Simulating copulas : stochastic models, sampling algorithms and applications / Jan-Frederik Mai, Matthias Scherer.

Format:

Book

Author/Creator:

Jan-Frederik, Mai.

Contributor:

Scherer, Matthias.

Series:

Series in quantitative finance ; v. 4.

Series in quantitative finance, 1756-1604 ; v. 4

Language:

English

Subjects (All):

Copulas (Mathematical statistics).

Multivariate analysis.

Distribution (Probability theory).

Physical Description:

1 online resource (310 p.)

Edition:

1st ed.

Place of Publication:

London : Imperial College Press, 2012.

Language Note:

English

Summary:

This book provides the reader with a 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 advanced undergraduate or graduate students with a firm background in stochastics. Alongside the theoretical foundation, ready-to-implement algorithms and many examples make this book a valuable tool for anyone who is applying the methodology.

Contents:

1. Introduction. 1.1. Copulas. 1.2. General classifications of copulas

2. Archimedean copulas. 2.1. Motivation. 2.2. Extendible Archimedean copulas. 2.3. Exchangeable Archimedean copulas. 2.4. Hierarchical (H-extendible) Archimedean copulas. 2.5. Other topics related to Archimedean copulas

3. Marshall-Olkin copulas. 3.1. The general Marshall-Olkin copula. 3.2. The exchangeable case. 3.3. The extendible case

4. Elliptical copulas. 4.1. Spherical distributions. 4.2. Elliptical distributions. 4.3. Parametric families of elliptical distributions. 4.4. Elliptical copulas. 4.5. Parametric families of elliptical copulas. 4.6. Sampling algorithms

5. Pair copula constructions. 5.1. Introduction to pair copula constructions. 5.2. Copula construction by regular vine trees. 5.3. Simulation from regular vine distributions. 5.4. Dependence properties. 5.5. Application

6. Sampling univariate random variables. 6.1. General aspects of generating random variables. 6.2. Generating uniformly distributed random variables. 6.3. The inversion method. 6.4. Generating exponentially distributed random numbers. 6.5. Acceptance-rejection method. 6.6. Generating normally distributed random numbers. 6.7. Generating lognormal random numbers. 6.8. Generating gamma-distributed random numbers. 6.9. Generating Chi-square-distributed RNs. 6.10. Generating t-distributed random numbers. 6.11. Generating Pareto-distributed random numbers. 6.12. Generating inverse Gaussian-distributed random numbers. 6.13. Generating stable-distributed random numbers. 6.14. Generating discretely distributed random numbers

7. The Monte Carlo method. 7.1. First aspects of the Monte Carlo method. 7.2. Variance reduction methods.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

9786613784209

9781281603517

1281603511

9781848168756

1848168756

OCLC:

808340697