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Quantile Mechanics 3: Series Representations and Approximation of some Quantile Functions appearing in Finance

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  • Asad Munir
  • William Shaw

Abstract

It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a satisfactory method of approximating these functions is not available. The main focus of this paper will be to develop Taylor and asymptotic series expansions for the quantile functions belonging to the following probability distributions; Variance Gamma, Generalized Inverse Gaussian, Hyperbolic and alpha-Stable. As a secondary matter, based on these analytic expressions we briefly investigate the problem of approximating the quantile function.

Suggested Citation

  • Asad Munir & William Shaw, 2012. "Quantile Mechanics 3: Series Representations and Approximation of some Quantile Functions appearing in Finance," Papers 1203.5729, arXiv.org, revised Apr 2012.
    • Handle: RePEc:arx:papers:1203.5729
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    References listed on IDEAS

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    1. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    2. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
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    Cited by:

    1. M. Assadsolimani & D. Chetalova, 2017. "Estimating VaR in credit risk: Aggregate vs single loss distribution," Papers 1702.04388, arXiv.org.

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