Arbeitspapier
Tail Probabilities and Partial Moments for Quadratic Forms in Multivariate Generalized Hyperbolic Random Vectors
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.
- Sprache
-
Englisch
- Erschienen in
-
Series: Tinbergen Institute Discussion Paper ; No. 13-001/III
- Klassifikation
-
Wirtschaft
Multiple or Simultaneous Equation Models: Instrumental Variables (IV) Estimation
Computational Techniques; Simulation Modeling
Portfolio Choice; Investment Decisions
Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
- Thema
-
Finite Samples
Characteristic Function
Transform Inversion
2SLS
CVaR
Expected Shortfall
- Ereignis
-
Geistige Schöpfung
- (wer)
-
Broda, Simon A.
- Ereignis
-
Veröffentlichung
- (wer)
-
Tinbergen Institute
- (wo)
-
Amsterdam and Rotterdam
- (wann)
-
2013
- Handle
- Letzte Aktualisierung
-
10.03.2025, 11:43 MEZ
Datenpartner
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Objekttyp
- Arbeitspapier
Beteiligte
- Broda, Simon A.
- Tinbergen Institute
Entstanden
- 2013
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