IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1408.3387.html
   My bibliography  Save this paper

Elliptical Tempered Stable Distribution and Fractional Calculus

Author

Listed:
  • Hassan A. Fallahgoul
  • Young S. Kim

Abstract

A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite divisible distribution, and particularly elliptical tempered stable distribution, with fractional calculus. Finally, some analytical approximations for the probability density function of tempered infinite divisible distribution, which elliptical tempered stable distributions are a subclass of them, are considered.

Suggested Citation

  • Hassan A. Fallahgoul & Young S. Kim, 2014. "Elliptical Tempered Stable Distribution and Fractional Calculus," Papers 1408.3387, arXiv.org, revised Aug 2014.
    • Handle: RePEc:arx:papers:1408.3387
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1408.3387
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Young Kim & Rosella Giacometti & Svetlozar Rachev & Frank Fabozzi & Domenico Mignacca, 2012. "Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model," Annals of Operations Research, Springer, vol. 201(1), pages 325-343, December.
    2. Hassan Fallahgoul & S. M. Hashemiparast & Young Shin Kim & Svetlozar T. Rachev & Frank J. Fabozzi, 2012. "Approximation of Stable and Geometric Stable Distribution," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 1(3), pages 1-8.
    3. Bianchi, Michele Leonardo & Rachev, Svetlozar T. & Kim, Young Shin & Fabozzi, Frank J., 2011. "Tempered infinitely divisible distributions and processes," Working Paper Series in Economics 26, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    4. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    Full references (including those not matched with items on IDEAS)

    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. Hassan A. Fallahgoul & Young S. Kim & Frank J. Fabozzi, 2016. "Elliptical tempered stable distribution," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1069-1087, July.
    2. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    3. Babaei, Sadra & Sepehri, Mohammad Mehdi & Babaei, Edris, 2015. "Multi-objective portfolio optimization considering the dependence structure of asset returns," European Journal of Operational Research, Elsevier, vol. 244(2), pages 525-539.
    4. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
    5. Young Shin Kim, 2022. "Portfolio optimization and marginal contribution to risk on multivariate normal tempered stable model," Annals of Operations Research, Springer, vol. 312(2), pages 853-881, May.
    6. Shao, Barret Pengyuan & Rachev, Svetlozar T. & Mu, Yu, 2015. "Applied mean-ETL optimization in using earnings forecasts," International Journal of Forecasting, Elsevier, vol. 31(2), pages 561-567.
    7. Hasan A. Fallahgoul & Young S. Kim & Frank J. Fabozzi & Jiho Park, 2019. "Quanto Option Pricing with Lévy Models," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1279-1308, March.
    8. Abhinav Anand & Tiantian Li & Tetsuo Kurosaki & Young Shin Kim, 2017. "The equity risk posed by the too-big-to-fail banks: a Foster–Hart estimation," Annals of Operations Research, Springer, vol. 253(1), pages 21-41, June.
    9. Young Shin Kim, 2020. "Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk," Papers 2007.13972, arXiv.org, revised Sep 2020.
    10. Young Shin Kim, 2023. "Portfolio Optimization with Relative Tail Risk," Papers 2303.12209, arXiv.org, revised Mar 2023.
    11. Paul Ormerod, 2010. "La crisis actual y la culpabilidad de la teoría macroeconómica," Revista de Economía Institucional, Universidad Externado de Colombia - Facultad de Economía, vol. 12(22), pages 111-128, January-J.
    12. Zhao, Zhibiao & Wu, Wei Biao, 2009. "Nonparametric inference of discretely sampled stable Lévy processes," Journal of Econometrics, Elsevier, vol. 153(1), pages 83-92, November.
    13. Barunik, Jozef & Vacha, Lukas, 2010. "Monte Carlo-based tail exponent estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4863-4874.
    14. Dominique Guégan & Wayne Tarrant, 2012. "On the necessity of five risk measures," Annals of Finance, Springer, vol. 8(4), pages 533-552, November.
    15. Alagidede, Paul & Panagiotidis, Theodore, 2009. "Modelling stock returns in Africa's emerging equity markets," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 1-11, March.
    16. Ben Klemens, 2013. "A Peer-based Model of Fat-tailed Outcomes," Papers 1304.0718, arXiv.org.
    17. Koutmos, Dimitrios, 2012. "An intertemporal capital asset pricing model with heterogeneous expectations," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(5), pages 1176-1187.
    18. Turvey, Calum G., 2001. "Random Walks And Fractal Structures In Agricultural Commodity Futures Prices," Working Papers 34151, University of Guelph, Department of Food, Agricultural and Resource Economics.
    19. Rodríguez, Mª Araceli, 2005. "Nueva Evidencia Empírica sobre las Turbulencias Cambiarias de la Peseta Española. 1989-1998/New Evidence about Turbulences on the Spanish Peseta. 1989-1998s," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 23, pages 207-230, Abril.
    20. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, 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:1408.3387. 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.