## Extreme Value Theory: Potential And Limitations As An Integrated Risk Management Tool (2000)

Venue: | Derivatives Use, Trading & Regulation |

Citations: | 33 - 0 self |

### BibTeX

@ARTICLE{Embrechts00extremevalue,

author = {Paul Embrechts},

title = {Extreme Value Theory: Potential And Limitations As An Integrated Risk Management Tool},

journal = {Derivatives Use, Trading & Regulation},

year = {2000},

volume = {6}

}

### Years of Citing Articles

### OpenURL

### Abstract

. Extreme Value Theory (EVT) is currently very much in the focus of interest in quantitative risk management. Originally conceived as the mathematical (probabilistic/statistical) theory for analysing rare events, it recently entered the risk management stage. In this paper I discuss some of the issues (mainly, but not exclusively) related to Value{at{Risk methodology. I try to come up with a virtues versus limitations assessment, both from an academic as well as from an end{user point of view. 1. Introduction Without any doubt, Value{at{Risk (VaR) thinking has revolutionised Integrated Risk Management (IRM), both at the quantitative (obvious) and at the qualitative (not so obvious) level. Originally conceived as a one{number summary of (short term) Market Risk, it is now being used in many dierent risk management systems like Credit Risk (Credit{VaR) and Operational Risk. Even the insurance world which could claim, through its actuarial skills, to be the master of risk, has im...

### Citations

567 |
Modelling Extremal Events for Insurance and Finance
- Embrechts, Klüppelberg, et al.
- 1997
(Show Context)
Citation Context ...erse function of FX (this may not be uniquely dened for non{strictly increasing FX , but in those cases, a slight modication yields an unambiguous denition; see Embrechts, Kluppelberg and Mikosch [6], p. 130). In Figure 1 we give a graphical presentation of (1). In practice, FX is referred to as the Prot{and{Loss (P&L) distribution function. Its calculation (better said: estimation) for market r... |

195 | Correlation and Dependence in Risk Management: Properties and Pitfalls
- Embrechts, McNeil, et al.
- 2002
(Show Context)
Citation Context ...is much related to the non{subadditivity of VaR for non{elliptical portfolios. See for instance the work on coherent risk measures by Artzner et al. [1] and the related discussion in Embrechts et al. =-=[7-=-]. | How can one optimally estimate VaR, including the calculation of condence intervals for VaR? | How to properly scale VaR, especially over (much) longer holding periods (a month to a year say)? | ... |

104 | Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach
- McNeil, Frey
- 2000
(Show Context)
Citation Context ...VaR, especially over (much) longer holding periods (a month to a year say)? | How to model VaR dynamically in a stochastic volatility or regime{switching environment; see for instance McNeil and Frey =-=[1-=-4] for a discussion on the former? | Give improved risk measures beyond VaR: a standard example being tail conditional VaR: E ( X j X VaR (X)) : (3) The latter measure yields a non{trivial improveme... |

103 |
Thinking coherently
- Artzner, Delbaen, et al.
- 1997
(Show Context)
Citation Context ...Can VaR be used to allocate capital? This question is much related to the non{subadditivity of VaR for non{elliptical portfolios. See for instance the work on coherent risk measures by Artzner et al. =-=[1-=-] and the related discussion in Embrechts et al. [7]. | How can one optimally estimate VaR, including the calculation of condence intervals for VaR? | How to properly scale VaR, especially over (much)... |

47 | Extreme Value Theory as a Risk Management Tool
- Embrechts, Resnick, et al.
- 1999
(Show Context)
Citation Context ... provide that manager with stochastic methodology needed for the construction of various components of such a global tool". I will not attempt to present EVT in \a short summary" form; see [=-=6], [13], [9]-=- and the references therein. The key point is that EVT gives the theory for describing extremes (maxima, minima, longest runs, longest time, ...) of random phenomena. In its easiest form, it yields th... |

44 |
Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management
- Diebold, Schuermann, et al.
- 2000
(Show Context)
Citation Context ...ult (the curse of dimensionality); see [5] for a start. And there are more: they are all true, but should be viewed in the light of the virtues alluded to above (the Smith, Tawn statements). See also =-=[3]-=- for an interesting discussion. My summary would be: if IRM is interested in the analysis of rare events, then EVT will play a small, though important role. So far I have restricted my discussion to I... |

26 | Extreme value theory for risk managers
- McNeil
- 1999
(Show Context)
Citation Context ...e will provide that manager with stochastic methodology needed for the construction of various components of such a global tool". I will not attempt to present EVT in \a short summary" form;=-= see [6], [13]-=-, [9] and the references therein. The key point is that EVT gives the theory for describing extremes (maxima, minima, longest runs, longest time, ...) of random phenomena. In its easiest form, it yiel... |

25 | Correlation: Pitfalls and alternatives - Embrechts, McNeil, et al. - 1999 |

21 |
Value at Risk. The new benchmark for controlling derivatives risk
- Jorion
- 1997
(Show Context)
Citation Context ...stress (or hysteria) factor. Formula (2) is currently in use within the Swiss Federal Banking Committee (EBK); see Jovic [12] for more details and further references. A standard text on VaR is Jorion =-=[11]-=-. In (2), 3 one very clearly sees the direct in uence of VaR on regulatory capital. A similar discussion could have been given for the notion of Credit{VaR where extreme quantile estimates occur as Ex... |

11 |
Stochastic simulation with a view towards stochastic processes
- ASMUSSEN
- 1999
(Show Context)
Citation Context ...e because rare (or extreme) event simulation is an art on its own. By denition of \rare" we may need many runs to actually produce some of these events. The interested reader should consult Asmus=-=sen [2]-=- and the references therein on the rare event simulation issue. 4. Conclusion Rather than reiterating (some of) the points made above, or delving deeper in some of the references, I would like to quot... |

6 | Modeling Multivariate Extremes
- Embrechts, Haan, et al.
- 2003
(Show Context)
Citation Context ...ight limit results for (5) have been worked out, estimation of extremal events (as for instance presented under Section 2) can be obtained; see again the above references for details. You may look at =-=[5]-=- for a discussion of multivariate extreme value theory. In its more advanced form, EVT describes the behaviour of extremal events for stochastic processes, evolving dynamically in time and space. The ... |

4 |
Why Non-linearities Can Ruin the Heavy-tailed Modeller’s Day
- RESNICK
- 1998
(Show Context)
Citation Context ... has to set the \optimal" threshold above which the data are to be used for tail estimation. There is no canonical \optimal" choice! | Non{linearities can ruin the heavy{tailed modeler's day=-= (Resnick [15]-=-). | Handling extremes for high dimensional portfolios is dicult (the curse of dimensionality); see [5] for a start. And there are more: they are all true, but should be viewed in the light of the vir... |

3 |
Risikoorientierte Eigenkapitalallokation und Performancemessung bei Banken
- JOVIC
- 1999
(Show Context)
Citation Context ...ure which is VaR based. The multiplier m t ( 3) stands for the hotly disputed stress (or hysteria) factor. Formula (2) is currently in use within the Swiss Federal Banking Committee (EBK); see Jovic [=-=12]-=- for more details and further references. A standard text on VaR is Jorion [11]. In (2), 3 one very clearly sees the direct in uence of VaR on regulatory capital. A similar discussion could have been ... |

1 |
presented during the one day workshop on The latest techniques and practical applications of Extreme Value Theory for enhanced Risk
- Gavin
(Show Context)
Citation Context ...ssue. 4. Conclusion Rather than reiterating (some of) the points made above, or delving deeper in some of the references, I would like to quote from someone from the banking industry who used EVT. In =-=[-=-10] John Gavin writes: | Conclusions: what EVT has to oer global risk management. Complements VaR model and Risk Factor Loss limits: exploits results from existing VaR model. Is Consistent between r... |