Simulating Copulas

Stochastic Models, Sampling Algorithms, and Applications

The book provides the background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for graduate and advanced undergraduate students with a firm background in stochastics. Besides the theoretical foundation, ready-to-implement algorithms and many examples make the book a valuable tool for anyone who is applying the methodology.

Contents:

• Introduction
• Archimedean Copulas
• Marshall–Olkin Copulas
• Elliptical Copulas
• Pair Copula Constructions
• Sampling Univariate Random Variables
• The Monte Carlo Method
• Further Copula Families with Known Extendible Subclass
• Appendix: Supplemental Material

Readership: Advanced undergraduate and graduate students in probability calculus and stochastics, practitioners who implement models in the financial industry and scientists.
Key Features:

• Explicit focus on stochastic representations of copulas in contrast to an analytical perspective
• Easy-to-implement simulation schemes given as pseudo code
• Explicit focus on high-dimensional models
• Focus on applicability of models, e.g. to portfolio credit risk or insurance