Fat tails, VaR and subadditivity

Danı́elsson, Jón; Jørgensen, Bjørn N.; Samorodnitsky, Gennady; Sarma, Mandira; Vries, Casper G. de

doi:10.1016/j.jeconom.2012.08.011

Cited by 108 publications

(72 citation statements)

References 19 publications

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“…A particular corollary of the result of Wirch and Hardy (2002) is that while the VaR is not a coherent risk measure, the TVaR is, for instance, and this has already been noted several times in the recent literature. It 5 should be acknowledged nonetheless that the VaR is subadditive (and therefore coherent) in the right tail under certain conditions, see Daníelsson et al (2013 Denuit et al, 2005, pp. 94-95).…”

Section: Wang Risk Measuresmentioning

confidence: 99%

Extreme versions of Wang risk measures and their estimation for heavy-tailed distributions

Methni¹,

Stupfler²

2017

STAT SINICA

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Abstract. Among the many possible ways to study the right tail of a real-valued random variable, a particularly general one is given by considering the family of its Wang distortion risk measures. This class of risk measures encompasses various interesting indicators, such as the widely used Value-at-Risk and Tail Value-at-Risk, which are especially popular in actuarial science, for instance. In this paper, we first build simple extreme analogues of Wang distortion risk measures and we show how this makes it possible to consider many standard measures of extreme risk, including the usual extreme Value-at-Risk or Tail-Value-at-Risk, as well as the recently introduced extreme Conditional Tail Moment, in a unified framework. We then introduce adapted estimators when the random variable of interest has a heavy-tailed distribution and we prove their asymptotic normality. The finite sample performance of our estimators is assessed on a simulation study and we showcase our techniques on two sets of real data.

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Section: Wang Risk Measuresmentioning

confidence: 99%

Extreme versions of Wang risk measures and their estimation for heavy-tailed distributions

Methni¹,

Stupfler²

2017

STAT SINICA

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“…This result also holds, for example, for the Student's t-distribution. In fact, Daníelsson et al (2010) show that for all fat tailed distributions, the VaR measure is subadditive in the tail area. So both for practical and theoretical reasons it is of interest to analyze how VaR is affected by the presence of autocorrelation in hedge fund returns.…”

Section: Value-at-riskmentioning

confidence: 95%

Risk Measures for Autocorrelated Hedge Fund Returns

Cesare

Stork²,

Vries

2014

JOURNAL OF FINANCIAL ECONOMETRICS

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176

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“…See BCBS [14] [15]. In recent research, Danielsson [16] and Danielsson et al [17] find that VaR is mostly sub-additive, except for the fattest tails that are quite unlikely except in extreme situations. Yamai and Yoshiba [18] find that it is difficult to back-test the ES method as a very large sample is required.…”

Section: Application: Computation Of Varmentioning

confidence: 99%

New Approach to Density Estimation and Application to Value-at-Risk

Lim¹,

Cheng²,

Yap³

2015

JMF

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The key contribution in this paper is to provide a new approach in estimating the physical distribution of the underlying asset return by using a quadratic Radon-Nikodym derivative function. The latter function transforms a fitted Variance Gamma risk-neutral distribution that is obtained from traded option prices. The generality of the VG distribution helps to avoid unnecessary mis-specification bias. The estimated empirical distribution is then used to find the risk measure of VaR. We show that possible underestimation of VaR risk using existing methods is largely not due to VaR itself but perhaps due to mis-specification errors which we minimize in our approach. Our method of measuring VaR clearly captures large tail risk in the empirical examples on S&P 500 index.

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Fat tails, VaR and subadditivity

Cited by 108 publications

References 19 publications

Extreme versions of Wang risk measures and their estimation for heavy-tailed distributions

Extreme versions of Wang risk measures and their estimation for heavy-tailed distributions

Risk Measures for Autocorrelated Hedge Fund Returns

New Approach to Density Estimation and Application to Value-at-Risk

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