RMBI 4210 Quantitative Methods for Risk Management
Tutorial 10 Copula functions
Copula functions (CreditMetrics uses the normal copula in its default correlation formula)
A copula function links univariate marginals to their full multivariate distribution and introduce the dependence structure to generate the joint probabilities.
Idea: 1) Randomly generate a set of univariate marginal distribution functions; 2) define/construct a copula function such that we can map those univariate functions to a multivariate distribution function that has our target dependence features (Sklar’s Theorem already proves the existence and uniqueness)
1-D case gives an exact form example of copula function U.
*Understand the derivations of survival copula and default copula (in HW we use Poisson process, i.e. exponential model for dependent defaults)
• Bivariate case
• Multivariate extension (joint 2-D marginal copula)
Brief Final Summary
• Understand all different types of financial risks, calculation and application of Delta and Gamma hedging
• Understand the meaning and calculation of VaR, ES and EC
• Mixture model (ideas / assumptions and the derivation of all the terms, e.g. expectation,
variance, etc)
• CreditRisk+
• CreditMetrics — Copula functions (understand the idea behind and familiar with the
derivations of copula, referring to the HW example)
Spring, 2021
Wang Jingjing Page 1