On quadratic forms in multivariate generalized hyperbolic random vectors

Expected shortfall: A natural coherent alternative to value at risk

Simon Broda and Juan Arismendi Zambrano ()

Biometrika, 2021, vol. 108, issue 2, 413-424

Abstract: SummaryThis article presents exact and approximate expressions for tail probabilities and partial moments of quadratic forms in multivariate generalized hyperbolic random vectors. The derivations involve a generalization of the classic inversion formula for distribution functions (Gil-Pelaez, 1951). Two numerical applications are considered: the distribution of the two-stage least squares estimator and the expected shortfall of a quadratic portfolio.

Keywords: Characteristic function; Conditional Value-at-Risk; Expected shortfall; Saddlepoint approximation; Transform inversion; Two-stage least squares (search for similar items in EconPapers)
Date: 2021
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