Financial Applications based on Gram-Charlier Expansions

Paola Biffi, Maria Zoia, Federica Nicolussi, 32945, DI ECONOMIA FACOLTA', finanziarie ed attuariali (DiMSEFA) MILANO - Dipartimento di Matematica per le Scienze economiche, 32979, FINANZIARIE E ASSICURATIVE FACOLTA' DI SCIENZE BANCARIE, MILANO - Dipartimento di Politica economica

Risultato della ricerca: Working paper

Abstract

The reliability of risk measures of financial portfolios crucially rests on the availability of sound representations of the involved random variables. The trade-off between adherence to reality and specification parsimony can find a fitting balance in a technique that "adjust" the moments of a density function by making use of its associated orthogonal polynomials. This approach essentially rests on the Gram-Charlier expansion of a Gaussian law which, allowing for leptokurtosis to an appreciable extent, makes the resulting random variable a tail-sensitive density function. In this paper we determine the density of sums of leptokurtic normal variables duly adjusted for excess kurtosis via their Gram-Charlier expansions based on Hermite polynomials. The aforesaid density can be properly used to compute some risk measures such as the Value at Risk and the expected short fall. An application to a portfolio of financial returns provides evidence of the effectiveness of the proposed approach.
Lingua originaleEnglish
EditoreVita e Pensiero
Numero di pagine34
ISBN (stampa)978-88-343-3183-5
Stato di pubblicazionePubblicato - 2016

Keywords

  • Expected shortfall
  • Gram-Charlier expansion
  • Value at risk

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