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## Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: an Extreme Value Approach (1998)

Venue: | Journal of Empirical Finance |

Citations: | 230 - 6 self |

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Citation Context ...to compare the GPD approach to tail estimation with the approach based on the Hill estimator and the approach based on the empirical distribution function (historical simulation). The Hill estimator (=-=Hill 1975-=-) is designed for data from heavy-tailed distributions admitting the representation (11) with > 0. The estimator for , based on the k exceedances of the (k + 1)th order statistic, is ^ (H) = ^ ... |

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Statistical aspects of ARCH and stochastic volatility
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Citation Context ...including models from the ARCH/GARCH family (Bollerslev, Chou, and Kroner 1992), HARCH processes (Muller, Dacarogna, Dave, Olsen, Pictet, and von Weizsacker 1995) and stochastic volatility models (=-=Shephard 1996-=-). In this paper we use the parsimonious but eective GARCH(1,1) process for the volatility and an AR(1) model for the dynamics of the conditional mean; the approach we propose extends easily to more ... |

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Citation Context ... time series via EVT is a topical issue which has given rise to some recent work (Embrechts, Resnick, and Samorodnitsky 1998b, Embrechts, Resnick, and Samorodnitsky 1998a, Longin 1997b, Longin 1997a, =-=McNeil 1997-=-, McNeil 1998, Danielsson and de Vries 1997b, Danielsson and de Vries 1997c, Danielsson, Hartmann, and de Vries 1998). In all these papers the focus is on estimating the unconditional (stationary) dis... |

85 |
From Value at Risk to Stress Testing: the Extreme Value Approach
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Citation Context ...urn distributions ofsnancial time series via EVT is a topical issue which has given rise to some recent work (Embrechts, Resnick, and Samorodnitsky 1998b, Embrechts, Resnick, and Samorodnitsky 1998a, =-=Longin 1997-=-b, Longin 1997a, McNeil 1997, McNeil 1998, Danielsson and de Vries 1997b, Danielsson and de Vries 1997c, Danielsson, Hartmann, and de Vries 1998). In all these papers the focus is on estimating the un... |

79 | Extreme value theory as a risk management tool - Embrechts, Resnick, et al. - 1999 |

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Citation Context ...via EVT is a topical issue which has given rise to some recent work (Embrechts, Resnick, and Samorodnitsky 1998b, Embrechts, Resnick, and Samorodnitsky 1998a, Longin 1997b, Longin 1997a, McNeil 1997, =-=McNeil 1998-=-, Danielsson and de Vries 1997b, Danielsson and de Vries 1997c, Danielsson, Hartmann, and de Vries 1998). In all these papers the focus is on estimating the unconditional (stationary) distribution of ... |

42 | The peaks over thresholds method for estimating high quantiles of loss distributions
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Citation Context ... 1 F (x) (1)=2 x ; so that this provides a very simple example of a symmetric distribution in this class, and the value of in the limiting GPD is the reciprocal of the degrees of freedom (=-=McNeil and Saladin 1997-=-). Fitting a GARCH model with t innovations can be thought of as estimating the in our GPD tail estimator by simpler means. Inspection of the form of the likelihood of the t{distribution shows that ... |

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Citation Context ...urn distributions ofsnancial time series via EVT is a topical issue which has given rise to some recent work (Embrechts, Resnick, and Samorodnitsky 1998b, Embrechts, Resnick, and Samorodnitsky 1998a, =-=Longin 1997-=-b, Longin 1997a, McNeil 1997, McNeil 1998, Danielsson and de Vries 1997b, Danielsson and de Vries 1997c, Danielsson, Hartmann, and de Vries 1998). In all these papers the focus is on estimating the un... |

6 | Scale Models - Diebold, Schuermann, et al. - 1998 |

5 | Vries (1997b): \Tail index and quantile estimation with very high frequency data - Danielsson, de |

4 | de Vries (1997a) ‘Beyond the sample: Extreme quantile and probability estimation.’ Mimeo. Tinbergen Institute - Danielsson, G |

4 | de Vries (1997a). “Tail index and quantile estimation with very high frequency data - Daníelsson, G |

3 | Coherent Measures of Risk," Universite de Strasbourg, preprint - Artzner, Delbaen, et al. - 1998 |

2 | Vries (1997c): \Value-at-Risk and extreme returns," FMGDiscussion - Danielsson, de |

2 | de Vries (1997b). “Value-at-Risk and extreme returns - Daníelsson, G |

1 | Coherent Measures of Risk," Universite de Strasbourg, preprint - Artzner, Delbaen, et al. - 1998 |

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1 | Vries (1998): \The cost of conservatism - Danielsson, Hartmann, et al. |

1 | Samorodnitsky (1998a): \Extreme Value Theory as a Risk Management Tool - Embrechts, Resnick, et al. |

1 | Samorodnitsky (1998b): \Living on the Edge - Embrechts, Resnick, et al. |

1 | ARCH-Models and Financial Applications, Springer Series in Statistics - eroux - 1997 |

1 | Weizs acker (1995): \Volatilities of dierent time resolutions { analyzing the dynamics of market components - uller, O, et al. |

1 | aric a (1995): \Consistency of Hill's estimator for dependent data - Resnick, St |

1 | aric a (1996): \Tail index estimation for dependent data - Resnick, St |

1 | Weizs acker (1995): \Volatilities of dierent time resolutions { analyzing the dynamics of market components - e, Pictet, et al. |

1 |
Consistency of Hill's estimator for dependent data
- unknown authors
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(Show Context)
Citation Context ...s of these estimators have been extensively investigated in the EVT literature; in particular, a number of recent papers show consistency of the Hill estimator for dependent data (Resnick and Staric=-=a 1995-=-, Resnick and Starica 1996) and develop bootstrap methods for optimal choice of the threshold z (k+1) (Danielsson and de Vries 1997a). In the simulation study we generate samples of size n = 1000 fr... |

1 |
Tail index estimation for dependent data
- unknown authors
- 1996
(Show Context)
Citation Context ...een extensively investigated in the EVT literature; in particular, a number of recent papers show consistency of the Hill estimator for dependent data (Resnick and Starica 1995, Resnick and Staric=-=a 1996-=-) and develop bootstrap methods for optimal choice of the threshold z (k+1) (Danielsson and de Vries 1997a). In the simulation study we generate samples of size n = 1000 from Student's tdistribution w... |

1 | Weizs acker (1997): \Volatilities of dierent time resolutions { analyzing the dynamics of market components - e, Pictet, et al. |