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Value-at-Risk Related Scholarly Compositions
See also:
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CAViaR: CONDITIONAL
AUTOREGRESSIVE VALUE AT RISK BY REGRESSION QUANTILES
by Robert F. Engle & Simone Manganelli
University of California, San Diego
July, 1999
Abstract
Recent financial disasters have emphasized the importance of
effective risk
management for financial institutions. The use of quantitative
risk measures has become an essential management tool to be
placed in parallel with the models of returns. These measures
are used for investment decisions, supervisory decisions, risk
capital allocation and external regulation...
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Conditional value-at-risk for
general loss distributions
by R. Tyrrell Rockafellar & Stanislav Uryasev
University of Washington & University of Florida
July, 2001
Abstract
Fundamental properties of conditional value-at-risk (CVaR), as a
measure of risk with significant advantages over value-at-risk (VaR),
are derived for loss distributions in finance that can involve
discreetness. Such distributions are of particular importance in
applications because of the prevalence of models based on
scenarios and finite sampling. CVaR is able to quantify dangers
beyond VaR and moreover it is coherent. It provides optimization
short-cuts which, through linear programming techniques, make
practical many large-scale calculations
that could otherwise be out of reach. The numerical efficiency
and stability of such calculations, shown in several case
studies, are illustrated further with an example of index
tracking.
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Evaluating Value at Risk
Methodologies: Accuracy versus Computational Time
by Matthew Pritsker
July, 1997
Abstract
Recent research has shown that different methods of computing
Value at Risk
(VAR) generate widely varying results, suggesting the choice of
VAR method is very important. This paper examines six VAR
methods, and compares their computational time requirements and
their accuracy when the sole source of inaccuracy is errors in
approximating nonlinearity. Simulations using portfolios of
foreign exchange options showed fairly wide variation in
accuracy and unsurprisingly wide variation in computational
time...
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Evaluation of Value-at-Risk
Models Using Historical Data
by Darryll Hendricks
The Federal Reserve Bank of New York
Abstract
Researchers in the field of financial economics have long
recognized the importance of measuring the risk of a
portfolio of financial assets or securities. Indeed, concerns go
back at least four decades, when Markowitz’s pioneering work on
portfolio selection (1959) explored the appropriate definition
and measurement of risk. In recent years, the growth of trading
activity and instances of financial market instability have
prompted new studies underscoring the need for market
participants to develop reliable risk measurement techniques...
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From value at risk to stress
testing: The extreme value approach
by Francois M. Longin
February, 1999
Abstract
This article presents an application of extreme value theory to
compute the value at risk of a market position. In statistics,
extremes of a random process refer to the lowest observation
(the minimum) and to the highest observation (the maximum) over
a given time-period. Extreme value theory gives some interesting
results about the distribution of extreme returns...
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New insights into smile,
mispricing and value at risk: the hyperbolic model
by Ernst Eberlein, Ulrich Keller, & Karsten Prause
Institut fur Mathematische Stochastik & Universitat Freiburg
April, 1997
Abstract
We investigate a new basic model for asset pricing, the
hyperbolic model, which allows an almost perfect statistical t
of stock return data. After a brief introduction into the theory
supported by an appendix we use also secondary market data to
compare the hyperbolic model to the classical Black-Scholes
model. We study implicit volatilities, the smile eect and the
pricing performance...
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Optimal portfolio selection in a
Value-at-Risk framework
by Rachel Campbell, Ronald Huisman, & Kees Koedijk
Erasmus University Rotterdam
July, 2000
Abstract
In this paper, we develop a portfolio selection model which
allocates financial assets by maximising expected return subject
to the constraint that the expected maximum loss should meet the
Value-at-Risk limits set by the risk manager. Similar to the
mean variance approach a performance index like the Sharpe index
is constructed. Further-more when expected returns are assumed
to be normally distributed we show that the model provides
almost identical results to the mean±variance approach...
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Optimization of Conditional
Value-at-Risk
by Tyrrell Rockafellar & Stanislav Uryasev
September 15, 1999
Abstract
A new approach to optimizing or hedging a portfolio of financial
instruments to reduce risk is presented and tested on
applications. It focuses on minimizing Conditional Value-at-Risk
CVaR rather than minimizing Value-at-Risk VaR, but portfolios
with low CVaR necessarily have low VaR as well. CVaR, also
called Mean Excess Loss, Mean Shortfall, or Tail VaR, is anyway
considered to be a more consistent measure of risk than VaR.
Central to the new approach is a technique for portfolio
optimization which calculates VaR and optimizes CVaR
simultaneously. This technique is suitable for use by investment
companies, brokerage firms, mutual funds, and any business that
evaluates risks. It can be combined with analytical or
scenario-based methods to optimize portfolios with large numbers
of instruments, in which case the calculations often come down
to linear programming or nonsmooth programming. The methodology
can be applied also to the optimization of percentiles in
contexts outside of finance.
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Portfolio Value-at-Risk with
Heavy-Tailed Risk Factors
by Paul Glasserman, Philip Heidelberger, & Perwez Shahabuddin
Columbia University & T.J. Watson Research Center
December, 2000
Abstract
This paper develops efficient methods for computing portfolio
value-at-risk (VAR) when the underlying risk factors have a
heavy-tailed distribution. In modeling heavy tails, we focus on
multivariate t distributions and some extensions thereof. We
develop two methods for VAR calculation that exploit a quadratic
approximation to the portfolio loss, such as the delta-gamma
approximation...
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Regulatory Evaluation of
Value-at-Risk Models
by Jose A. Lopez
Federal Reserve Bank of San Francisco
June 30, 1999
Abstract
Beginning in 1998, U.S. commercial banks may determine their
regulatory capital
requirements for financial market risk exposure using
value-at-risk (VaR) models. Currently, regulators have available
three hypothesis-testing methods for evaluating the accuracy of
VaR models: the binomial, interval forecast and distribution
forecast methods. Given the low power often exhibited by their
corresponding hypothesis tests, these methods can often
misclassify forecasts from inaccurate models as acceptably
accurate. An alternative evaluation method using loss functions
based on probability forecasts is proposed. Simulation results
indicate that this method is only as capable of differentiating
between forecasts from accurate and inaccurate models as the
other methods. However, its ability to directly incorporate
regulatory loss functions into model evaluations make it a
useful complement to the current regulatory evaluation of VaR
models.
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Risk2: Measuring the Risk in
Value at Risk
by Philippe Jorion
December, 1996
Abstract
Jorion shows how value at risk (VAR), a measure of worst-case
loss for a derivatives position, is itself subject to estimation
risk. He evaluates two methods of estimation, the sample
quantile method and the sample standard deviation method. A more
precise VAR measure is obtained when derived as a weighted
function of the standard deviation of portfolio value...
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Risk Measurement: An Introduction
to Value at Risk
by Thomas J. Linsmeier & Neil D. Pearson
University of Illinois at Urbana-Champaign
January, 1999
Abstract
This paper is a self-contained introduction to the concept and
methodology of “value at risk,” which is a new tool for
measuring an entity’s exposure to market risk. We explain the
concept of value at risk, and then describe in detail the three
methods for computing it: historical simulation; the
variance-covariance method; and Monte Carlo or stochastic
simulation. We then discuss the advantages and disadvantages of
the three methods for computing value at risk...
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Using Copulae to bound the
Value-at-Risk for functions of dependent risks
by Paul Embrechts, Andrea Hoing, & Alessandro Juri
Department of Mathematics ETHZ, CH-8092 Zurich, Switzerland
Abstract
The theory of copulae is known to provide a useful tool for
modelling
dependence in integrated risk management. In the present paper
we review and
extend some of the more recent results for finding
distributional bounds for
functions of dependent risks. As an example, the main emphasis
is put on
Value-at-Risk as a risk measure...
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Value-at-Risk Based Risk
Management: Optimal Policies and Asset Prices
by Suleyman Basak & Alex Shapiro
London Business School & New York University
February, 2001
Abstract
This article analyzes optimal, dynamic portfolio and
wealth/consumption policies of utility maximizing investors who
must also manage market-risk exposure using Value-at-Risk (VaR).
We find that VaR risk managers often optimally choose a larger
exposure to risky assets than non risk managers, and
consequently incur larger losses, when losses occur. We suggest
an alternative risk-management model, based on the expectation
of a loss, to remedy the shortcomings of VaR...
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Value at Risk Calculations,
Extreme Events, and Tail Estimation
by Salih N. Neftci
Department of Mathematics ETHZ, CH-8092 Zurich, Switzerland
Abstract
The notion of extreme movements in asset prices is implicit in
current risk management practices. Capital adequacy assumes a
threshold that classifies
observed changes in market risk factors either as extreme or
ordinary. A probability is first chosen to measure the
“extremeness” of events that may affect a particular portfolio.
This probability then determines the proper threshold...
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Value–at–Risk and Extreme Returns
by Jon Danielsson & Casper G. de Vries
London School of Economics & Tinbergen Institute
January, 2000
Abstract
Accurate prediction of the frequency of extreme events is of
primary importance in many financial applications such as
Value–at–Risk (VaR) analysis. We propose a semi–parametric
method for VaR evaluation. The largest risks are modelled
parametrically, while smaller risks are captured by the
non–parametric empirical distribution function...
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VALUE AT RISK WHEN DAILY CHANGES
IN MARKET VARIABLES ARE NOT NORMALLY DISTRIBUTED
by John Hull & Alan White
November, 1997
Abstract
This paper proposes a new model for calculating VaR where the
user is free to choose any probability distributions for daily
changes in the market variables and parameters of the
probability distributions are subject to updating schemes such
as GARCH. Transformations of the probability distributions are
assumed to be multivariate normal. The model is appealing in
that the calculation of VaR is relatively straightforward and
can make use of the RiskMetrics or a similar database...
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Back to Scholarly Compositions
See also:
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News,
Value-at-Risk Related Books,
or
Value-at-Risk Home Page.
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