Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/87253
Authors: 
Broda, Simon A.
Year of Publication: 
2013
Series/Report no.: 
Tinbergen Institute Discussion Paper 13-001/III
Abstract: 
Countless test statistics can be written as quadratic forms in certain random vectors, or ratios thereof. Consequently, their distribution has received considerable attention in the literature. Except for a few special cases, no closed-form expression for the cdf exists, and one resorts to numerical methods. Traditionally the problem is analyzed under the assumption of joint Gaussianity; the algorithm that is usually employed is that of Imhof (1961). The present manuscript generalizes this result to the case of multivariate generalized hyperbolic (MGHyp) random vectors. The MGHyp is a very exible distribution which nests, amongothers, the multivariate t, Laplace, and variance gamma distributions. An expression for the first partial moment is also obtained, which plays a vital role in financial risk management. The proof involves a generalization of the classic inversion formula due to GilPelaez (1951).Two applications are considered: first, the nite-sample distribution of the 2SLS estimatorof a structural parameter. Second, the Value at Risk and Expected Shortfall of a quadraticportfolio with heavy-tailed risk factors.
Subjects: 
Finite Samples
Characteristic Function
Transform Inversion
2SLS
CVaR
Expected Shortfall
JEL: 
C16
C36
C63
G11
G32
Document Type: 
Working Paper

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