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THE EXPECTED SHORTFALL OF QUADRATIC PORTFOLIOS WITH HEAVY‐TAILED RISK FACTORS
Author(s) -
Broda Simon A.
Publication year - 2012
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2011.00482.x
Subject(s) - quadratic equation , expected shortfall , mathematics , value at risk , quadratic form (statistics) , multivariate statistics , expression (computer science) , econometrics , statistics , economics , risk management , finance , computer science , geometry , programming language
Computable expressions are derived for the Expected Shortfall of portfolios whose value is a quadratic function of a number of risk factors, as arise from a Delta–Gamma–Theta approximation. The risk factors are assumed to follow an elliptical multivariate t distribution, reflecting the heavy‐tailed nature of asset returns. Both an exact expression and a uniform asymptotic expansion are presented. The former involves only a single rapidly convergent integral. The latter is essentially explicit, and numerical experiments suggest that its error is negligible compared to that incurred by the Delta–Gamma–Theta approximation.