
liquidity
, 338–342
liquidity risk
, 14
microstructure
, 332–336
microstructure theory
, 339
order
, 332–333, 337, 365
portfolio (see Tangency portfolio)
segmentation
, 449
transactions
, 304
Market index
, 3, 406, 526
Market prices
, 332
funding vs. market liquidity
, 338–342
market microstructure
, 332–336
price formation
, 336–338
of risk
, 194–196, 536
Market risk (see also Financial risk)
, 11, 19, 130–131, 217–220
metrics
, 218–227
quantile metrics and value-at-risk
, 220–224
VaR
, 455
VaR calculation methods
, 228–234
VaR rationale and definition
, 224–226
Market risk hedging (see also Credit risk hedging)
, 456
cost of hedging
, 460–463
delta hedging
, 456–458
gamma and Vega hedging
, 458–460
Marking to market
, 181
Markov chains
, 169, 509
Markov process
, 29
for transition matrices
, 332–329
Markowitz, Harry
, 40, 44
Markowitz model
, 45
Markowitz Portfolio Theory
, 50
Martingale
, 276
Mass function of binomial distribution
, 101
Matching approach
, 290
Mathematical in-depth analysis
, 455
Maturity date
, 175, 178, 183, 310, 359
Maturity model
, 386
Maximum likelihood estimator/estimation (MLE)
, 69–72, 332
for Binomial distribution
, 103
Maximum likelihood methods
, 69–72
Mean of binomial distribution
, 102
Mean reversion effect
, 28–29
Mean-excess function (MEF)
, 137–138
Merton latent variable model
, 131
Metrics
, 360–361
Mezzanine
, 444
Minimal errors
, 164
Minimum variance portfolio (MVP)
, 45
Mispricing
, 27
Model back testing
, 249–251
Modeling financial comovements
, 80
conditional correlation
, 81–83
conditional covariance
, 80–81
Modern capital markets
, 528
Modern corporate business
, 370
Modern credit risk management
, 297
Modern portfolio theory (MPT) (see also Extreme value theory (EVT))
, 40, 52
optimal portfolios of risky assets
, 44–47
optimal portfolios with risk-free asset
, 48–51
risk/return trade-off
, 40–44
Modern securitization
, 419
Modified duration
, 268, 286, 288–289, 291
Modified Monte-Carlo and scenario analysis
, 495–496
Moment matching approach
, 151
Money market account
, 276
Monte Carlo approach
, 391
Monte Carlo Integration
, 114–115
Monte Carlo kernel
, 131
Monte Carlo methods
, 472–475
Monte Carlo simulation
, 231–233, 324
of Copulas
, 133
Moody’s Risk Management Services
, 305–306
Moral hazard
, 38
Morgan, J. P.
, 80, 315
Mortgage-backed securities (MBS)
, 447
Multi-factor models
, 280–282
Multi-risk product
, 499–501
Multidimensional approach
, 14
Multiperiod model
, 60
Multivariate GARCH models (MGARCH models)
, 159–160
Multivariate Gaussian distribution
, 124
Multivariate return distributions
, 158–161
n-dimensional copula
, 124–125
n-dimensional covariance matrix
, 80
Nationally Recognized Statistical Rating Organization (NRSRO)
, 423
Natural monopoly
, 37
Negative autocorrelation
, 88, 90
Negative externalities
, 37
Net cash outflows (NCO)
, 355, 357
Net present values (NPVs)
, 112
Net Stable Funding Ratio (NSFR)
, 358–359
Net-liquidity demand (NLD)
, 339
Netting
, 303, 464
agreement
, 464–465
of positions
, 470
rules
, 465
Newton-Raphson method
, 434, 441
No-arbitrage
condition
, 179, 263–264, 291
models
, 279
principle
, 24–25
Non-linear securities
, 490
Non-normal distribution percentile
, 349–350
Non-parallel shifts
, 267, 477, 480, 484
Non-stationary financial returns
, 91
Nonlinearity
, 91, 248
Normal distribution
, 40–42, 71
VaR
, 221
Normal market
, 40, 42, 179, 235, 343
Normality
, 123, 218
NORMSINV function
, 33
Notional principal
, 183, 190, 435, 438, 442, 451
Null hypothesis
, 89–90, 141–142, 250
Numeraire
, 483
Numerical procedure
, 65, 496
Off-balance sheet liquidity exposures
, 359
One factor copula model
, 132
Operational risk
, 14, 19, 374, 388
Basel II approach
, 393–396
identification and assessment
, 388–391
treatment and control
, 391–392
Opportunity costs
, 17
Optimal asset value
, 342
Optimal execution theory
, 344
Optimal portfolios
with risk-free asset
, 48–51
of risky assets
, 44–47
Optimal trading model
, 344
Optimization approaches
, 404
Optimization program
, 4
Option pricing models (see also Capital asset pricing model (CAPM))
, 197
binomial trees
, 198–202
BSM model
, 202–207
Option pricing theory
, 248
Optionality
, 284
Options
, 172
in investment opportunity
, 195
structure and payout
, 175–177
Order, types of
, 332–333
Order-driven markets
, 336
Ordinary least squares (OLS)
, 84
Organization for Economic Cooperation and Development (OECD)
, 516, 521
Out-of-sample VaR
, 139
Over-the-counter (OTC)
, 176
insurance derivatives
, 502
Par value
, 232, 431–433, 435
Parallel shift
, 267, 280, 475–477
Parametric method
, 229–231
Pareto distribution
, 96–100
Passive acceptance of risk
, 22
Past stock price
, 26
Path dependent simulation
, 465
Payer swaption, Delta of
, 190
Payoff
of forward contract
, 178
of long position in put option
, 175
Peak over threshold (POT)
, 136, 139
Perfect hedge
, 172
Piecewise constant random function
, 30
Plain rolling averages
, 80
Plain vanilla IRSs
, 183
Poisson decay process
, 474
Poisson distribution
, 103–109
Portfolio hedging
, 207
cost of hedging
, 212–214
Delta hedging
, 207–210
Gamma and Vega hedging
, 210–212
Portfolios
, 45
of financial assets
, 79
immunization
, 258, 477
optimization in Excel
, 50–51
P/L
, 226
return
, 43, 49
value
, 42
VaR for portfolios of derivatives
, 150–151
variance
, 49, 59
weights
, 49
Position limit
, 245, 405
Positive autocorrelation
, 88, 90
Positive externality
, 37
Post-crisis perspectives
, 522
Potential future exposure (PFE)
, 302
Power Law (PL)
, 513
for intraday data
, 513–514
Premium
, 51, 73, 176, 182, 263, 537
Price formation
, 332, 336–338
in market
, 166
Price(s) (see also Market prices)
, 63
actuarial
, 5
ask
, 166, 335, 337, 339–341, 351, 507
bond
, 12, 258–263, 300, 436
commodity
, 11, 217, 533–534
delivery
, 179, 401
dynamics
, 345
energy
, 532–533
forward
, 178–179, 263
past stock
, 26
reference
, 217
sensitivity hedge ratio
, 290
simulation process
, 465
stock
, 26, 233
tree
, 200
Pricing theta
, 461
Primary contracts
, 498–501
Prime rates
, 283
Principal component analysis
, 238, 255
of term structure
, 295–296
Probabilistic approaches
, 109
decision trees
, 110–113
scenario analysis
, 109–110
simulations
, 113–115
Probability
of company insolvency
, 224
mass function
, 103
measure
, 100
theory
, 440
Probability density function (p.d.f.)
, 40, 71, 100, 493
of Pareto distribution
, 97
Probability of default (PD)
, 436, 468
Product copula
, 125
Profit/loss data (P/L data)
, 218–219
Project quality
, 453
Proportion of failures test (POF test)
, 141, 250
Public economic policies
, 6
Public goods
, 37
Put options
, 175
Put-call parity formula
, 403
Q-Q plot
, 137
Quadratic ARCH (QARCH)
, 168, 509
Quadratic VaR methods
, 150
Quantile metrics
, 220–224
Quantile of return distribution
, 147
Quantitative standards
, 396
Quasi-Monte Carlo methods (QMC methods)
, 495
Quick ratio
, 20
Rainbow products
, 534
RAND() function
, 33
Random error component
, 26
Random number generators
, 232
Random variable, characteristic function of
, 107
Random walk theory of financial assets
, 6
Randomness
, 2–5
Rating procedures
, 529
Rational expectations theory
, 6
Rationality
, 5–10
Real option
, 171
Rebalancing
, 27, 271
Recovery rate (RR)
, 13, 301
Reduced-form models
, 317
CreditRisk+™ model
, 321–324
Duffie-Singleton model
, 320–321
Jarrow-Turnbull model
, 317–320
Reference entity
, 320, 430, 435–436, 439–440, 451
Reference obligation
, 435, 439, 448
Reference price
, 217
Regression errors
, 89
Regression model
, 58
Regret operator
, 247
Reinsurers
, 498, 503
Relative Risk Aversion (RRA)
, 15
Remuneration
, 517, 519–521
system
, 515
Repo transaction
, 531
Reporting risks
, 374
Required amount of stable funding (RSF)
, 358–359
Reset dates
, 186, 189
Resiliency
, 339
Response management
, 381
Return of Equity (ROE)
, 449
Return on asset (ROA)
, 20
Reuters
, 164
Rho
, 212, 461, 463
neutral
, 214
Rights
, 175, 502
Risk
, 1–2, 39, 387–388
acceptance
, 22, 380
arbitrage
, 24–25
assessment
, 20, 376
aversion
, 5–10
avoidance
, 22
in corporations and financial institutions
, 16–19
currency risk
, 397–405
dashboards
, 382
gamma swaps
, 413–414
hedging in FX markets
, 404–405
identification, measurement, and mitigation
, 19–21, 23
impact
, 21
likelihood
, 21
limits
, 143, 154
management
, 16–23
mapping
, 229, 380
market price of
, 194–196
measurement
, 7, 234
mitigation
, 392
modeling
, 197
operational risk
, 388–396
premiums
, 8, 22, 27, 51, 53, 195, 273, 425
priority
, 21
process
, 17, 19
randomness and uncertainty
, 2–5
rationality
, 5–10
repository
, 380
response
, 22–23, 376
risk-adjusted NPV
, 114
scoring
, 382
theory of markets
, 23–33
tolerance
, 22
types
, 10–15
volatility measure
, 83
volatility risk
, 405–413
Risk and return, relationship between
, 4, 40, 44–45, 55, 62, 444
Risk management
, 95, 537
Big data and risk
, 538–539
Fintech, impact of
, 538
systems
, 524
Risk-adjusted return on capital (RAROC)
, 417–418
Risk-assessment methodology
, 468
Risk-averse investors
, 50
Risk-free asset, optimal portfolios with
, 48–51
Risk-free interest rate
, 265, 313, 438
Risk-free rate
, 50
Risk-management
function
, 369
process
, 396
techniques
, 528
Risk-neutral probability
, 199, 201, 299
of default
, 314
Risk-neutral valuation
, 194, 198
Risk-neutral world
, 196, 437
Risk-purchasing groups
, 498
Risk-retention groups
, 498
RiskMetrics©
, 80, 145
Risk–return trade-off
, 39–44
Risky assets, optimal portfolios of
, 44–47
Rough volatility measure
, 167
Sarbanes-Oxley act
, 519
Scaling laws
, 92, 167, 507–508
Scorecards
, 391
Second order Taylor approximation
, 150
Securities and Exchange Commission (SEC)
, 423–424
Securitization
, 419, 423, 442, 523
advantages and disadvantages
, 448–450
CDO
, 444–448
structure and participants
, 442
Security market line (SML)
, 51, 55–59
Semi-strong-form version of EMH
, 26
Semi-variance operator
, 246
Senior management
, 383
Sensitivity-based risk
, 246
Setting limits
, 527
Shape parameter
, 135
Sharpe ratio
, 195
Short call
, 176
Short hedge
, 486
Short position
, 173, 175–176, 180, 208, 284, 343, 412, 445, 461
Short put
, 177
Short rate models
, 272
multi-factor models
, 280–282
single-factor models
, 276–280
term structure of interest rates
, 272–275
Short selling
, 46
Short strangle
, 182
Short term risk free rate (see Short rate models)
Sigma (see Vega)
Simulations
, 113–115, 286, 529
Single-factor models
, 276–280
Skeweness
, 93
Sklar’s theorem
, 124
Slope of CML
, 56
Small Capitalization stocks
, 61
Small firm effect
, 28
Small minus big capitalization stocks (SMB capitalization stocks)
, 61
Sophisticated corporate treasuries
, 404
Sovereign credit risk
, 535
Sovereign risk dynamics
, 535–537
Spearman’s rho
, 128–129
Special purpose vehicle (SPV)
, 442, 444–445
model of
, 453–454
Specialized analytics
, 381
Specific risk
, 11
Speculation
, 173–174
Speculators
, 173–174
Spot price
, 178–180, 186, 338
Spot rate
, 164, 203, 262, 266, 400, 486
Spot volatility approach
, 188
Spread option
, 533
Spread transaction
, 166, 507
Squared returns, autocorrelation of
, 92
Stable funding
, 358
Standard & Poor’s 496 (S&P 496)
, 54
Standard delta-normal approach
, 150
Standard Delta-VaR methods
, 490
Standard deviation
, 40, 168
Standard duration
, 476
Standard GARCH models
, 167, 508
Standard normal distribution
, 77–78
Standardized Method (SM)
, 302
Static risk-management processes
, 370
Static simulations
, 286
Stationary GARCH
, 86
Statistical analysis (see also Conditional risk analysis; Time series analysis)
, 95
distributions
, 96–109
probabilistic approaches
, 109–115
Steady state distribution function
, 30
Stickiness
, 357
Stochastic process
, 29–30, 33, 69, 120, 194, 291, 465, 476
Stochastic variable
, 120, 282
Stochastic volatility model
, 534–535
Stock prices
, 6, 18, 26, 202, 233
distribution of stock price fluctuations
, 92
geometric Brownian motion
, 32
Stop order
, 333
Stop-loss order
, 333
Stop-loss rules
, 343
Storage cost
, 180, 338
Straddles
, 504
Strangles, volatility strategy with
, 182
Strategic risks
, 374
Stress testing
, 251–253, 527
Strike
, 175
Strike price
, 174–175, 182, 309, 407, 534
Strip
, 301, 413
Strong-form version of theory
, 26–27
Structural models
, 308
CreditMetrics™ model
, 315–317
first passage models
, 312–315
KMV-Merton approach
, 308–312
Student-t factor model
, 473
Student’s t-copula
, 125
Stylized facts
, 91–93
Subadditivity
, 143
Survival function of Pareto variable
, 96
Swap dealers
, 185
Swap rate
fixed forward
, 190
market
, 431
Swaps
asset
, 430–434
callable asset
, 433
catastrophe reinsurance
, 502
CDS
, 435–438
commodity
, 183
credit
, 183
currency
, 183, 399–400, 403, 414
equity
, 183
gamma
, 413–414
IRS
, 171, 183–185, 482
variance
, 410–413
Swaptions
, 188–191
Sydney Futures Exchange (SFE)
Symmetric distribution
, 40
Synthetic option
, 343
System integration
, 382
Systematic risk
, 11, 51
Tactical hedging
, 404
Tail dependence of copulas
, 129
Tail index
, 124, 138–139, 167, 507
Tangency portfolio
, 49–50, 53, 57
Tax breaks
, 430
Tax shield
, 18, 453
Tech-supported surveys
, 381
Temperature derivatives
, 501, 503–504
Temporary market
, 345
Tenor
, 185–186, 188, 503, 531
Term structure, principal component analysis of
, 295–296
Terminal value
, 272
Theta
, 191, 463
price for unit
, 461
pricing
, 213, 461
Three factor model
, 61
Threshold
, 138
Tick frequencies
, 164
Tightness
, 339–340
Time horizon
, 232
Time series analysis (see also Statistical analysis)
, 79, 83–93
ARCH/GARCH models
, 83–87
autocorrelation of financial returns
, 87–91
stylized facts
, 91–93
Time series models
, 69
Time until first failure test (TUFF test)
, 141, 250
Time value
, 218, 406
Traceable models
, 348–352
Traders in market
, 172–175
Trades
, 165
Trading
limits
, 527
process
, 335–336
strategy
, 344–345
Traditional equity risk
, 246
Traditional LCR
, 361
Traditional portfolio credit models
, 132
Traditional VaR
, 153
Tranches
, 323, 443–446, 449
Trans-European Automated Real-time Gross Settlement Express Transfer System (TARGET system)
, 425
Transaction
exposure
, 398
function
, 348
risk
, 397
Transfer risk
, 22
Transition matrices, Markov process for
, 332–329
Transition thresholds
, 317
Translation risk
, 404
Transparency
, 335
Transparent financial reporting
, 21
Treasury bill
, 264
Tree nodes
, 111
Trial-and-error approach
, 261
Two-factor Hull-White model
, 282
Unbiased estimator
, 70
Uncertainty
, 2–5, 18
Underlying variable
, 194–195
Unencumbered assets
, 361
Unsystematic risk (see Specific risk)
Upper boundary for VaR
, 224
Upper tail dependence, coefficient of
, 129–130
US Treasury Department
, 429–430
Utility function of investor
, 4–5
Utility functions, common forms of
, 15
Value at risk (VaR) (see also Interest rate risk (IRR))
, 12, 123, 140, 154, 217, 220–224, 241, 246, 302
analytic approximations
, 247–249
back testing
, 123, 140–142
calculation methods
, 228–234
choice of parameters for
, 227
CVaR
, 145–147, 156–158
decomposition
, 241–245
ES
, 154–156
expected shortfall
, 143–145
factor mapping for
, 238–239, 255–256
features
, 241
limitations
, 245–247
model back testing
, 249–251
for portfolios of derivatives
, 150–151
rationale and definition
, 224–226
stress testing
, 251–253
testing
, 249
VaR-looking models
, 526
VaR advances
, 489–490
historical simulation revisiting
, 493–495
modified Delta VaR
, 490–493
modified Monte-Carlo and scenario analysis
, 495–496
Variable trigger
, 501
Variance
of binomial distribution
, 102
decomposition of returns
, 59
of HARCH(2) process
, 168
of portfolio
, 43–44
of random variable
, 66
rate
, 203
Variance swaps
, 410–413
Variance-covariance matrix
, 46
Vasicek model
, 276–278
VEC model
, 159–160
Vega
, 191
hedging
, 210–212, 458–460
Volatility
, 62
asset return
, 406
clustered
, 91
financial
, 63
heterogeneous
, 167–169, 508–510
historical
, 63
implied
, 63–65, 406–407
parameter
, 65
smile patterns
, 411
strategy with strangles
, 182
surface
, 406–407
swap
, 412
types
, 63–66
Volatility risk
, 387, 405
callable bonds
, 407–410
implied volatility
, 406–407
variance swaps
, 410–413
Weak-form efficiency
, 26
Weekend effects
, 92
Weibull distribution
, 135
Weighted spread approach
, 352
Wiener process
, 29
Worst-case-scenario (WCS)
, 496
Yield curve
, 273
risk
, 283
Yield shifts
, 267–272
Yields
, 258–263
Zero curve
, 187–188
Zero rate
, 188
Zero-coupon bond
, 260, 270–271, 274–275, 300, 320
Zero-coupon rate
, 266, 476
Zero-coupon yields
, 273, 482
Zero-volatility spread
, 434
Zipf’s law
, 513
- 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: Beyond Normality and Correlation
- Chapter 6: Conditional Risk Analysis
- Chapter 7: High-frequency Data
- Chapter 8: Financial Derivatives
- Chapter 9: Option Pricing and Risk Modeling
- Chapter 10: Market Risk
- Chapter 11: Inside Value at Risk
- Chapter 12: Interest Rate Risk
- Chapter 13: Credit Risk
- Chapter 14: Liquidity Risk
- Chapter 15: Enterprise Risk
- Chapter 16: Other Risks
- Chapter 17: Financial Crisis and Securitization
- Chapter 18: Hedging Techniques
- Chapter 19: Advanced Topics
- Chapter 20: The Future of Financial Risk Management
- Index