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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 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 obtain 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 expansio
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Suggested Citation

  • Anders Eriksson & Lars Forsberg & Eric Ghysels, 2004. "Approximating the Probability Distribution of Functions of Random Variables: A New Approach," CIRANO Working Papers 2004s-21, CIRANO.
    • Handle: RePEc:cir:cirwor:2004s-21
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    File URL: https://cirano.qc.ca/files/publications/2004s-21.pdf
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    Cited by:

    1. Mencia, Javier F. & Sentana, Enrique, 2004. "Estimation and testing of dynamic models with generalised hyperbolic innovations," LSE Research Online Documents on Economics 24742, London School of Economics and Political Science, LSE Library.
    2. Bunčák, Tomáš, 2013. "Jump Processes in Exchange Rates Modeling," MPRA Paper 49882, University Library of Munich, Germany.
    3. Ciprian Necula & Gabriel Drimus & Walter Farkas, 2019. "A general closed form option pricing formula," Review of Derivatives Research, Springer, vol. 22(1), pages 1-40, April.
    4. 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.
    5. Insan Tunali & Berk Yavuzoglu, 2018. "Edgeworth Expansion Based Correction Of Selectivity Bias In Models Of Double Selection," Working Papers 1802, Nazarbayev University, Department of Economics, revised Nov 2018.
    6. Hainaut, Donatien, 2016. "Impact of volatility clustering on equity indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 367-381.
    7. Liyuan Jiang & Shuang Zhou & Keren Li & Fangfang Wang & Jie Yang, 2018. "A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps," Papers 1808.05289, arXiv.org, revised Feb 2019.
    8. Lillestøl, Jostein, 2007. "Some new bivariate IG and NIG-distributions for modelling covariate nancial returns," Discussion Papers 2007/1, Norwegian School of Economics, Department of Business and Management Science.

    More about this item

    Keywords

    normal inverse Gaussian; Edgeworth expansions; Gram-Charlier; distribution normale inverse gaussienne; expansions d'Edgeworth; Gram-Charlier;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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