IDEAS home Printed from https://ideas.repec.org/a/ksa/szemle/353.html
   My bibliography  Save this article

Idősor-modellezés és opcióárazás csonkolt Lévy-eloszlással
[Time-series modelling and option pricing with a truncated Lévy distribution]

Author

Listed:
  • Janecskó, Balázs

Abstract

Statisztikusok és pénzügyi adatelemzők számára jól ismert empirikus tény, hogy a pénzügyi ingadozások természete eltér a klasszikus, normális (Gauss) eloszláson alapuló leírástól. A pénzügyi matematika, illetve az elméleti pénzügyi irodalom mégis paradigmaként kezeli tovább a normális megközelítést egyszerűsége és például az opcióárazási vagy portfólióoptimalizálási feladatban mutatott elegáns analitikus tulajdonságai miatt. E cikk célja az árfolyam-ingadozások realisztikusabb statisztikai képének bemutatása, valamint egy erre a modellre alapított opcióárazási megközelítés felvázolása. Nem célunk matematikai és technikai részleteket közölni ezeket a hivatkozásaink alapján részletesen át lehet tanulmányozni , hanem inkább az új modell szemléletes megvilágítására, illetve gyakorlati alkalmazhatóságának igazolására koncentrálunk. Árfolyam-ingadozási adatainkat a napi BUX záróárfolyam-idősorból származtattuk, az új statisztikai modell illesztését a napi BUX-hozamok példáján illusztráljuk, és az opcióárazási feladat megoldását a BUX-indexre vonatkozó európai call opciókra mutatjuk be. A bemutatott új modell a csonkolt Lévy-modell vonzó tulajdonsága, hogy három paraméteren keresztül képes az ingadozások széles tartományában pontosan leírni a fluktuációk valószínűségét, továbbá a ,,skála, farokvastagsági és csonkolási paramétereknek" szemléletes jelentés is tulajdonítható. Az új modell általában a piaci kockázatkezelésnek is hasznos eszköze lehet, különösen amiatt, hogy a gyakorlatban megfigyelt extrém események valószínűségére is reális számokat ad.

Suggested Citation

  • Janecskó, Balázs, 2000. "Idősor-modellezés és opcióárazás csonkolt Lévy-eloszlással [Time-series modelling and option pricing with a truncated Lévy distribution]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(11), pages 899-917.
    • Handle: RePEc:ksa:szemle:353
    as

    Download full text from publisher

    File URL: http://www.kszemle.hu/tartalom/letoltes.php?id=353
    Download Restriction: Registration and subscription. 3-month embargo period to non-subscribers.
    ---><---

    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. Jánosi, Imre M & Janecskó, Balázs & Kondor, Imre, 1999. "Statistical analysis of 5 s index data of the Budapest Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 111-124.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Kullmann, L & Töyli, J & Kertesz, J & Kanto, A & Kaski, K, 1999. "Characteristic times in stock market indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 98-110.
    4. Palágyi, Zoltán & Mantegna, Rosario N., 1999. "Empirical investigation of stock price dynamics in an emerging market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 132-139.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. 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..
    7. Andrew Matacz, 2000. "Financial Modeling And Option Theory With The Truncated Levy Process," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 143-160.
    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. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    2. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    3. Bauer, Rob M M J & Nieuwland, Frederick G M C & Verschoor, Willem F C, 1994. "German Stock Market Dynamics," Empirical Economics, Springer, vol. 19(3), pages 397-418.
    4. Menn, Christian & Rachev, Svetlozar T., 2005. "A GARCH option pricing model with [alpha]-stable innovations," European Journal of Operational Research, Elsevier, vol. 163(1), pages 201-209, May.
    5. He, Xue-Zhong & Li, Youwei, 2015. "Testing of a market fraction model and power-law behaviour in the DAX 30," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 1-17.
    6. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    7. Kaehler, Jürgen & Marnet, Volker, 1993. "Markov-switching models for exchange-rate dynamics and the pricing of foreign-currency options," ZEW Discussion Papers 93-03, ZEW - Leibniz Centre for European Economic Research.
    8. Issler, João Victor, 1999. "Estimating and forecasting the volatility of Brazilian finance series using arch models (Preliminary Version)," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 347, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    9. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    10. David Daewhan Cho, 2004. "Uncertainty in Second Moments: Implications for Portfolio Allocation," Econometric Society 2004 Far Eastern Meetings 433, Econometric Society.
    11. Constantinides, A. & Savel’ev, S.E., 2013. "Modelling price dynamics: A hybrid truncated Lévy Flight–GARCH approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2072-2078.
    12. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    13. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2023. "Microfounding GARCH models and beyond: a Kyle-inspired model with adaptive agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(3), pages 599-625, July.
    14. Mondher Bellalah & Marc Lavielle, 2002. "A Decomposition of Empirical Distributions with Applications to the Valuation of Derivative Assets," Multinational Finance Journal, Multinational Finance Journal, vol. 6(2), pages 99-130, June.
    15. Tim Bollerslev & Ray Y. Chou & Narayanan Jayaraman & Kenneth F. Kroner - L, 1991. "es modéles ARCH en finance : un point sur la théorie et les résultats empiriques," Annals of Economics and Statistics, GENES, issue 24, pages 1-59.
    16. Aldrich, Eric M. & Heckenbach, Indra & Laughlin, Gregory, 2016. "A compound duration model for high-frequency asset returns," Journal of Empirical Finance, Elsevier, vol. 39(PA), pages 105-128.
    17. Goddard, John & Onali, Enrico, 2012. "Self-affinity in financial asset returns," International Review of Financial Analysis, Elsevier, vol. 24(C), pages 1-11.
    18. Katerina Simons, 1997. "Model error," New England Economic Review, Federal Reserve Bank of Boston, issue Nov, pages 17-28.
    19. Liu, Chang & Chang, Chuo, 2021. "Combination of transition probability distribution and stable Lorentz distribution in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    20. repec:adr:anecst:y:1991:i:24:p:01 is not listed on IDEAS
    21. Giulia Di Nunno & Kęstutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From Constant to Rough: A Survey of Continuous Volatility Modeling," Mathematics, MDPI, vol. 11(19), pages 1-35, October.

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:ksa:szemle:353. 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: Odon Sok (email available below). General contact details of provider: http://www.kszemle.hu .

    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.