IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v59y1995i2p217-233.html
   My bibliography  Save this article

Sample quantiles of heavy tailed stochastic processes

Author

Listed:
  • Embrechts, Paul
  • Samorodnitsky, Gennady

Abstract

Distributions of sample quantiles of measurable stochastic processes are important for the purpose of rational pricing of "look-back" options. In this paper we compute the exact tail behavior of the sample quantile distribution for a large class of infinitely divisible stochastic processes with heavy tails.

Suggested Citation

  • Embrechts, Paul & Samorodnitsky, Gennady, 1995. "Sample quantiles of heavy tailed stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 217-233, October.
    • Handle: RePEc:eee:spapps:v:59:y:1995:i:2:p:217-233
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(95)00044-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Miura, Ryozo, 1992. "A Note on Look-Back Options Based on Order Statistics," Hitotsubashi Journal of commerce and management, Hitotsubashi University, vol. 27(1), pages 15-28, November.
    2. Braverman, Michael & Samorodnitsky, Gennady, 1995. "Functionals of infinitely divisible stochastic processes with exponential tails," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 207-231, April.
    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. Marcel Brautigam & Michel Dacorogna & Marie Kratz, 2019. "Pro-Cyclicality of Traditional Risk Measurements: Quantifying and Highlighting Factors at its Source," Papers 1903.03969, arXiv.org, revised Dec 2019.
    2. Marcel Bräutigam & Michel Dacorogna & Marie Kratz, 2018. "Predicting risk with risk measures : an empirical study," Working Papers hal-01791026, HAL.
    3. Rosnan, Chotard & Michel, Dacorogna & Marie, Kratz, 2016. "Risk Measure Estimates in Quiet and Turbulent Times:An Empirical Study," ESSEC Working Papers WP1618, ESSEC Research Center, ESSEC Business School.
    4. Christian Genest & Johanna G. Nešlehová, 2020. "A Conversation With Paul Embrechts," International Statistical Review, International Statistical Institute, vol. 88(3), pages 521-547, December.
    5. Marcel Bräutigam & Michel Dacorogna & Marie Kratz, 2023. "Pro‐cyclicality beyond business cycle," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 308-341, April.
    6. Braverman, Michael & Samorodnitsky, Gennady, 1998. "Distribution tails of sample quantiles and subexponentiality," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 45-60, August.

    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. Dell'Era Mario, M.D., 2008. "Pricing of Double Barrier Options by Spectral Theory," MPRA Paper 17502, University Library of Munich, Germany.
    2. Marcel Brautigam & Michel Dacorogna & Marie Kratz, 2019. "Pro-Cyclicality of Traditional Risk Measurements: Quantifying and Highlighting Factors at its Source," Papers 1903.03969, arXiv.org, revised Dec 2019.
    3. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, August.
    4. Dell'Era Mario, M.D., 2008. "Pricing of the European Options by Spectral Theory," MPRA Paper 17429, University Library of Munich, Germany.
    5. Braverman, Michael, 1997. "Suprema and sojourn times of Lévy processes with exponential tails," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 265-283, June.
    6. Braverman, Michael, 2010. "On suprema of Lévy processes with light tails," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 541-573, April.
    7. Griffin, Philip S. & Maller, Ross A. & Roberts, Dale, 2013. "Finite time ruin probabilities for tempered stable insurance risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 478-489.
    8. Neofytos Rodosthenous & Hongzhong Zhang, 2017. "Beating the Omega Clock: An Optimal Stopping Problem with Random Time-horizon under Spectrally Negative L\'evy Models," Papers 1706.03724, arXiv.org.
    9. Pospisil, Libor & Vecer, Jan & Xu, Mingxin, 2007. "Tradable measure of risk," MPRA Paper 5059, University Library of Munich, Germany.
    10. Carolyn E. Phelan & Daniele Marazzina & Guido Germano, 2021. "Pricing methods for $\alpha$-quantile and perpetual early exercise options based on Spitzer identities," Papers 2106.06030, arXiv.org.
    11. Djilali Ait Aoudia & Jean-Franc{c}ois Renaud, 2016. "Pricing occupation-time options in a mixed-exponential jump-diffusion model," Papers 1603.09329, arXiv.org.
    12. Braverman, Michael, 1999. "Remarks on suprema of Lévy processes with light tailes," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 41-48, May.
    13. Ning Cai & Nan Chen & Xiangwei Wan, 2010. "Occupation Times of Jump-Diffusion Processes with Double Exponential Jumps and the Pricing of Options," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 412-437, May.
    14. Sparago, Pietro, 2025. "Note on the weak convergence of hyperplane α-quantile functionals and their continuity in the Skorokhod J1 topology," LSE Research Online Documents on Economics 126207, London School of Economics and Political Science, LSE Library.
    15. Braverman, Michael, 2005. "On a class of Lévy processes," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 179-189, December.
    16. Albin, J. M. P., 1999. "Extremes of totally skewed [alpha]-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 185-212, February.
    17. Braverman, Michael & Samorodnitsky, Gennady, 1998. "Distribution tails of sample quantiles and subexponentiality," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 45-60, August.
    18. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    19. Ramprasath, L. & Singh, Kesar, 2007. "Statistical options: Crash resistant financial contracts based on robust estimation," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 196-203, January.
    20. Braverman, Michael, 2000. "Suprema of compound Poisson processes with light tails," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 145-156, November.

    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:59:y:1995:i:2:p:217-233. 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.