By Umberto Cherubini, Fabio Gobbi (auth.), Piotr Jaworski, Fabrizio Durante, Wolfgang Karl Härdle (eds.)
Copulas are mathematical gadgets that totally catch the dependence constitution between random variables and accordingly provide nice flexibility in construction multivariate stochastic types. due to the fact their advent within the early Nineteen Fifties, copulas have won enormous attractiveness in different fields of utilized arithmetic, specially finance and assurance. this present day, copulas symbolize a familiar software for marketplace and credits versions, aggregation of hazards, and portfolio choice. traditionally, the Gaussian copula version has been some of the most universal types in credits probability. notwithstanding, the hot monetary challenge has underlined its obstacles and disadvantages. actually, regardless of their simplicity, Gaussian copula versions significantly underestimate the danger of the incidence of joint severe occasions. contemporary theoretical investigations have positioned new instruments for detecting and estimating dependence and threat (like tail dependence, time-varying versions, and so forth) within the highlight. All such investigations have to be extra constructed and promoted, a target this publication pursues. The ebook contains surveys that offer an updated account of crucial features of copula types in quantitative finance, in addition to the prolonged models of talks chosen from papers provided on the workshop in Cracow.
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Extra info for Copulae in Mathematical and Quantitative Finance: Proceedings of the Workshop Held in Cracow, 10-11 July 2012
Cambridge University Press, Cambridge (2009) 51. : Bayesian inference for multivariate copulas using pair-copula constructions. J. Financ. Econom. 8(4), 511–546 (2010) 52. : Bayesian model selection for D-vine pair-copula constructions. Can. J. Stat. 39, 239–258 (2011) 53. : Counting vines. , Joe, H. ) Dependence Modeling: Vine Copula Handbook. World Scientific, Singapore (2011) 54. : Vine copulas with asymmetric tail dependence and applications to financial return data. Comput. Stat. Data Anal.
Math. Artif. Intell. 32, 245–268 (2001) 9. : Vines: a new graphical model for dependent random variables. Ann. Stat. 30(4), 1031–1068 (2002) 2 Selection of Vine Copulas 35 10. : Models for construction of higher-dimensional dependence: a comparison study. Eur. J. Financ. 15, 639–659 (2009) 11. : Truncated and simplified regular vines and their applications. Master’s thesis, Technische Universit¨at M¨unchen (2010) 12. : Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50.
In view of the linked nature of the vine tree structure the sequential approach is a natural approach. However as in the case of covariate selection in linear models, this might not yield the best fit to the data. In addition the approaches so far primarily considered in-sample fit and model comparisons. More empirical work is needed to validate the models in an out-of-sample performance study. However this is now feasible and tractable and is the subject of current investigations. It has been recently recognized by  that even the flexible class of simplified regular vines might be insufficient for some data sets.