445 research outputs found
Copulas and bivariate risk measures : an application to hedge funds
With hedge funds, managers develop risk management models that mainly aim to play on the effect of decorrelation. In order to achieve this goal , companies use the correlation coefficient as an indicator for measuring dependencies existing between (i) the various hedge funds strategies and share index returns and (ii) hedge funds strategies against each other. Otherwise, copulas are a statistic tool to model the dependence in a realistic and less restrictive way, taking better account of the stylized facts in finance. This paper is a practical implementation of the copulas theory to model dependence between different hedge fund strategies and share index returns and between these strategies in relation to each other on a "normal" period and a period during which the market trend is downward. Our approach based on copulas allows us to determine the bivariate VaR level curves and to study extremal dependence between hedge funds strategies and share index returns through the use of some tail dependence measures which can be made into useful portfolio management tools.Hedge fund strategies, share index, dependence, copula, tail dependence, bivariate Value at Risk
Modeling Dependencies in Finance using Copulae
In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the cop- ulae model the dependency structure between random variables, next we explain the link between the copulae and common dependency measures, such as Kendall's tau and Spearman's rho. In the next section the copulae are generalized to the multivariate case. In this general setup we discuss and provide an intensive literature review of estimation and simulation techniques. Separate section is devoted to the goodness-of-fit tests. The importance of copulae in finance we illustrate on the example of asset allocation problems, Value-at-Risk and time series models. The paper is complemented with an extensive simulation study and an application to financial data.Distribution functions, Dimension Reduction, Risk management, Statistical models
Weak & Strong Financial Fragility
The stability of the financial system at higher loss levels is either characterized by asymptotic dependence or asymptotic independence. If asymptotically independent, the dependency, when present, eventually dies out completely at the more extreme quantiles, as in case of the multivariate normal distribution. Given that financial service firms' equity returns depend linearly on the risk drivers, we show that the marginals' distributions maximum domain of attraction determines the type of systemic (in-)stability. A scale for the amount of dependency at high loss lovels is designed. This permits a characterization of systemic risk inherent to different financial network structures. The theory also suggests the functional form of the economically relevant limit copulas
Testing the Gaussian Copula Hypothesis for Financial Assets Dependences
Using one of the key property of copulas that they remain invariant under an
arbitrary monotonous change of variable, we investigate the null hypothesis
that the dependence between financial assets can be modeled by the Gaussian
copula. We find that most pairs of currencies and pairs of major stocks are
compatible with the Gaussian copula hypothesis, while this hypothesis can be
rejected for the dependence between pairs of commodities (metals).
Notwithstanding the apparent qualification of the Gaussian copula hypothesis
for most of the currencies and the stocks, a non-Gaussian copula, such as the
Student's copula, cannot be rejected if it has sufficiently many ``degrees of
freedom''. As a consequence, it may be very dangerous to embrace blindly the
Gaussian copula hypothesis, especially when the correlation coefficient between
the pair of asset is too high as the tail dependence neglected by the Gaussian
copula can be as large as 0.6, i.e., three out five extreme events which occur
in unison are missed.Comment: Latex document of 43 pages including 14 eps figure
Quantile Coherency: A General Measure for Dependence between Cyclical Economic Variables
In this paper, we introduce quantile coherency to measure general dependence
structures emerging in the joint distribution in the frequency domain and argue
that this type of dependence is natural for economic time series but remains
invisible when only the traditional analysis is employed. We define estimators
which capture the general dependence structure, provide a detailed analysis of
their asymptotic properties and discuss how to conduct inference for a general
class of possibly nonlinear processes. In an empirical illustration we examine
the dependence of bivariate stock market returns and shed new light on
measurement of tail risk in financial markets. We also provide a modelling
exercise to illustrate how applied researchers can benefit from using quantile
coherency when assessing time series models.Comment: paper (49 pages) and online supplement (31 pages), R codes to
replicate the figures in the paper are available at
https://github.com/tobiaskley/quantile_coherency_replicatio
Estimation of value-at-risk and expected shortfall using copulas
Includes bibliographical references (leaves 76-77)
New general dependence measures: construction, estimation and application to high-frequency stock returns
We propose a set of dependence measures that are non-linear, local, invariant
to a wide range of transformations on the marginals, can show tail and risk
asymmetries, are always well-defined, are easy to estimate and can be used on
any dataset. We propose a nonparametric estimator and prove its consistency and
asymptotic normality. Thereby we significantly improve on existing (extreme)
dependence measures used in asset pricing and statistics. To show practical
utility, we use these measures on high-frequency stock return data around
market distress events such as the 2010 Flash Crash and during the GFC.
Contrary to ubiquitously used correlations we find that our measures clearly
show tail asymmetry, non-linearity, lack of diversification and endogenous
buildup of risks present during these distress events. Additionally, our
measures anticipate large (joint) losses during the Flash Crash while also
anticipating the bounce back and flagging the subsequent market fragility. Our
findings have implications for risk management, portfolio construction and
hedging at any frequency
Implied volatility of basket options at extreme strikes
In the paper, we characterize the asymptotic behavior of the implied
volatility of a basket call option at large and small strikes in a variety of
settings with increasing generality. First, we obtain an asymptotic formula
with an error bound for the left wing of the implied volatility, under the
assumption that the dynamics of asset prices are described by the
multidimensional Black-Scholes model. Next, we find the leading term of
asymptotics of the implied volatility in the case where the asset prices follow
the multidimensional Black-Scholes model with time change by an independent
increasing stochastic process. Finally, we deal with a general situation in
which the dependence between the assets is described by a given copula
function. In this setting, we obtain a model-free tail-wing formula that links
the implied volatility to a special characteristic of the copula called the
weak lower tail dependence function
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