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On Multivariate Generalised Pareto Distributions and High Risk Scenarios
Company: ETH Zurich
Year Of Publication: 2006
Month Of Publication: March
Pages: 111
Download Count: 477
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Comment Num: 0
Language: EN
Who Can Read: Free
Date: 12-28-2006
Publisher: Administrator
AbstractConsider a large investor’s market position, which may comprise a several hundredassets. Such a market position can be thought of as a d-dimensional vector, whosecomponents are the prices or log-prices of the individual assets. Risk managers areinterested in the value of the position at some fixed future date, say one or ten tradingdays ahead—a customary time horizon in market risk management in banking. Whilethe present position is known, z0 2 Rd, the future position is unknown and may bedescribed by a d-dimensional random vector Z whose distribution is concentratedaround the value z0.A major concern in financial risk management is that the market drifts off inan undesirable direction. Put differently, situations where Z will lie in some riskyregion far away from z0 raise worries. In order to apply standard risk managementtools such as the calculation of Value-at-Risk (VaR) or expected shortfall (ES) it isdesirable to have a multivariate model for the random vector Z.Amongst others, parts of a theory developed by Balkema and Embrechts [6] arediscussed in this thesis. The approach was developed to suit a setup as describedabove. In univariate extreme value theory (EVT), the concept of exceedances overthresholds has been soundly studied and is well understood. According to the wellknownPickands-Balkema-de Haan Theorem, the distribution of appropriately scaledexceedances over high thresholds is well approximated by a generalised Pareto distribution(GPD). The extension of this concept to the multivariate case is howevernot straightforward, mainly due to the lack of a natural ordering relation. Althoughthere has been much less research, some useful approaches emerged. Tajvidi’s [36] aswell as Balkema and Embrechts’ [6] contributions are discussed more extensiv
Degen, Matthias Sign in to follow this author
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