Measuring and Analysing Marginal Systemic Risk Contribution using CoVaR: A Copula Approach (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].
Integrating Systemic Risk and Risk Analysis Using Copulas
International Journal of Disaster Risk Science
Systemic risk research is gaining traction across diverse disciplinary research communities, but has as yet not been strongly linked to traditional, well-established risk analysis research. This is due in part to the fact that systemic risk research focuses on the connection of elements within a system, while risk analysis research focuses more on individual risk to single elements. We therefore investigate how current systemic risk research can be related to traditional risk analysis approaches from a conceptual as well as an empirical point of view. Based on Sklar's Theorem, which provides a one-to-one relationship between multivariate distributions and copulas, we suggest a reframing of the concept of copulas based on a network perspective. This provides a promising way forward for integrating individual risk (in the form of probability distributions) and systemic risk (in the form of copulas describing the dependencies among such distributions) across research domains. Copulas can link continuous node states, characterizing individual risks, with a gradual dependency of the coupling strength between nodes on their states, characterizing systemic risk. When copulas are used for describing such refined coupling between nodes, they can provide a more accurate quantification of a system's network structure. This enables more realistic systemic risk assessments, and is especially useful when extreme events (that occur at low probabilities, but have high impacts) affect a system's nodes. In this way, copulas can be informative in measuring and quantifying changes in systemic risk and therefore be helpful in its management. We discuss the advantages and limitations of copulas for integrative risk analyses from the perspectives of modeling, measurement, and management.
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.
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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.
Chapter XX Measuring Systemic Risk – Structural Approaches
2017
The financial crisis of 2007/08 has demonstrated that factors for financial distress of large parts of the economy depend to a large extent on the interrelations between the financial institutions. Risks threatening the financial sector can be decomposed into risks based in the individual factors for single institutions and risks which can be attributed to the financial system as a whole. This part of the risks is called systemic risk. We review several approaches for quantifying systemic risk, most of them based on structural credit modeling. In particular we present an approach which is inspired by the fact that the joint probability distributions can be represented by their individual marginals and the copula function, which represents the interrelations.
Measuring Systemic Risk: Structural Approaches
Theory and Practice, 2015
The financial crisis of 2007/08 has demonstrated that factors for financial distress of large parts of the economy depend to a large extent on the interrelations between the financial institutions. Risks threatening the financial sector can be decomposed into risks based in the individual factors for single institutions and risks which can be attributed to the financial system as a whole. This part of the risks is called systemic risk. We review several approaches for quantifying systemic risk, most of them based on structural credit modeling. In particular we present an approach which is inspired by the fact that the joint probability distributions can be represented by their individual marginals and the copula function, which represents the interrelations.
2012
Copulas provide a useful way to model different types of dependence structures explicitly. Instead of having one correlation number that encapsulates everything known about the dependence between two variables, copulas capture information on the level of dependence as well as whether the two variables exhibit other types of dependence, for example tail dependence. Tail dependence refers to the instance where the variables show higher dependence between their extreme values. A copula is defined as a multivariate distribution function with uniform marginals. A useful class of copulas is known as Archimedean copulas that are constructed from generator functions with very specific properties. The main aim of this thesis is to construct multivariate Archimedean copulas by nesting different bivariate Archimedean copulas using the vine construction approach. A characteristic of the vine construction is that not all combinations of generator functions lead to valid multivariate copulas. Est...
Systemic Risk Modeling with Lévy Copulas
Journal of Risk and Financial Management, 2021
We investigate a systemic risk measure known as CoVaR that represents the value-at-risk (VaR) of a financial system conditional on an institution being under distress. For characterizing and estimating CoVaR, we use the copula approach and introduce the normal tempered stable (NTS) copula based on the Lévy process. We also propose a novel backtesting method for CoVaR by a joint distribution correction. We test the proposed NTS model on the daily S&P 500 index and Dow Jones index with in-sample and out-of-sample tests. The results show that the NTS copula outperforms traditional copulas in the accuracy of both tail dependence and marginal processes modeling.
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2009
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 ...
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SSRN Electronic Journal, 2000
Banks' internal credit risk assessment may take into account not only publicly available ratings but also internal measures of credit risk. We present a credit rating model of credit risk that permits banks to employ their own risk assessment in addition to public rating information.