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Papers by Brice Hakwa
Communications on Stochastic Analysis
The main challenge by the analysis and the regulation of systemic risk is the measurement of the ... more 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].
SSRN Electronic Journal, 2000
SSRN Electronic Journal, 2000
This paper is devoted to the quantification and analysis of marginal risk contribution of a given... more 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...
Communications on Stochastic Analysis
The main challenge by the analysis and the regulation of systemic risk is the measurement of the ... more 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].
SSRN Electronic Journal, 2000
SSRN Electronic Journal, 2000
This paper is devoted to the quantification and analysis of marginal risk contribution of a given... more 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...