2019
DOI: 10.1002/jae.2741
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Multivariate dynamic intensity peaks‐over‐threshold models

Abstract: Summary We propose a multivariate dynamic intensity peaks‐over‐threshold model to capture extremes in multivariate return processes. The random occurrence of extremes is modeled by a multivariate dynamic intensity model, while temporal clustering of their size is captured by an autoregressive multiplicative error model. Applying the model to daily returns of three major stock indexes yields strong empirical support for a temporal clustering of both the occurrence and the size of extremes. Backtesting value‐at‐… Show more

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Cited by 8 publications
(12 citation statements)
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References 53 publications
(76 reference statements)
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“…However, there is a plethora of VaR models in the literature—therefore, there are no two or three candidate specifications against which the SEP-POT model should be benchmarked and compared. Only among the point process-based POT models there have been variants put forward, including the ACD-POT model (which is based on the dynamic specifications of time, i.e., duration, that elapses between consecutive extreme losses [ 6 , 7 , 8 ]) or the ACI-POT model (with its multivariate extensions) that provides an explicit autoregressive specification for the intensity function [ 13 ]. All these dynamic versions of POT models exploit both strands of the literature: the point process theory and the EVT, accounting for the clustering of extreme losses and the heavy-tailness of the loss distribution.…”
Section: Resultsmentioning
confidence: 99%
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“…However, there is a plethora of VaR models in the literature—therefore, there are no two or three candidate specifications against which the SEP-POT model should be benchmarked and compared. Only among the point process-based POT models there have been variants put forward, including the ACD-POT model (which is based on the dynamic specifications of time, i.e., duration, that elapses between consecutive extreme losses [ 6 , 7 , 8 ]) or the ACI-POT model (with its multivariate extensions) that provides an explicit autoregressive specification for the intensity function [ 13 ]. All these dynamic versions of POT models exploit both strands of the literature: the point process theory and the EVT, accounting for the clustering of extreme losses and the heavy-tailness of the loss distribution.…”
Section: Resultsmentioning
confidence: 99%
“…The more recent dynamic versions of the classical POT model found in several studies (i.e., [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ]), are directly motivated by the behavior of the non-homogeneous Poisson point process, where the intensity rate of threshold exceedances, , can vary over time due to the temporal bursts in volatility. According to such a point process approach to POT models, the first factor on the left-hand side of Equation ( 3 ) (i.e., the conditional probability of a threshold exceedance over day ) can be derived based on the (time varying) conditional intensity function as follows: because the probability of no events in (i.e., ) can be given as [ 21 ].…”
Section: Methodsmentioning
confidence: 99%
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“…A related approach is the so-called self-exciting POT (SEPOT) suggested by McNeil et al [21], where one Hawkes process influences the intensity of both event times and marks. The various conditional POT models were reviewed in [3,[22][23][24], and extended to a multivariate framework by Grothe et al [25] and Hautsch and Herrera [26]. Conditional POT models are based on similar ideas as the epidemic-type aftershock sequence (ETAS) model proposed by Ogata [27], which is designed to describe the occurrence of earthquakes based on previous ones and was further explored for example by Helmstetter and Sornette [28].…”
Section: Introductionmentioning
confidence: 99%