Business Context
An investment bank needs to estimate the Value at Risk (VaR) of a diversified portfolio containing Equities, Bonds, and Commodities. The goal is to model the dependency structure between these assets, specifically capturing the tail dependence (extreme market crashes) which Normal copulas often underestimate. The Risk Management team requires a t-Copula model fitted using Maximum Likelihood Estimation to accurately assess joint downside risks.
Data Preparation
Simulation of 5000 daily returns for three asset classes (Equity, Bond, Commodity) with built-in correlation and heavy tails.
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| 1 | |
| 2 | DATA mycas.portfolio_returns; |
| 3 | call streaminit(12345); |
| 4 | array r[3] equity bond commodity; |
| 5 | DO i = 1 to 5000; |
| 6 | DO j = 1 to 3; |
| 7 | r[j] = rand('t', 5); |
| 8 | END; |
| 9 | OUTPUT; |
| 10 | END; |
| 11 | |
| 12 | RUN; |
| 13 |
Étapes de réalisation
1
Fit a t-Copula to the asset returns using MLE, specifying 5 degrees of freedom as an initial guess, and save the model for future scoring.
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| 2 | PROC CAS; |
| 3 | copula.copulaFit / TABLE={name='portfolio_returns'}, var={'equity', 'bond', 'commodity'}, copulatype='T', method='MLE', df=5, store={name='risk_model_t', replace=true}; |
| 4 | |
| 5 | RUN; |
| 6 | |
| 7 | QUIT; |
| 8 |
2
Generate diagnostic plots to visually verify the tail dependence capture.
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| 1 | |
| 2 | PROC CAS; |
| 3 | copula.copulaFit / TABLE={name='portfolio_returns'}, var={'equity', 'bond', 'commodity'}, copulatype='T', plot={tail=true, scatter=true}; |
| 4 | |
| 5 | RUN; |
| 6 | |
| 7 | QUIT; |
| 8 |
Expected Result
The action should successfully converge and output the parameter estimates for the t-Copula, specifically the degrees of freedom and the correlation matrix. The 'risk_model_t' item store is created in the CAS library. Diagnostic plots confirm the presence of tail dependence.