IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v116y2006i8p1161-1184.html
   My bibliography  Save this article

On fractional tempered stable motion

Author

Listed:
  • Houdré, C.
  • Kawai, R.

Abstract

Fractional tempered stable motion (fTSm) is defined and studied. FTSm has the same covariance structure as fractional Brownian motion, while having tails heavier than Gaussian ones but lighter than (non-Gaussian) stable ones. Moreover, in short time it is close to fractional stable Lévy motion, while it is approximately fractional Brownian motion in long time. A series representation of fTSm is derived and used for simulation and to study some of its sample paths properties.

Suggested Citation

  • Houdré, C. & Kawai, R., 2006. "On fractional tempered stable motion," Stochastic Processes and their Applications, Elsevier, vol. 116(8), pages 1161-1184, August.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:8:p:1161-1184
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(06)00010-X
    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. Serge Cohen & Murad S. Taqqu, 2004. "Small and Large Scale Behavior of the Poissonized Telecom Process," Methodology and Computing in Applied Probability, Springer, vol. 6(4), pages 363-379, December.
    2. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, 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. Sung Ik Kim, 2022. "ARMA–GARCH model with fractional generalized hyperbolic innovations," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-25, December.
    2. Imai, Junichi & Kawai, Reiichiro, 2011. "On finite truncation of infinite shot noise series representation of tempered stable laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4411-4425.
    3. Kawai, Reiichiro, 2021. "A general approach to sample path generation of infinitely divisible processes via shot noise representation," Statistics & Probability Letters, Elsevier, vol. 174(C).
    4. Lim, C.Y. & Meerschaert, M.M. & Scheffler, H.-P., 2014. "Parameter estimation for operator scaling random fields," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 172-183.
    5. Vladas Pipiras & Murad S. Taqqu, 2008. "Small and Large Scale Asymptotics of some Lévy Stochastic Integrals," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 299-314, June.

    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. Mancini, Cecilia, 2011. "The speed of convergence of the Threshold estimator of integrated variance," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 845-855, April.
    2. 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.
    3. Young Shin Kim, 2018. "First Passage Time for Tempered Stable Process and Its Application to Perpetual American Option and Barrier Option Pricing," Papers 1801.09362, arXiv.org.
    4. Constantinos Kardaras, 2009. "No‐Free‐Lunch Equivalences For Exponential Lévy Models Under Convex Constraints On Investment," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 161-187, April.
    5. 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.
    6. 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.
    7. 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.
    8. Álvaro Cartea & Thilo Meyer-Brandis, 2010. "How Duration Between Trades of Underlying Securities Affects Option Prices," Review of Finance, European Finance Association, vol. 14(4), pages 749-785.
    9. José Azevedo‐Pereira & Gualter Couto & Cláudia Nunes, 2010. "Optimal timing of relocation," International Journal of Managerial Finance, Emerald Group Publishing Limited, vol. 6(2), pages 143-163, April.
    10. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    11. Svetlana Boyarchenko & Sergei Levendorskii, 2004. "Universal bad news principle and pricing of options on dividend-paying assets," Papers cond-mat/0404108, arXiv.org.
    12. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
    13. repec:eid:wpaper:06/10 is not listed on IDEAS
    14. Eric Jacquier & Cedric Okou, 2013. "Disentangling Continuous Volatility from Jumps in Long-Run Risk-Return Relationships," CIRANO Working Papers 2013s-14, CIRANO.
    15. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
    16. Sanjay K. Nawalkha & Xiaoyang Zhuo, 2020. "A Theory of Equivalent Expectation Measures for Contingent Claim Returns," Papers 2006.15312, arXiv.org, revised May 2022.
    17. Kazutoshi Yamazaki, 2017. "Inventory Control for Spectrally Positive Lévy Demand Processes," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 212-237, January.
    18. Rong Du & Duy-Minh Dang, 2023. "Fourier Neural Network Approximation of Transition Densities in Finance," Papers 2309.03966, arXiv.org, revised May 2024.
    19. A. Christian Silva & Ju-Yi Yen, 2010. "Stochastic resonance and the trade arrival rate of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 461-466.
    20. Lorenzo Torricelli, 2012. "Valuation of asset and volatility derivatives using decoupled time-changed L\'evy processes," Papers 1210.5479, arXiv.org, revised Jan 2015.
    21. Zbigniew Palmowski & Jos'e Luis P'erez & Kazutoshi Yamazaki, 2020. "Double continuation regions for American options under Poisson exercise opportunities," Papers 2004.03330, arXiv.org.

    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:116:y:2006:i:8:p:1161-1184. 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.