CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation
AbstractThe estimation of multivariate GARCH models remains a challenging task, even in modern computer environments. This manuscript shows how Independent Component Analysis can be used to estimate the Generalized Orthogonal GARCH model in a fraction of the time otherwise required. The proposed method is a two-step procedure, separating the estimation of the correlation structure from that of the univariate dynamics, thus facilitating the incorporation of non-Gaussian innovations distributions in a straightforward manner. The generalized hyperbolic distribution provides an excellent parametric description of financial returns data and is used for the univariate fits, but its convolutions, necessary for portfolio risk calculations, are intractable. This restriction is overcome by a saddlepoint approximation to the required distribution function, which is computationally cheap and extremely accurate most notably in the tail, which is crucial for risk calculations. A simulation study and an application to stock returns demonstrate the validity of the procedure.
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Bibliographic InfoPaper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 08-08.
Length: 24 pages
Date of creation: Nov 2006
Date of revision: Feb 2008
Empirical Finance; Saddlepoint Approximation; Value at Risk;
Other versions of this item:
- Simon A. Broda & Marc S. Paolella, 2009. "CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(4), pages 412-436, Fall.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
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- Fajardo, José & Farias, Aquiles, 2010. "Derivative pricing using multivariate affine generalized hyperbolic distributions," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1607-1617, July.
- Alp, Tansel & Demetrescu, Matei, 2010. "Joint forecasts of Dow Jones stocks under general multivariate loss function," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2360-2371, November.
- Simon A. BRODA & Markus HAAS & Jochen KRAUSE & Marc S. PAOLELLA & Sven C. STEUDE, .
"Stable Mixture GARCH Models,"
Swiss Finance Institute Research Paper Series
11-39, Swiss Finance Institute.
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