Copula_R 1 - Introduction Popular copula families...

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Introduction Popular copula families Simulation Parameter estimation Model selection Model evaluation Examples Extensions Summary USING COPULAS An introduction for practitioners DANIEL BERG DnBNOR Asset Management Norwegian ASTIN society. Oslo - November 2008 Daniel Berg Using copulas
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Introduction Popular copula families Simulation Parameter estimation Model selection Model evaluation Examples Extensions Summary DnBNOR Kapitalforvaltning ASA . Stor bredde og dybde i forvalterkompetanse, 100 analytikere og porteføljeforvaltere . Bredt produktspekter - og gode dokumenterte forvaltningsresultater. . Gode systemer for risikostyring og - kontroll. Store volumer - kostnadseffektiv forvaltning . Kontinuerlig prosess med produktutvikling og -forbedring. . Ca 300 aarsverk. Ca NOK 500 milliarder til forvaltning. Personkunder Institusjonelle investorer ± Ca 500 kunder i Norge og Sverige ± Viktigste kundesegmenter: pensjonskasser, kommuner, bedrifter, organisasjoner/stiftelser ± Høy raadgivningskompetanse Strategiske mandat ± Vital ± Skandia Liv ± Skandia Fonder Daniel Berg Using copulas
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Introduction Popular copula families Simulation Parameter estimation Model selection Model evaluation Examples Extensions Summary Outline . Introduction . Popular copula families . Simulation . Parameter estimation . Model selection . Model evaluation . Examples (uranium, river flow/temp, precipitation, . ..) . Extensions . Summary Daniel Berg Using copulas
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Introduction Popular copula families Simulation Parameter estimation Model selection Model evaluation Examples Extensions Summary Introduction Motivation Figure: Simulations from two models, both with standard normal margins and correlation 0 . 7. Daniel Berg Using copulas
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Introduction Popular copula families Simulation Parameter estimation Model selection Model evaluation Examples Extensions Summary Introduction Motivation . For several applications empirical evidence has proved multinormal distribution inadequate for several reasons: . Empirical marginal distributions are e.g. skewed and heavy-tailed . Possibilities of extreme co-movements, in contrast to the multinormal distribution Daniel Berg Using copulas
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Introduction Popular copula families Simulation Parameter estimation Model selection Model evaluation Examples Extensions Summary Introduction Brief historical background . 1940: Hoeffding studies properties of multivariate distributions . 1959: The word copula appears for the first time (Sklar, 1959) . 1999: Introduced to financial applications (Embrechts et al., 1999) . 2008: Widely used in insurance, finance, energy, hydrology, survival analysis, etc. Daniel Berg Using copulas
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Introduction Popular copula families Simulation Parameter estimation Model selection Model evaluation Examples Extensions Summary Introduction Definition & theorem Definition (Copula) A d-dimensional copula is a multivariate distribution function C with standard uniform marginal distributions.
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Copula_R 1 - Introduction Popular copula families...

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