IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1203.5729.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1203.5729
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pablo Su'arez-Garc'ia & David G'omez-Ullate, 2012. "Scaling, stability and distribution of the high-frequency returns of the IBEX35 index," Papers 1208.0317, arXiv.org.
    2. Borak, Szymon & Misiorek, Adam & Weron, Rafał, 2010. "Models for heavy-tailed asset returns," SFB 649 Discussion Papers 2010-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Suárez-García, Pablo & Gómez-Ullate, David, 2013. "Scaling, stability and distribution of the high-frequency returns of the Ibex35 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1409-1417.
    4. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    5. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    6. Rafał Weron, 2009. "Heavy-tails and regime-switching in electricity prices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 457-473, July.
    7. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    8. Lynn Boen & Florence Guillaume, 2020. "Towards a $$\Delta $$Δ-Gamma Sato multivariate model," Review of Derivatives Research, Springer, vol. 23(1), pages 1-39, April.
    9. Fu, Qi & So, Jacky Yuk-Chow & Li, Xiaotong, 2024. "Stable paretian distribution, return generating processes and habit formation—The implication for equity premium puzzle," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    10. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    11. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
    12. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, December.
    13. Lingyan Cao & Zheng-Feng Guo, 2012. "A Comparison Of Delta Hedging Under Two Price Distribution Assumptions By Likelihood Ratio," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 6(1), pages 25-34.
    14. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.
    15. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    16. Luca Spadafora & Marco Dubrovich & Marcello Terraneo, 2014. "Value-at-Risk time scaling for long-term risk estimation," Papers 1408.2462, arXiv.org.
    17. Steven L. Heston & Alberto G. Rossi, 2017. "A Spanning Series Approach to Options," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 7(1), pages 2-42.
    18. Jabłońska-Sabuka, Matylda & Teuerle, Marek & Wyłomańska, Agnieszka, 2017. "Bivariate sub-Gaussian model for stock index returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 628-637.
    19. Lingyan Cao & Zheng-Feng Guo, 2012. "A Comparison Of Gradient Estimation Techniques For European Call Options," Accounting & Taxation, The Institute for Business and Finance Research, vol. 4(1), pages 75-81.
    20. Davide Lauria & Wyatt D. Phillips, 2021. "Insuring Hollywood: A Movie Returns Index and the American Stock Market," JRFM, MDPI, vol. 14(5), pages 1-33, April.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1203.5729. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.