IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v129y2019i7p2341-2375.html
   My bibliography  Save this article

A bound on the Wasserstein-2 distance between linear combinations of independent random variables

Author

Listed:
  • Arras, Benjamin
  • Azmoodeh, Ehsan
  • Poly, Guillaume
  • Swan, Yvik

Abstract

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ℓ2(N∗). We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.

Suggested Citation

  • Arras, Benjamin & Azmoodeh, Ehsan & Poly, Guillaume & Swan, Yvik, 2019. "A bound on the Wasserstein-2 distance between linear combinations of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2341-2375.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:7:p:2341-2375
    DOI: 10.1016/j.spa.2018.07.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918303259
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2018.07.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Kusuoka, Seiichiro & Tudor, Ciprian A., 2012. "Stein’s method for invariant measures of diffusions via Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1627-1651.
    3. Cacoullos, T. & Papathanasiou, V., 1989. "Characterizations of distributions by variance bounds," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 351-356, April.
    4. Eden, Richard & Víquez, Juan, 2015. "Nourdin–Peccati analysis on Wiener and Wiener–Poisson space for general distributions," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 182-216.
    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. Serres, Jordan, 2023. "Stability of higher order eigenvalues in dimension one," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 459-484.

    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. Robert E. Gaunt, 2020. "Wasserstein and Kolmogorov Error Bounds for Variance-Gamma Approximation via Stein’s Method I," Journal of Theoretical Probability, Springer, vol. 33(1), pages 465-505, March.
    2. Gaunt, Robert E., 2019. "Stein operators for variables form the third and fourth Wiener chaoses," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 118-126.
    3. Christophe Ley & Gesine Reinert & Yvik Swan, 2014. "Approximate Computation of Expectations: the Canonical Stein Operator," Working Papers ECARES ECARES 2014-36, ULB -- Universite Libre de Bruxelles.
    4. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
    5. Mikami, Toshio, 1998. "Equivalent conditions on the central limit theorem for a sequence of probability measures on R," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 237-242, March.
    6. Mei Xing, 2017. "Existence Conditions of Super-Replication Cost in a Multinomial Model," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(4), pages 185-195, August.
    7. 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.
    8. Yun, Jaeho, 2014. "Out-of-sample density forecasts with affine jump diffusion models," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 74-87.
    9. Simi, Wei W. & Wang, Xiaoli, 2013. "Time-changed Lévy jump processes with GARCH model on reverse convertibles," Review of Financial Economics, Elsevier, vol. 22(4), pages 206-212.
    10. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    11. Mahmoud Zarepour & Thierry Bedard & Andre Dabrowski, 2008. "Return and Value at Risk using the Dirichlet Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(3), pages 205-218.
    12. 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.
    13. Nicolas Huth & Frédéric Abergel, 2012. "The times change: multivariate subordination, empirical facts," Post-Print hal-00620841, HAL.
    14. Jose Cruz & Daniel Sevcovic, 2020. "On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models," Papers 2003.03851, arXiv.org.
    15. Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472, arXiv.org, revised Mar 2020.
    16. Samuel Asante Gyamerah & Philip Ngare & Dennis Ikpe, 2018. "Regime-Switching Temperature Dynamics Model for Weather Derivatives," International Journal of Stochastic Analysis, Hindawi, vol. 2018, pages 1-15, July.
    17. Ricardo Crisóstomo, 2021. "Estimating real‐world probabilities: A forward‐looking behavioral framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(11), pages 1797-1823, November.
    18. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    19. Lam, K. & Chang, E. & Lee, M. C., 2002. "An empirical test of the variance gamma option pricing model," Pacific-Basin Finance Journal, Elsevier, vol. 10(3), pages 267-285, June.
    20. Kun Gao & Roger Lee, 2014. "Asymptotics of implied volatility to arbitrary order," Finance and Stochastics, Springer, vol. 18(2), pages 349-392, April.

    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:eee:spapps:v:129:y:2019:i:7:p:2341-2375. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.