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Introduction to Copulas B. Wade Brorsen Oklahoma State University
Problem Multivariate pdf or cdf when marginal distributions are not normally distributed and not independent.
Where Used? Risk and Simulation Value at Risk (VaR) Valuing Derivatives Insurance
Extreme Value Theory Tail Dependence –Housing bubble –Collateralized Debt Obligations (CDO) –Hurricane –Crop disease –Bank failures –Long Term Capital Management
Agricultural Economics Taylor (1990) Richardson/Simetar Heuristic
Gaussian Copula Multivariate-t Copula Most Copulas are Bivariate Two Main Multivariate Copulas
A copula C(u, v) is C:[0, 1] 2 →[0, 1] Other properties
Sklar’s Theorem Any cdf H(X 1, X 2 ) with margins F(X 1 ) and G(X 2 ) can be represented as H(X 1, X 2 ) = C[F(X 1 ), G(X 2 )] Where C[ ] is a unique copula function.
Gaussian Copula H(Ψ -1 (u), Ψ -1 (v)) H is bivariate normal cdf Ψ -1 is inverse of a univariate normal cdf
Estimation Inference for margins (IFM) Maximum likelihood Simulation
SAS Program u = cdf (‘normal’, x1, 2, 2); v = cdf (‘normal’, x2, 5, 5); z1 = probit (u); z2 = probit (v); PROC CORR; /* IFM Method */ Var z1, z2;
SAS Program u = cdf (‘gamma’, x1, r1, lambda1); v = cdf (‘gamma’, x2, r2, lambda 2); z1 = probit (u); z2 = probit (v); PROC CORR; Var z1, z2;
Summary Copulas can give us a multivariate cdf for nonnormal distributions Agricultural economists should use copulas
Copula Representation of Joint Risk Driver Distribution
N 3 = 7 Input (s) Output X(s) s1s1 s2s2 s3s3 sPsP m = Number of Input Points (=3) n i = Number of Outputs at Input s i X (i) = Set of Outputs X j (i) at.
NORMAL OR GAUSSIAN DISTRIBUTION Chapter 5. General Normal Distribution Two parameter distribution with a pdf given by:
Probabilistic Analysis of Hydrological Loads to Optimize the Design of Flood Control Systems B. Klein, M. Pahlow, Y. Hundecha, C. Gattke and A. Schumann.
THE DEVIL IS IN THE TAILS: ACTUARIAL MATHEMATICS AND THE SUBPRIME MORTGAGE CRISIS.
A. The Basic Principle We consider the multivariate extension of multiple linear regression – modeling the relationship between m responses Y 1,…,Y m and.
INTRODUCTION TO COPULAS
Copula Regression By Rahul A. Parsa Drake University &
Pattern Recognition and Machine Learning
Financial Risk Management of Insurance Enterprises Collateralized Debt Obligations (CDOs)
Donald F. Behan Society of Actuaries Meeting Phoenix, AZ1 Using Copulas to Model Extreme Events by Donald F. Behan and Sam Cox Georgia State University.
Modelling with parameter- mixture copulas October 2006 Xiangyuan Tommy Chen Econometrics & Business Statistics The University of Sydney
Econ. & Mat. Enrique Navarrete Palisade Risk Conference
XIV International Conference on Economic and Social Development, 2-5 April 2013, Moscow A new copula approach for high-dimensional real world portfolios.
Factor Model Based Risk Measurement and Management R/Finance 2011: Applied Finance with R April 30, 2011 Eric Zivot Robert Richards Chaired Professor of.
© Prof. Jayanth R. Varma, Indian Institute of Management, Ahmedabad Risk Management at Indian Exchanges Going Beyond SPAN and VaR.
Copula Functions and Bivariate Distributions: Applications to Political Interdependence Alejandro Quiroz Flores, Wilf Department of Politics, NYU Motivation.
Pair-copula constructions of multiple dependence Workshop on ''Copulae: Theory and Practice'' Weierstrass Institute for Applied Analysis and.
Master thesis presentation Joanna Gatz TU Delft 29 of July 2007 Properties and Applications of the T copula.
Models for construction of multivariate dependence Workshop on Copulae and Multivariate Probability distributions in Finance – Theory, Applications,
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