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Approximating the Probability Distribution of Functions of Random Variables: A New Approach

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  • Anders Eriksson
  • Lars Forsberg
  • Eric Ghysels

    ()

Abstract

We introduce a new approximation method for the distribution of functions of random variables that are real-valued. The approximation involves moment matching and exploits properties of the class of normal inverse Gaussian distributions. In the paper we examine the how well the different approximation methods can capture the tail behavior of a function of random variables relative each other. This is done by simulate a number functions of random variables and then investigate the tail behavior for each method. Further we also focus on the regions of unimodality and positive definiteness of the different approximation methods. We show that the new method provides equal or better approximations than Gram-Charlier and Edgeworth expansions. Nous introduisons une nouvelle méthode pour approximer la distribution de variables aléatoires. L'approximation est basée sur la classe de distribution normale inverse gaussienne. On démontre que la nouvelle approximation est meilleure que les expansions Gram-Charlier et Edgeworth.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2004s-21.

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Date of creation: 01 May 2004
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Handle: RePEc:cir:cirwor:2004s-21

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Related research

Keywords: normal inverse Gaussian; Edgeworth expansions; Gram-Charlier; distribution normale inverse gaussienne; expansions d'Edgeworth; Gram-Charlier;

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Cited by:
  1. Mencía, Javier & Sentana, Enrique, 2005. "Estimation and Testing of Dynamic Models with Generalized Hyperbolic Innovations," CEPR Discussion Papers 5177, C.E.P.R. Discussion Papers.
  2. Lillestøl, Jostein, 2007. "Some new bivariate IG and NIG-distributions for modelling covariate nancial returns," Discussion Papers 2007/1, Department of Finance and Management Science, Norwegian School of Economics.
  3. Puzanova, Natalia & Siddiqui, Sikandar & Trede, Mark, 2009. "Approximate value-at-risk calculation for heterogeneous loan portfolios: Possible enhancements of the Basel II methodology," Journal of Financial Stability, Elsevier, vol. 5(4), pages 374-392, December.

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