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by Francois Longin
Extreme Events in Finance
Cover
Financial Engineering and Econometrics
Title Page
Copyright
About the Editor
About the Contributors
Chapter 1: Introduction
1.1 Extremes
1.2 History
1.3 Extreme value theory
1.4 Statistical Estimation of Extremes
1.5 Applications in Finance
1.6 Practitioners' points of view
1.7 A broader view on modeling extremes
1.8 Final words
1.9 Thank You Note
References
Chapter 2: Extremes Under Dependence—Historical Development and Parallels with Central Limit Theory
2.1 Introduction
2.2 Classical (I.I.D.) Central Limit and Extreme Value Theories
2.3 Exceedances of Levels, kth Largest Values
2.4 CLT and EVT for Stationary Sequences, Bernstein's Blocks, and Strong Mixing
2.5 Weak Distributional Mixing for EVT, D(un), Extremal Index
2.6 Point Process of Level Exceedances
2.7 Continuous Parameter Extremes
References
Chapter 3: The Extreme Value Problem in Finance: Comparing the Pragmatic Program with the Mandelbrot Program
3.1 The Extreme Value Puzzle in Financial Modeling
3.2 The Sato Classification and the Two Programs
3.3 Mandelbrot's Program: A Fractal Approach
3.4 The Pragmatic Program: A Data-driven Approach
3.5 Conclusion
Acknowledgments
References
Chapter 4: Extreme Value Theory: An Introductory Overview
4.1 Introduction
4.2 Univariate Case
4.3 Multivariate Case: Some Highlights
Further reading
Acknowledgments
References
Chapter 5: Estimation of the Extreme Value Index
5.1 Introduction
5.2 The Main Limit Theorem Behind Extreme Value Theory
5.3 Characterizations of the Max-Domains of Attraction and Extreme Value Index Estimators
5.4 Consistency and Asymptotic Normality of the Estimators
5.5 Second-order Reduced-bias Estimation
5.6 Case Study
5.7 Other Topics and Comments
References
Chapter 6: Bootstrap Methods in Statistics of Extremes
6.1 Introduction
6.2 A Few Details on EVT
6.3 The Bootstrap Methodology in Statistics of Univariate Extremes
6.4 Applications to Simulated Data
6.5 Concluding Remarks
Acknowledgments
References
Chapter 7: Extreme Values Statistics for Markov Chains with Applications to Finance and Insurance
7.1 Introduction
7.2 On the (pseudo) Regenerative Approach for Markovian Data
7.3 Preliminary Results
7.4 Regeneration-based Statistical Methods for Extremal Events
7.5 The Extremal Index
7.6 The Regeneration-Based Hill Estimator
7.7 Applications to Ruin Theory and Financial Time Series
7.8 An Application to the CAC40
7.9 Conclusion
References
Chapter 8: Lévy Processes and Extreme Value Theory
8.1 Introduction
8.2 Extreme Value Theory
8.3 Infinite Divisibility and Lévy Processes
8.4 Heavy-tailed Lévy Processes
8.5 Semi-heavy-tailed Lévy Processes
8.6 Lévy Processes and Extreme Values
8.7 Conclusion
References
Chapter 9: Statistics of Extremes: Challenges and Opportunities
9.1 Introduction
9.2 Statistics of Bivariate Extremes
9.3 Models Based on Families of Tilted Measures
9.4 Miscellanea
References
Chapter 10: Measures of Financial Risk
10.1 Introduction
10.2 Traditional Measures of Risk
10.3 Risk Estimation
10.4 “Technical Analysis” of Financial Data
10.5 Dynamic Risk Measurement
Properties of
10.6 Open Problems and Further Research
10.7 Conclusion
Acknowledgment
References
Chapter 11: On the Estimation of the Distribution of Aggregated Heavy-Tailed Risks: Application to Risk Measures
11.1 Introduction
11.2 A Brief Review of Existing Methods
11.3 New Approaches: Mixed Limit Theorems
11.4 Application to Risk Measures and Comparison
11.5 Conclusion
References
Chapter 12: Estimation Methods for Value at Risk
12.1 Introduction
12.2 General Properties
12.3 Parametric Methods
12.4 Nonparametric Methods
12.5 Semiparametric Methods
12.6 Computer Software
12.7 Conclusions
Acknowledgment
References
Chapter 13: Comparing Tail Risk and Systemic Risk Profiles for Different Types of U.S. Financial Institutions
13.1 Introduction
13.2 Tail Risk and Systemic Risk Indicators
13.3 Tail Risk and Systemic Risk Estimation
13.4 Empirical Results
13.5 Conclusions
References
Chapter 14: Extreme Value Theory and Credit Spreads
14.1 Preliminaries
14.2 Tail Behavior of Credit Markets
14.3 Some Multivariate Analysis
14.4 Approximating Value at Risk for Credit Portfolios
14.5 Other Directions
References
Chapter 15: Extreme Value Theory and Risk Management in Electricity Markets
15.1 Introduction
15.2 Prior Literature
15.3 Specification of VR Estimation Approaches
15.4 Empirical Analysis
15.5 Conclusion
Acknowledgment
References
Chapter 16: Margin Setting and Extreme Value Theory
16.1 Introduction
16.2 Margin Setting
16.3 Theory and Methods
16.4 Empirical Results
16.5 Conclusions
Acknowledgment
References
Chapter 17: The Sortino Ratio and Extreme Value Theory: An Application to Asset Allocation
17.1 Introduction
17.2 Data Definitions and Description
17.3 Performance Ratios and Their Estimations
17.4 Performance Measurement Results and Implications
17.5 Concluding Remarks
Acknowledgments
References
Chapter 18: Portfolio Insurance: The Extreme Value Approach Applied to the CPPI Method
18.1 Introduction
18.2 The CPPI Method
18.3 CPPI and Quantile Hedging
18.4 Conclusion
References
Chapter 19: The Choice of the Distribution of Asset Returns: How Extreme Value Can Help?1
19.1 Introduction
19.2 Extreme Value Theory
19.3 Estimation of the Tail Index
19.4 Application of Extreme Value Theory to Discriminate Among Distributions of Returns
19.5 Empirical Results
19.6 Conclusion
References
Chapter 20: Protecting Assets Under Non-Parametric Market Conditions
20.1 Investors' “Known Knowns”
20.2 Investors' “Known Unknowns”
20.3 Investors' “Unknown Knowns”
20.4 Investors' “Unknown Unknowns”
20.5 Synthesis
References
Chapter 21: EVT Seen by a Vet: A Practitioner's Experience on Extreme Value Theory
21.1 What has the vet done?
21.2 Why Use EVT?
21.3 What EVT could additionally bring to the party?
21.4 A final thought
References
Chapter 22: The Robotization of Financial Activities: A Cybernetic Perspective
22.1 An Increasingly Complex System
22.2 Human Error
22.3 Concretely, What Do We Need to Do To Transform A Company Into A Machine?
References
Chapter 23: Two Tales of Liquidity Stress
23.1 The French Money Market Fund Industry. How history has Shaped a Potentially Vulnerable Framework
23.2 The 1992–1995 Forex Crisis
23.3 Four Mutations Paving the Way for Another Meltdown
23.4 The Subprime Crisis Spillover. How Some MMFs were Forced to Lock and Some Others Not
23.5 Conclusion. What Lessons can be Drawn from these Two Tales?
Further Reading
Chapter 24: Managing Operational Risk in the Banking Business – An Internal Auditor Point of View
Further Reading
References
Annexes
Chapter 25: Credo Ut Intelligam
25.1 Introduction
25.2 “Anselmist” Finance
25.3 Casino or Dance Hall?
25.4 Simple-Minded Diversification
25.5 Homo Sapiens Versus Homo Economicus
Acknowledgement
References
Chapter 26: Bounded Rationalities, Routines, and Practical as well as Theoretical Blindness: On the Discrepancy Between Markets and Corporations
26.1 Introduction: Expecting the Unexpected
26.2 Markets and Corporations: A Structural and Self-Disruptive Divergence of Interests
26.3 Making A Step Back From A Dream: On People Expectations
26.4 How to Disentangle People From A Unilateral Short-Term Orientation?
References
Name Index
Subject Index
Financial Engineering and Econometrics
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Financial Engineering and Econometrics
Index
A
aggregation
high frequency
sample size
algorithms
bootstrap
alternative Hill plot
alpha-stable distributions
analytical comparison
annual maxima.
see
block maxima
anti-Leibnizian
anything but Mandelbrot (ABM)
aperiodicity
application-driven approach
applications to finance
approximation
Berry–Esséen bounds
Berry–Esséen inequality
Edgeworth expansion
Hermite polynomial
moments
normal approximation
numerical approximation
Zaliapin method
asset returns
asymptotic independence
asymptotic mean-squared error (AMSE)
AT&T
autoregression
autoregressive conditional heteroscedasticity (ARCH) process
B
bank contagion
banking market index
bank loans
bank run
Barndorff–Nielsen
Bessel function
Basel Committee on Banking Supervision
Bernstein polynomials
beta distribution
bivariate extreme value distribution
bivariate normal distribution function
Black Monday
crash
Black–Scholes model
block maxima
blocking techniques
bootstrap methodology
bounded rationality
BP
breakout (fractal) signal
Brownian
Brownian motion
Brownian virus
C
CAC
capital-guarantee
central limit theorem
CGMY model
Citigroup
credit default swaps (CDS) spread
classical (IID) CLT and EVT
clearinghouses
London Clearing House (LCH)
CLT and EVT for stationary sequences
Berman's condition
Bernstein block methods
Bernstein blocks, strong mixing
EVT under m-dependence
EVT under strong mixing
Gaussian sequences
general ETT
Rosenblatt's, strong mixing
cluster
collateralized loan obligation (CLO)
communication of risk
complexity
compound Poisson–normal process
compositional data
computer software
conditional value-at-risk (CVaR)
estimator
constant proportion portfolio insurance (CPPI)
cushion
exposure
floor
method
multiple
continuous parameter extremes
ETT for continuous parameter processes
EVT for random fields
exceedances of multiple levels
point processes of, upcrossings
convergence in distribution
convergence in probability
copula
corporation
correlations
in stressed markets
coverage test
conditional
independence
unconditional
Cramer–Lundberg model
credit index
tail behavior
tail dependence with equities
credit spreads
data quality
financials (tail dependence)
industrials (tail dependence)
multivariate analysis
tail index independent of initial spread
term structure (inverted in distress)
volatility proportional to initial spread
cybernetic
autoadaptivity
feed-back
homeostasis
self learning
D
data
financial assets
insurance data
log returns
market risk data
Meuse river data
SOA insurance data
software R
S&P 500 data
data-smoothing
Datastream
default correlation
degeneration
dependence
deterministic binary approach
distribution
comparison of distributions
conditional distribution
cumulative distribution function
empirical distribution function
exponential
extended Pareto
extreme value
fat-tailed
Fréchet
Gaussian
generalized
extreme value (GEV) distribution
generalized hyperbolic distributions
generalized Pareto distribution (GPD)
Gnedenko
Gumbel
heavy-tailed
kurtosis
light-tailed
loss distribution
mixture of Gaussian
normal
Pareto
semi-heavy-tailed
stable
Student-
tail distribution
thin-tailed
truncated Pareto
unconditional
Weibull
diversification
Dodd–Frank Act
durations between excesses over high thresholds (DPOT)
duration-times-spread (DTS)
dynamic measure of risk
E
early warning indicator
earnings growth (EPS)
economic value added (EVA)
econophysics program (EP)
electricity
EEX
electricity
mean-reversion
PJM
power market
PWX
seasonality
electricity markets
Elliott wave
vertexes
empirical likelihood
endpoint
estimation
Enron
estimation
distribution
(extreme) quantile
estimation method
Bayesian
jackknife
maximum likelihood
method of moments
reduced-bias
Euclidean likelihood
exceedance probability
exceedances of levels,
k
th largest values
expected shortfall
expected utility
expert systems
exponential families for heavy-tailed data
extremal index
extremal limit
for
k
th largest order statistic
for maxima
for minima
extreme
extreme quantiles
extreme value
analysis
distribution
index
puzzle
theorem
extreme value index (EVI)
estimation
extreme value theory (EVT)
application
approach
copula
cumulative distribution function (CDF)
determining tail observations
early
history of EVT
first-order conditions
Fisher–Tippett theorem
GEV
GPD
history
intermediate order statistics
log-excesses
maximum domains of attraction
order statistics
parameter estimates
PDF
Pickands theorem
plots
second and higher-order conditions
F
families of tilted measures
Fannie Mae
conservatorship
Fast MCD algorithm
Financial Crisis Inquiry Commission
financial innovation
derivatives
subordinated debt
financial institutions
financial returns
Fisher–Tippett
forecasting
Fourier
fractal (breakout) signal
Fréchet distribution
Freddie Mac
conservatorship
function
slowly varying
fundamental analysis (FA)
futures
LIFFE
G
Gaussian distribution
generalized autoregressive conditional heteroskedasticity (GARCH)
generalized hyperbolic distributions
generalized Jenkinson–von Mises distribution
generalized extreme distribution
generalized extreme value distribution (GEV)
generalized hyperbolic (GH) distribution
generalized Pareto distribution
global financial crisis (2008)
great recession
Gumbel distribution
H
heavy-tailed
data
distribution
stable distributions
Lévy measure
heuristics
high quantile estimation
high yield tail index
Hill estimator
asymptotic normal distribution
bias reduction
multivariate
historical simulation
human error
assurance quality
hyperbolic distribution
I
independent and identically distributed (IID)
informational asymetry
internal audit
irreducibility
J
Jenkinson–von Mises distribution
Journal Extremes
jump-diffusion models
K
known
knowns
known unknowns
kurtosis distribution
L
Laplace
large and complex banking organizations (LCBOs)
Ledford and Tawn approach
Lehman Brothers
failure
Leibnizian
Lévy–Khintchine formula
Lévy processes
alpha-stable distributions
characteristic function
CGMY and VG distributions
econophysics
generalized hyperbolic distributions
infinitely divisible distributions
laws of maxima
MDA of the Gumbel law
normal distribution
Poisson processes
power of power laws
Lévy measure
limit theorems for sums
central limit theorem (CLT)
conditional limit theorem
generalized central limit theorem (GCLT)
max method
mixed limit theorems
mixed normal extreme limit
Normex
trimmed sums
weighted normal limit
liquidity
for credit portfolios
market price
rule-of-thumb scaling factors
stress
and systemic shocks
local extrema
log-return
long-short credit portfolios
M
Mandelbrot program
ARCH models
continually discontinuous
discontinuity and scaling
fractal description of markets
leptokurtic phenomenon
price behavior
margin requirements
margin setting
initial margin
margin call
margin level
SPAN system
variation margin
marginal expected shortfall (MES)
market-based indicators
market conditions matrix
market crash
magnitude
market efficiency
markets
Markov chains
maturity transformation
max-domain of attraction
condition
Fréchet
Gumbel
multivariate
Weibull
maximum domain of attraction (MDA)
maximum existing moment
mean excess
function
plot
mean excess function
measure-dependent measure
measures of risk
beta
CVaR
dynamic
extreme systematic risk
m
+
m
TA
properties
spikes
VaR
methods
Max method
Normex
QQ plot
supervised
vs.
unsupervised methods
weighted normal limit
Zaliapin method
minimum/maximum approach
minimum-variance reduced-bias
mixture of Gaussian
modern portfolio theory
asset allocation
CAPM
diversified portfolio
downside risk
portoflio weights
safety first
modified Bessel functions
moments
moments estimator
money market funds
dynamic money market funds
Monte Carlo simulation
moral hazard
Morgenstern distribution
moving average (MA)
moving average convergence divergence (MACD)
divergence signal
multivariate extremes
dimension reduction
spatial
spectral density ratios
multivariate Hill estimator
N
Natura non facit saltus
negative/positive approach
non-Gaussian Merton–Black–Scholes theory
nonparametric estimation methods
bootstrap
filtered historical
historical
importance sampling
Kernel
nonparametric market conditions
nonstationary bivariate extremes
normal inverse Gaussian (NIG) distribution
normality
numerical study
O
objective Bayes
open-high-low-close (OHLC) prices
operational risk
advanced measurement approach (AMA)
basic indicator approach (BIA)
data collection exercise
industry definition of operational risk
standardized approach (STA)
option-based portfolio insurance (OBPI)
order statistics
conditional distribution of order statistics
distribution of order statistics
moments of order statistics
Pareto order statistics
ordinary least-squares (OLS)
outer correlations
P
parametric esimtation methods
ARCH
ARMA–GARCH
asymmetric Laplace
asymmetric power
Bayesian
Brownian motion
capital asset pricing
copula
Cornish–Fisher
Dagum
delta-gamma
discrete
elliptical
Fourier transform
GARCH
Gaussian mixture
generalized hyperbolic
Gram–Charlier
Johnson family
location-scale
log folded t
Pareto-positive stable
principal components
quadratic forms
quantile regression
RiskMetrics
Student's
Tukey
variance-covariance
Weibull
Paretian distribution
Pareto
peaks-over-random-threshold (PORT)
peaks-over-threshold (POT)
performance ratios
lower partial moment (LPM)
Sharpe ratio
Sortino ratio
Petrobras
Pickands estimator
dependence function
estimator
theorem
point processes of level exceedances
compound Poisson limits
Exceedance clusters
portfolio insurance
portfolio theory
pragmatic program (PP)
price patterns
probability estimator
procedure of choosing the tuning parameter
process of ARCH
properties of VaR
inequalities
multivariate
ordering
risk concentration
upper comonotonicity
proportional tails model
Pseudo-regeneration
Nummelin splitting trick
times
Q
QQ-plot
generalized Pareto
Pareto
quantile
R
radical program (RP)
rank correlation
pre-crisis
vs
. crisis
Spearman
tail risk and tail-
β
cross-industry comparison
rate of convergence
rate of return
ratio estimator of the tail index (RE)
rationality
bounded
expectations
pure and perfect
real estate investment trusts (REITs)
correlation with S&P
GARCH
statistical description
Tax Reform Act
reflexive effects
regeneration
based estimators
cycle submaxima
hitting times
minorization condition
properties
small set
regular variation
regulation
machine
mechanization
prudential
standards
robotization
standardization
relative strength index (RSI)
resampling methods
return period
returns
risk
aggreagation
credit risk
default risk
mild randomness
extreme systematic
wild randomness
risk management
stress scenarios
value at risk
risk measures
alternative
coherence
estimation
expected shortfall
financial crisis
quantile
solvency
subadditivity (& asymptotic subadditivity)
tail-value-at-risk
traditional
value-at-risk
variance
tail risk
tail cut-off point
Hill statistic
robotization
robustness
routines
Ruin theory
S
sample fraction estimation
Sato classification
activity and variation of
Lévy processes
light of
scale of fluctuations
scaling law
scedasis function
second-order parameters' estimation
semi-heavy-tailed Lévy processes
generalized hyperbolic distributions
tempered stable distributions
VG and CGMY models
semiparametric estimation methods
extreme value
generalized Champernowne
generalized Pareto
M-estimation
short term and long term
Sortino ratio
smirk phenomenon
spectral density ratio model
spectral measures
family
predictor-dependent
smoothed
spectral surface
definition
estimation
S&P 500 index
choice of distribution
correlation with REITs
data
GARCH
statistical description
tail index estimate
square-root-of-time rule
standard deviation
stock index futures
stock market waves
stress scenarios
synthetic assets (ETF, ETN)
systemic risk indicator
bivariate parametric distribution function
Hill plots
systemic shocks
and tail dependence of credit spreads
T
tail
dependence function
of credit spreads
tail estimator
tail independence
tail index
in credit markets
risk indicator/tail-
β
tail index estimator
adaptive
asymptotic behaviour of
Dekkers and De Haan
empirical method on high frequency financial data
extreme value index
generalized quantiles
Hill estimator
Kernel
mean square error (MSE)
minimum-variance reduced-bias (MVRB)
mixed moment
non-parametric method
parametric method
peaks over random threshold (PORT)
Pickands
QQ estimator
tail probability
tempered stable models
Texaco
theory
organizational theory
political philosophy
self-realizing prophecy
speculation of
threshold
adaptive selection
time
trimmed sum
U
unexpected events
unforseen correlation
unknown knowns
unknown unknowns
V
value at risk (VaR)
applications
definition
history
out-of-sample
quantile
significance level (a)
time horizon (t)
violation ratio
value discrepancies
variance gamma (VG) model
volatility smile
volatility (VIX, VXD, VXN)
Volkswagen
W
waiting time
weak (distributional) mixing for EVT, D(un)
associated independent sequence
ETT under D(un)
extremal index
Weibull
distribution
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