Modeling asset returns with alternative stable distributions<sup>*</sup>

Mittnik, Stefan; Rachev, Svetlozar T.

doi:10.1080/07474939308800266

Cited by 256 publications

(88 citation statements)

References 71 publications

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“…By appealing to a mixture representation property of stable distributions, we link formally the Rent-a-Trader system to stable distributions. More generally, as shown in early work by Mandelbrot (1963) and Fama (1965), stable distributions accommodate well heavy-tailed financial series, with the consequence that it produces measures of risk based on the tails of the distribution, such as value at risk, which are more reliable (see in particular Rachev, 1993, andMittnik, Paolella and. We generally investigate the robustness of VaR subadditivity in the context of portfolios with stable distributions.…”

Section: Introductionmentioning

confidence: 99%

Proper Conditioning for Coherent VaR in Portfolio Management

García

Renault²,

Tsafack

2007

Management Science

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Value at Risk (VaR) is a central concept in risk management. As stressed by Artzner et al. (1999), VaR may not possess the subadditivity property required to be a coherent measure of risk. The key idea of this paper is that, when tail thickness is responsible for violation of subadditivity, eliciting proper conditioning information may restore VaR rationale for decentralized risk management. The argument is threefold. First, since individual traders are hired because they possess a richer information on their specific market segment than senior management, they just have to follow consistently the prudential targets set by senior management to ensure that decentralized VaR control will work in a coherent way. The intuition is that if one could build a fictitious conditioning information set merging all individual pieces of information, it would be rich enough to restore VaR subadditivity. Second, in this decentralization context, we show that if senior management has access ex-post to the portfolio shares of the individual traders, it amounts to recovering some of their private information. These shares can be used to improve backtesting in order to check that the prudential targets have been enforced by the traders. Finally, we stress that tail thickness required to violate subadditivity, even for small probabilities, remains an extreme situation since it corresponds to such poor conditioning information that expected loss appears to be infinite. We then conclude that lack of coherency of decentralized VaR management, that is VaR non-subadditivity at the richest level of information, should be an exception rather than a rule.

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Section: Introductionmentioning

confidence: 99%

Proper Conditioning for Coherent VaR in Portfolio Management

García

Renault²,

Tsafack

2007

Management Science

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“…The result is well-known; see, for example, Teichrow (1957), Andrews and Mallows (1974); while Linden (2001) also provides a proof. The Laplace distribution is particularly appealing not only because of its emergence from the mixture framework, but also because of other favorable features, for example, its stability properties (Mittnik and Rachev, 1993;and Kotz, Podgorski and Kozubowski, 2001). The Laplace distribution arises from the geometric summation process, a probabilistic scheme which has some resemblance with Clark's (1973) subordinated process.…”

Section: Introductionmentioning

confidence: 99%

“…The role of the Laplace distribution in the family of geometric-stable distributions is analogous to that of the normal distribution among the class of (non-geometric) stable distributions. The process is attractive, because geometric-stable random variables are closed under geometric summation and have domains of attraction, providing certain robustness to model misspecification (for details, see Mittnik and Rachev, 1993).…”

Section: Introductionmentioning

confidence: 99%

Modeling and Predicting Market Risk With Laplace-Gaussian Mixture Distributions

2005

Self Cite

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“…For instance, products and ratios of Weibull random variables is studied by Nadarajah and Kotz [6]. Lieblein and Zelen [7], Kao [8], Mann [9], Nelson [10], Whittemore and Altschuler [11], Calabria and Pulcini [12], Mittnik and Reachev [13], Jiang et al [14] and Abo-Eleneen [15] among others, utilized the Weibull distribution in their works.…”

Section: Introductionmentioning

confidence: 99%

Estimation under a finite mixture of modified Weibull distributions based on censored data via EM algorithm with application

Ateya¹,

Alharthi²

2014

JSTA

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In this paper, the maximum likelihood estimates (MLE's) of the parameters of a finite mixture of modified Weibull ( distributions are obtained based on type-I and type-II censored samples using the EM algorithm. A simulation study is carried out to study the behavior of the mean squared errors. A real data set is introduced and analyzed using a mixture of two distributions and also using a mixture of two distributions. A comparison is carried out between the mentioned mixtures based on the corresponding Kolmogorov-Smirnov (K-S) test statistic to emphasize that the mixture model fits the data better than the other mixture model.

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Modeling asset returns with alternative stable distributions^*

Cited by 256 publications

References 71 publications

Proper Conditioning for Coherent VaR in Portfolio Management

Proper Conditioning for Coherent VaR in Portfolio Management

Modeling and Predicting Market Risk With Laplace-Gaussian Mixture Distributions

Estimation under a finite mixture of modified Weibull distributions based on censored data via EM algorithm with application

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Modeling asset returns with alternative stable distributions*

Cited by 256 publications

References 71 publications

Proper Conditioning for Coherent VaR in Portfolio Management

Proper Conditioning for Coherent VaR in Portfolio Management

Modeling and Predicting Market Risk With Laplace-Gaussian Mixture Distributions

Estimation under a finite mixture of modified Weibull distributions based on censored data via EM algorithm with application

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Modeling asset returns with alternative stable distributions^*