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This paper proposes a novel methodology to calibrate the magnitude of the countercyclical capital buffer (CCyB) using market-based stress tests. The macroprudential authority in our paper aims to contain the possibility of a breach of a minimum capital ratio in the event of a severe system-wide shock within a certain permissible failure probability. We apply the methodology by stress-testing major banks in six advanced economies on a quarterly basis over a period of 27 years. The estimates suggest that the cap on the CCyB should not be less than around 1.7 percent of total assets. Its potential normal-times level is estimated at approximately 0.8 percent of total assets.

Expectiles define the only law-invariant, coherent and elicitable risk measure apart from the expectation. The popularity of expectile-based risk measures is steadily growing and their properties have been studied for independent data, but further results are needed to establish that extreme expectiles can be applied with the kind of dependent time series models relevant to finance. In this article we provide a basis for inference on extreme expectiles and expectile-based marginal expected shortfall in a general β-mixing context that encompasses ARMA and GARCH models with heavy-tailed innovations. Our methods allow the estimation of marginal (pertaining to the stationary distribution) and dynamic (conditional on the past) extreme expectile-based risk measures. Simulations and applications to financial returns show that the new estimators and confidence intervals greatly improve on existing ones when the data are dependent.

In the context of bivariate random variables $\left (Y^{(1)},Y^{(2)}\right )$ , the marginal expected shortfall, defined as $\mathbb {E}\left (Y^{(1)}|Y^{(2)} \ge Q_{2}(1-p)\right )$ for p small, where Q2 denotes the quantile function of Y(2), is an important risk measure, which finds applications in areas like, e.g., finance and environmental science. Our paper pioneers the statistical modeling of this risk measure when the random variables of main interest $\left (Y^{(1)},Y^{(2)}\right )$ are observed together with a random covariate X, leading to the concept of the conditional marginal expected shortfall. The asymptotic behavior of an estimator for this conditional marginal expected shortfall is studied for a wide class of conditional bivariate distributions, with heavy-tailed marginal conditional distributions, and where p tends to zero at an intermediate rate. The finite sample performance is evaluated on a small simulation experiment. The practical applicability of the proposed estimator is illustrated on flood claim data.

We study the asymptotic behavior of the marginal expected shortfall when the two random variables are asymptotic independent but positively associated, which is modeled by the so-called tail dependent coefficient. We construct an estimator of the marginal expected shortfall, which is shown to be asymptotically normal. The finite sample performance of the estimator is investigated in a small simulation study. The method is also applied to estimate the expected amount of rainfall at a weather station given that there is a once every 100 years rainfall at another weather station nearby.

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We derive several popular systemic risk measures in a common framework and show that they can be expressed as transformations of market risk measures (e.g., beta). We also derive conditions under which the different measures lead to similar rankings of systemically important financial institutions (SIFIs). In an empirical analysis of US financial institutions, we show that (1) different systemic risk measures identify different SIFIs and that (2) firm rankings based on systemic risk estimates mirror rankings obtained by sorting firms on market risk or liabilities. One-factor linear models explain most of the variability of the systemic risk estimates, which indicates that systemic risk measures fall short in capturing the multiple facets of systemic risk.

We examine systemic risk in the Chinese banking system by estimating the conditional value at risk (CoVaR), the marginal expected shortfall (MES), the systemic impact index (SII) and the vulnerability index (VI) for 16 listed banks in China for the 2007-2014 period. We find that these measures show different patterns, capturing different aspects of systemic risk of Chinese banks. However, rankings of banks based on these measures are significantly correlated. The time series results for the CoVaR and MES measures suggest that systemic risk in the Chinese banking system decreased after the global financial crisis but started rising in 2014. Postprint

International audience; We propose an estimator of the marginal expected shortfall by considering a log transformation of a variable which has an infinite expectation. We establish the asymptotic normality of our estimator under general assumptions. A simulation study suggests that the estimation procedure is robust with respect to the choice of tuning parameters. Our estimator has lower bias and mean squared error than the empirical estimator when the latter is applicable. We illustrate our method on a tsunami dataset.

Levent Güntay (MEF Author) The literature proposes several stock return-based measures of systemic risk but does not include a classical hypothesis tests for detecting systemic risk. Using a joint null hypothesis of Gaussian returns and the absence of systemic risk, we develop a hypothesis test statistic to detect systemic risk in stock returns data. We apply our tests on conditional value-at-risk (CoVaR) and marginal expected shortfall (MES) estimates of the 50 largest US financial institutions using daily stock return data between 2006 and 2007. The CoVaR test identifies only one institution as systemically important while the MES test identifies 27 firms including some of the financial institutions that experienced distress in the past financial crisis. We perform a simulation analysis to assess the reliability of our proposed test statistics and find that our hypothesis tests have weak power, especially tests using CoVaR. We trace the power issue to the inherent variability of the nonparametric CoVaR and MES estimators that have been proposed in the literature. These estimators have large standard errors that increase as the tail dependence in stock returns strengthens. WOS:000378149400004 2-s2.0-84975728106 Social Sciences Citation Index Q3 Article Uluslararası işbirliği ile yapılan - EVET Haziran 2016 YÖK - 2015-16

We use tail expectiles to estimate alternative measures to the Value at Risk (VaR), Expected Shortfall (ES) and Marginal Expected Shortfall (MES), three instruments of risk protection of utmost importance in actuarial science and statistical finance. The concept of expectiles is a least squares analogue of quantiles. Both expectiles and quantiles were embedded in the more general class of M-quantiles as the minimizers of an asymmetric convex loss function. It has been proved very recently that the only M-quantiles that are coherent risk measures are the expectiles. Moreover, expectiles define the only coherent risk measure that is also elicit able. The elicit ability corresponds to the existence of a natural backtesting methodology. The estimation of expectiles did not, however, receive yet any attention from the perspective of extreme values. The first estimation method that we propose enables the usage of advanced high quantile and tail index estimators. The second method joins together the least asymmetrically weighted squares estimation with the tail restrictions of extreme-value theory. A main tool is to first estimate the large expectile-based VaR, ES and MES when they are covered by the range of the data, and then extrapolate these estimates to the very far tails. We establish the limit distributions of the proposed estimators when they are located in the range of the data or near and even beyond the maximum observed loss. We show through a detailed simulation study the good performance of the procedures, and also present concrete applications to medical insurance data and three large US investment banks.

This research examines and compares the performances in terms of systemic risk ranking for three different systemic risk metrics based on daily frequency publicly available data, specifically: Marginal Expected Shortfall (ES), Component Expected Shortfall (CES) and Delta Conditional Value-at-Risk (ΔCoVaR). We compute ΔCoVaR, MES and CES by utilizing EVT principles for modelling marginal distributions and Student’s t copula for describing the dependence structure between every bank and the banking system. Our objective is to attest whether different systemic risk metrics detect the same banks as systemically dangerous institutions with refer to a sample of European banks over the time span 2004-2015. For each bank in the sample we also calculate three traditional market risk measures, like Market VaR, Sharpe’s beta and the correlation between every bank and the banking system (European STOXX 600 Banks Index). Another aim is to explore the existence of a link among systemic risk measures and traditional risk metrics. In addition, the classification results obtained by the different risk metrics are compared with the ranking in terms of systemic riskiness (for European banks) calculated by Financial Stability Board (2015) using end-2014 data and collected in its list of Global Systemically Important Banks (G-SIBs). With refer to the entire sample period, we find a good coherence of ranking results among the three different systemic risk metrics, in particular between CES and ΔCoVaR. Moreover, we find for MES and ΔCoVaR a strong linkage with beta and correlation metrics respectively. Finally, CES metric shows the highest level of concordance with the list of G-SIBs by FSB with refer to European banks.

This paper compares four commonly used systemic risk metrics using data on U.S. financial institutions over the period 2005–2014. The four systemic risk measures examined are the (i) marginal expected shortfall, (ii) codependence risk, (iii) delta conditional value at risk, and (iv) lower tail dependence. Our results demonstrate that the alternative measurement approaches produce very different estimates of systemic risk. Furthermore, we show that the different systemic risk metrics may lead to contradicting assessments about the riskiness of different types of financial institutions. Overall, our findings suggest that systemic risk assessments based on a single risk metric should be approached cautiously.

This paper provides a new estimation method for the marginal expected shortfall (MES) based on multivariate extreme value theory. In contrast to previous studies, the method does not assume specific dependence structure among bank equity returns and is applicable to both large and small systems. Furthermore, our MES estimator inherits the theoretical additive property. Thus, it serves as a tool to allocate systemic risk. We apply the proposed method to 29 global systemically important financial institutions (G-SIFIs) to evaluate the cross sections and dynamics of the systemic risk allocation. We show that allocating systemic risk according to either size or individual risk is imperfect and can be unfair. Between the allocation with respect to individual risk and that with respect to size, the former is less unfair. On the time dimension, both allocation fairness across all the G-SIFIs has decreased since 2008.

This paper investigates the meaning of systemic risk in energy markets and proposes a methodology to measure it. Energy Systemic Risk is defined by the risk of an energy crisis raising the prices of all energy commodities with negative consequences for the real economy. Measures of the total cost (EnSysRISK) and the net impact (ΔMES) of an energy crisis on the rest of the economy are proposed. The measures are derived from the Marginal Expected Shortfall (MES) capturing the tail dependence between the asset and the energy market factor. The adapted MES accounts for causality and dynamic exposure to common latent factors. The methodology is applied to the European Energy Exchange and the DAX industrial index, where a minor decline in industrial productivity is observed from recent energy shocks.

This paper proposes a component approach to systemic risk which allows to decompose the risk of the aggregate financial system (measured by Expected Shortfall, ES) while accounting for the firm characteristics. Developed by analogy with the Component Value-at-Risk concept, our new systemic risk measure, called Component ES (CES), presents several advantages. It is a hybrid measure, which combines the Too Interconnected To Fail and the Too Big To Fail logics. CES relies only on publicly available daily data and encompasses the popular Marginal ES measure. CES can be used to assess the contribution of a firm to systemic risk at a precise date but also to forecast its contribution over a certain period. The empirical application verifies the ability of CES to identify the most systemically risky firms during the 2007-2009 financial crisis. We show that our measure identifies the institutions labeled as SIFIs by the Financial Stability Board.

Recent literature has proposed new methods for measuring the systemic risk of financial institutions based on observed stock returns. In this paper we examine the reliability and robustness of such risk measures, focusing on CoVaR, marginal expected shortfall, and option-based tail risk estimates. We show that CoVaR exhibits undesired characteristics in the way it responds to idiosyncratic risk. In the presence of contagion, the risk measures provide conflicting signals on the systemic risk of infectious and infected banks. Finally, we explore how limited data availability typical of practical applications may limit the measures' performance. We generate systemic tail risk through positions in standard index options and describe situations in which systemic risk is misestimated by the three measures. The observations raise doubts about the informativeness of the proposed measures. In particular, a direct application to regulatory capital surcharges for systemic risk could create wrong incentives for banks.

We use tail expectiles to estimate alternative measures to the Value at Risk (VaR) and Marginal Expected Shortfall (MES), two instruments of risk protection of utmost importance in actuarial science and statistical _nance. The concept of expectiles is a least squares analogue of quantiles. Both are M-quantiles as the minimizers of an asymmetric convex loss function, but expectiles are the only M-quantiles that are coherent risk measures. Moreover, expectiles de_ne the only coherent risk measure that is also elicitable. The estimation of expectiles has not, however, received any attention yet from the perspective of extreme values. Two estimation methods are proposed here, either making use of quantiles or relying directly on least asymmetrically weighted squares. A main tool is to _rst estimate large values of expectile-based VaR and MES located within the range of the data, and then to extrapolate the obtained estimates to the very far tails. We establish the limit distributions of both of the resulting intermediate and extreme estimators. We show via a detailed simulation study the good performance of the procedures, and present concrete applications to medical insurance data and three large US investment banks.