Sampling from Archimedean copulas

References

• Abramowitz , M and Stegun , I . 1965 . Handbook of Mathematical Functions , Edited by: Abramowitz , M and Stegun , I . New York : Dover .
   Google Scholar
• Ahrens , J and Dieter , U . 1974 . Computer methods for sampling from gamma, beta, Poisson and binomial distributions . Computing , 12 : 223 – 46 .
   Web of Science ®Google Scholar
• Barbe , P , Genest , C , Ghoudi , K and Rémillard , B . 1996 . On Kendall's process . J. Multivariate Anal. , 58 : 197 – 229 .
   Web of Science ®Google Scholar
• Bouyé , E , Durrleman , V , Nikeghbali , A , Riboulet , G and Roncalli , T . 2000 . “ Copulas for finance: a reading guide and some applications, Groupe de Recherche Opérationnelle, Crédit Lyonnais ” . In Preprint
   Google Scholar
• Corliss , G , Faure , C , Griewank , A and Hascoet , L . 2002 . Automatic Differentiation of Algorithms , Edited by: Corliss , G , Faure , C , Griewank , A and Hascoet , L . Berlin : Springer .
   Google Scholar
• Devroye , L . 1986 . Non-Uniform Random Variate Generation , New York : Springer .
   Google Scholar
• Embrechts , P , Lindskog , F and McNeil , A . 2001 . “ Modelling dependence with copulas and applications to risk management ” . In Preprint ETH
   Google Scholar
• Embrechts , P , McNeil , A and Straumann , D . 2001b . “ Correlation and dependence in risk management: properties and pitfalls ” . In Risk Management: Value at Risk and Beyond , Edited by: M , Dempster and Moffat , H . Cambridge : Cambridge University Press .
   Google Scholar
• Frey , R and McNeil , A J . 2003 . “ Dependent defaults in models of portfolio credit risk, in preparation ” .
   Google Scholar
• Genest , C and Rivest , L . 1993 . Statistical inference procedures for bivariate Archimedean copulas . J. Am. Stat. Assoc. , 88 : 1034 – 43 .
   Web of Science ®Google Scholar
• Hirayama , H . 2001 . Numerical integration on the complex plane . IPSJ SIGNotes Numerical Analysis Abstract , : 022 – 003 .
   Google Scholar
• Höffding , W . 1940 . Masstabinvariante Korrelationstheorie . Schriften des Mathematischen Seminars und des Instituts für Angewandte Mathematik der Universität Berlin , 5 : 181 – 233 .
   Google Scholar
• Joe , H . 1997 . “ Multivariate models and dependence concepts ” . In Monographs on Statistics and Applied Probability, No. 37 , London : Chapman and Hall .
   Google Scholar
• Kendall , M and Stuart , A . 1979 . Handbook of Statistics , London : Griffin and Company .
   Google Scholar
• Kimberling , C . 1974 . A probabilistic interpretation of complete monotonicity . Aequationes Mathematicæ , 10 : 152 – 64 .
   Google Scholar
• Laurent , J-P and Gregory , J . 2002 . “ Basket default swaps, cdo's and factor copulas (Available at laurent.jeanpaul.free.fr) ” .
   Google Scholar
• Li , D X . 2000 . On default correlation: a copula function approach . J. Fixed Income , 9 : 43 – 54 .
   Google Scholar
• Marshall , A W and Olkin , I . 1988 . Families of multivariate distributions . J. Am. Stat. Assoc. , 83 : 834 – 41 .
   Web of Science ®Google Scholar
• Nelsen , R . 1999 . “ An introduction to copulas ” . In Lecture Notes in Statistics , New York : Springer . No. 139
   Google Scholar
• Oberhettinger , F . 1990 . Tables of Fourier Transforms and Fourier Transforms of Distributions , Berlin : Springer .
   Google Scholar
• Press , W , Teukolsky , S A , Vetterling , W T and Flannery , B P . 1992 . Numerical Recipes in C , 2nd edn , Cambridge : Cambridge University Press .
   Google Scholar
• Rall , L B . 1981 . Automatic Differentiation: Techniques and Applications , Vol. 120 , Berlin : Springer . Lecture Notes in Computer Science
   Google Scholar
• Razak , S . 2003 . “ Default intensities from copulas, in preparation ” .
   Google Scholar
• Schoenberg , I J . 1938 . Metric spaces and completely monotone functions . Ann. Math. , 39 : 811 – 41 .
   Google Scholar
• Schönbucher , P J . 2003 . Credit Derivatives Pricing Models , Chichester : Wiley .
   Google Scholar
• Schönbucher , P J and Schubert , D . 2001 . “ Copula-dependent default risk in intensity models ” . In Preprint Department of Statistics, Bonn University
   Google Scholar
• Sklar , A . 1959 . Fonctions de répartition à n dimensions et leurs marges . Publications de l'Institut de Statistique de L'Université de Paris , 8 : 229 – 31 .
   Google Scholar