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Paper provided by Bank of Canada in its series Working Papers with number 00-20.

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Length: 31 pages Abstract: Extreme value theory (EVT) has been applied in fields such as hydrology and insurance. It is a tool used to consider probabilities associated with extreme and thus rare events. EVT is useful in modelling the impact of crashes or situations of extreme stress on investor portfolios. Contrary to value-at-risk approaches, EVT is used to model the behaviour of maxima or minima in a series (the tail of the distribution). However, implementation of EVT faces many challenges, including the scarcity of extreme data, determining whether the series is “fat-tailed,” choosing the threshold or beginning of the tail, and choosing the methods of estimating the parameters. This paper focuses on the univariate case; the approach is not easily extended to the multivariate case, because there is no concept of order in a multidimensional space and it is difficult to define the extremes in the multivariate case. Following a review of the theoretical literature, univariate EVT techniques are applied to a series of daily exchange rates of Canadian/U.S. dollars over a 5-year period (1995–2000).
Date of creation: 2000
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Handle: RePEc:bca:bocawp:00-20

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Related research

Keywords: impact of crashes; implementation;

Find related papers by JEL classification:
C0 - Mathematical and Quantitative Methods - - General
C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
C5 - Mathematical and Quantitative Methods - - Econometric Modeling
G1 - Financial Economics - - General Financial Markets

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1. Pamela Cardozo, . "Valor en Riesgo de los Activos Financieros Colombianos Aplicando la Teoría de Valor Extremo," Borradores de Economia 304, Banco de la Republica de Colombia. [Downloadable!]
2. Younes Bensalah, 2002. "Asset Allocation Using Extreme Value Theory," Working Papers 02-2, Bank of Canada. [Downloadable!]
3. Suarez, R, 2001. "Improving Modeling of Extreme Events using Generalized Extreme Value Distribution or Generalized Pareto Distribution with Mixing Unconditional Disturbances," MPRA Paper 17443, University Library of Munich, Germany. [Downloadable!]
4. Suarez, Ronny, 2009. "Improving Modeling of Extreme Events using Generalized Extreme Value Distribution or Generalized Pareto Distribution with Mixing Unconditional Disturbances," MPRA Paper 17482, University Library of Munich, Germany. [Downloadable!]

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