Systemic Risk Modeling with Lévy Copulas (original) (raw)
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Communications on Stochastic Analysis
The main challenge by the analysis and the regulation of systemic risk is the measurement of the adverse financial effect that the bankruptcy of one single financial institution can cause to the financial system. One of the main tools that has been proposed for this purpose is the risk measure ∆CoV aR of Adrian and Brunnermeier in [2]. The main contribution of this paper is to propose a general and flexible framework for the computation of ∆CoV aR in a more general stochastic setting compared to those provided so far. The formula that we propose here is based on Copula's theory. It allows us to stay not only in the Gaussian but also in the non-Gaussian setting. We also discuss the properties of our formula and analyse many examples, involving in particular elliptical and Archimedean copula, as well as convex combination of copulas. We also propose alternative models to those in [2].
Measuring and Analysing Marginal Systemic Risk Contribution using CoVaR: A Copula Approach
This paper is devoted to the quantification and analysis of marginal risk contribution of a given single financial institution i to the risk of a financial system s. Our work expands on the CoVaR concept proposed by Adrian and Brunnermeier as a tool for the measurement of marginal systemic risk contribution. We first give a mathematical definition of CoVaR_{\alpha}^{s|L^i=l}. Our definition improves the CoVaR concept by expressing CoVaR_{\alpha}^{s|L^i=l} as a function of a state l and of a given probability level \alpha relative to i and s respectively. Based on Copula theory we connect CoVaR_{\alpha}^{s|L^i=l} to the partial derivatives of Copula through their probabilistic interpretation and definitions (Conditional Probability). Using this we provide a closed formula for the calculation of CoVaR_{\alpha}^{s|L^i=l} for a large class of (marginal) distributions and dependence structures (linear and non-linear). Our formula allows a better analysis of systemic risk using CoVaR in t...
Measuring Systemic Risk: Vine Copula- GARCH Model
2015
We analyze each U.S. Equity sector's risk contribution ΔVaR, the difference between the Value-at-Risk of a sector and the Value-at-Risk of the system (S&P 500 Index), by using vine Copula-based ARMA-GARCH (1, 1) modeling. Vine copula modeling not only has the advantage of extending to higher dimensions easily, but also provides a more flexible measure to capture an asymmetric dependence among assets. We investigate systemic risk in 10 S&P 500 sector indices in the U.S. stock market by forecasting one-day ahead Copula VaR and Copula ΔVaR during the 2008 financial subprime crisis. Our evidence reveals vine Copula-based ARMA-GARCH (1, 1) is the appropriate model to forecast and analyze systemic risk. Index Terms—Copula, Time Series, GARCH, Systemic Risk, VaR
Measuring financial risks with copulas
International Review of Financial Analysis, 2004
This paper is concerned with the statistical modeling of the dependence structure of multivariate financial data using the concept of copulas. We select some special copulas and identify the type of dependency captured by each one. We fit copulas to daily returns and simulate from the fitted models. We compare the effect of the choice of copula on risk measures and assess the variability of one-step-ahead predictions of portfolio losses. We analyze extreme scenarios and fit extreme value copulas to the block maxima and minima from daily returns. The stress scenarios constructed are compared to those obtained using models from the extreme value theory. We illustrate the usefulness of the copula approach using two stock market indexes.
Extremal Copulas and Tail Dependence in Modeling Stochastic Financial Risk
European Journal of Pure and Applied Mathematics
These last years the stochastic modeling became essential in financial risk management related to the ownership and valuation of financial products such as assets, options and bonds. This paper presents a contribution to the modeling of stochastic risks in finance by using both extensions of tail dependence coefficients and extremal dependance structures based on copulas. In particular, we show that when the stochastic behavior of a set of risks can be modeled by a multivariate extremal process a corresponding form of the underlying copula describing theirdependence is determined. Moreover a new tail dependence measure is proposed and properties of this measure are established.
Measuring systemic risk using vine-copula
We present an intuitive model of systemic risk to analyse the complex interdependencies between different borrowers. We characterise systemic risk by the way that financial institutions are interconnected. Using their probability of default, we classify different international financial institutions into five rating groups. Then we use the state-of-the-art canonical (C-) and D-vine copulae to investigate the partial correlation structure between the rating groups. Amongst many interesting findings, we discover that the second tier financial institutions pay a larger contribution to the systemic risk than the top tier borrowers. Further, we discuss an application of our methodology for pricing credit derivative swaps.
Analysis of Systemic Risk : A Vine Copula-based ARMA-GARCH Model
In this paper, a model for analyzing each U.S. Equity sector's risk contribution (VaR ratio), the ratio of the Value-at-Risk of a sector to the Value-at-Risk of the system (S&P 500 Index), with vine Copula-based ARMA-GARCH (1, 1) modeling is presented. Vine copula modeling not only has the advantage of extending to higher dimensions easily, but also provides a more flexible measure to capture an asymmetric dependence among assets. We investigate systemic risk in 10 S&P 500 sector indices in the U.S. stock market by forecasting one-day ahead VaR and one-day ahead VaR ratio during the 2008 financial subprime crisis. Our evidence reveals vine Copula-based ARMA-GARCH (1, 1) is the appropriate model to forecast and analyze systemic risk.
In order to minimize risks and create a safe investing environment, financial risk management is becoming more and more crucial for individuals, financial organizations, and even entire nations. Accurately assessing financial risks and using that information to inform wise investment choices can ..., 2024
In order to minimize risks and create a safe investing environment, financial risk management is becoming more and more crucial for individuals, financial organizations, and even entire nations. Accurately assessing financial risks and using that information to inform wise investment choices can give an investor a competitive edge as well as significant returns. In actuality, real-world financial variables limit the ability to estimate financial risks. On the other hand, a wealth of data indicates that financial variables typically have asymmetric dependency, skewness, and fat tails. In three ways, the conventional approaches to financial risk management based on normally distributed hypotheses are put to the test by these stylized characteristics of financial variables. First, the univariate normal distribution or other elliptical distributions are unable to adequately fit the distribution of the univariate variable. Second, despite their straightforward tractability, multivariate variables' extra kurtosis and skewness are not captured by their normal distribution. As a result, the dependence risks associated with multivariate financial variables may be underestimated. Finally, when the joint distribution of various variables is non-elliptical, linear correlation which is typically employed to characterize the dependence of various variables in traditional portfolio risk management is likewise insufficient. This research uses a promising technique based on copulas in conjunction with GARCH and realized volatility models to examine the risks associated with multivariate financial variables in order to address these issues. The multivariate distributions are constructed using copulas in conjunction with GARCH and Realized Volatility models which are then utilized to evaluate portfolio risks in financial market. The findings demonstrate that copula-based models outperform conventional models in fitting financial data. Second, a variety of marginal models have a notable impact on the value at risk of the portfolio, including the GARCH and realized volatility models. Lastly, both the dependence structure and the marginal distribution exhibit notable skewness. Consequently, compared to the normal or Student-t distribution, the skewed Student-t distribution fits some datasets better.
SSRN Electronic Journal, 2000
ABSTRACT This paper aims to provide an introductory review of copulae and their potential application finance, in particular in capturing the dependence between financial assets that follow non-gaussian distributions and hence for modelling credit risk, pricing options and portfolio design. We briefy review the failure of methods based on multivariate normality and where dependency is measured by correlation. Using a copula approach enables us to measure the different relationships that may exist between financial assets in different ranges of their behaviour- for instance do assets exhibit similar dependency patterns in the tails of their distributions as they do around their means? We review different measures of association and show that when these dependency measures can be expressed simply as functions of a copula they will be invariant to strictly monotone transformations of the random variables and hence the units in which we choose to express our data. The standard Pearson Correlation statistic is not in general invariant to scale changes in the data. We then discuss several statistical issues relating to the estimation of Copulae and their empirical application through both parametric and non parametric methods. An important issue lies in the statistical discrimination between copulae and we propose a encompassing framework based on simulation for discriminating between what are effectively separate statistical families. We then consider several applications, modelling default risk, tail dependence, quantile regression and portfolio design for non-gaussian assets.