CS计算机代考程序代写 RMBI 4210 Quantitative Methods for Risk Management

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