Multivariate Tail Estimation With Application to Analysis of Covar

Nguyen, Tilo; Samorodnitsky, Gennady

doi:10.1017/asb.2013.13

Cited by 8 publications

(6 citation statements)

References 19 publications

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“…Mainik and Schaanning (2012) compared two possible concepts of CVaR available in the current literature, studied their general dependency consistency, and presented their performance in several stochastic models. Nguyen and Samorodnitsky (2013) proposed a multivariate tail estimator involving CVaR sequential statistical tests. Bernardino et al (2014) constructed two multivariate CVaRs at the level of multivariate distribution functions and provided new risk measures based on Copula structure and random ordering of marginal distributions.…”

Section: Shrinkage Estimationmentioning

confidence: 99%

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Sun¹,

Liu

et al. 2019

JRFM

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The literature on portfolio selection and risk measurement has considerably advanced in recent years. The aim of the present paper is to trace the development of the literature and identify areas that require further research. This paper provides a literature review of the characteristics of financial data, commonly used models of portfolio selection, and portfolio risk measurement. In the summary of the characteristics of financial data, we summarize the literature on fat tail and dependence characteristic of financial data. In the portfolio selection model part, we cover three models: mean-variance model, global minimum variance (GMV) model and factor model. In the portfolio risk measurement part, we first classify risk measurement methods into two categories: moment-based risk measurement and moment-based and quantile-based risk measurement. Moment-based risk measurement includes time-varying covariance matrix and shrinkage estimation, while moment-based and quantile-based risk measurement includes semi-variance, VaR and CVaR.

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Section: Shrinkage Estimationmentioning

confidence: 99%

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Sun¹,

Liu

et al. 2019

JRFM

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“…However, in their comparative analysis an elliptically contoured model is used which indeed may not be flexible enough for an application at hand. Different nonparametric consistent estimators for spectral density have been proposed recently (see Nguyen and Samorodnitsky [2013], Eastoe et al [2014], among others); however, these methods do not fit in our framework.…”

Section: Parametric Evt Estimationmentioning

confidence: 99%

“…NS Estimator One drawback of the ES estimator is the difficulty to choose the tail threshold k. Nguyen and Samorodnitsky [2013] proposed a method that allows for systematic decision on what part of the sample corresponds to "tail observations". This method is based on the rank method, where the rank statistics are defined as…”

Section: Es Estimatormentioning

confidence: 99%

Conditional Extremes in Asymmetric Financial Markets

Nolde

Zhang

2018

Journal of Business & Economic Statistics

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The project focuses on the estimation of the probability distribution of a bivariate random vector given that one of the components takes on a large value. These conditional probabilities can be used to quantify the effect of financial contagion when the random vector represents losses on financial assets and as a stress-testing tool in financial risk management. However, it is tricky to quantify these conditional probabilities when the main interest lies in the tails of the underlying distribution. Specifically, empirical probabilities fail to provide adequate estimates while fully parametric methods are subject to large model uncertainty as there is too little data to assess the model fit in the tails. We propose a semi-parametric framework using asymptotic results in the spirit of extreme values theory. The main contributions include an extension of the limit theorem in Abdous et al. [Canad. J. Statist. 33 (2005)] to allow for asymmetry, frequently encountered in financial and insurance applications, and a new approach for inference. The results are illustrated using simulations and two applications in finance. 5.3 Simulation results based on 1000 samples of size 1000 from a bivariate skew-t distribution with parameters ξ = (3,1), α = (1,-3), ν =2, ρ = 0.5 and ω = diag(2, 3) for the scale matrix. Each cell provides the average (standard deviation) of the estimates of η(x, y) under various methods; see Section 5.5 for details. Forη AF G (x, y), η 1 (x, y),η 2 (x, y) and η lim (x, y) we used z = ω 1 y/ω 2 x−ρ in the limit results. Values of x and y are chosen as the theoretical marginal quantiles with probability p, where p labels columns and rows.. . 41 vii List of Tables 6.1 Point estimation of extreme conditional excess probability for 28 financial institutions. Daily losses are computed using log returns and are filtered by the AR(1)-GARCH(1,1) process. The threshold values of x and y are, respectively, 99.9% quantile of losses on DJUSFN and average of 99% quantile of losses on cross-sectional stocks. The sample period is from

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“…12 These include kernel estimators (e.g., [23,24]), moment estimators (e.g., [25]), probability weighted moment estimators (e.g., [26]), and weighted least squares estimators (e.g., [27]). See also Gomes et al [28] for weighted log-excesses, Nguyen and Samorodnitsky [29] for the multivariate case, and the monographies by Embrechts et al [8], Beirlant et al [9] for a general overview. 13 We exclude on-shore energy exposures, and do not study the split between physical damage and business interruption in our claims.…”

Section: Empirical Evidencementioning

confidence: 99%

Tail Risk in Commercial Property Insurance

Biffis¹,

Chavez

2014

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: We present some new evidence on the tail distribution of commercial property losses based on a recently constructed dataset on large commercial risks. The dataset is based on contributions from Lloyd's of London syndicates, and provides information on over three thousand claims occurred during the period 2000-2012, including detailed information on exposures. We use occupancy characteristics to compare the tail risk profiles of different commercial property exposures, and find evidence of substantial heterogeneity in tail behavior. The results demonstrate the benefits of aggregating granular information on both claims and exposures from different data sources, and provide warning against the use of reserving and capital modeling approaches that are not robust to heavy tails. Terms of use: Documents in

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Multivariate Tail Estimation With Application to Analysis of Covar

Cited by 8 publications

References 19 publications

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Conditional Extremes in Asymmetric Financial Markets

Tail Risk in Commercial Property Insurance

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