IDEAS home Printed from https://ideas.repec.org/p/yon/wpaper/2014rwp-73.html
   My bibliography  Save this paper

Option Pricing with Heavy Tailed Distribution : Application to Barrier Options

Author

Listed:
  • Joocheol Kim

    (Yonsei University)

  • Jeonggyu Heo

    (Yonsei University)

Abstract

Although the market prefers the Black-Scholes model, there are problems that the BS model doesn¡¯t reflect the skewness or kurtosis of the return distribution. Under the GEV model, Markose(2001) derives the closed-form solutions for vanilla options, and also removes the distortion of the market only with an additional parameter. In this paper, we use the technique in Rubinstein(1991) to get the closed-form solutions for GEV-based vanilla options, and to compare those solutions with the BS model applying to the Global credit crisis. As the BS model underestimate the probability of barrier hit while the credit crisis, we can confirm that the model undervalue in-type barrier options and overvalue out-type barrier options.

Suggested Citation

  • Joocheol Kim & Jeonggyu Heo, 2014. "Option Pricing with Heavy Tailed Distribution : Application to Barrier Options," Working papers 2014rwp-73, Yonsei University, Yonsei Economics Research Institute.
    • Handle: RePEc:yon:wpaper:2014rwp-73
    as

    Download full text from publisher

    File URL: http://121.254.254.220/repec/yon/wpaper/2014rwp-73.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    2. Markose, Sheri M & Alentorn, Amadeo, 2005. "The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing," Economics Discussion Papers 3726, University of Essex, Department of Economics.
    3. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    4. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Mandelbrot, Benoit B, 1972. "Correction of an Error in "The Variation of Certain Speculative Prices" (1963)," The Journal of Business, University of Chicago Press, vol. 45(4), pages 542-543, October.
    6. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
    7. 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.
    8. 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. Brisset, Nicolas, 2017. "On Performativity: Option Theory And The Resistance Of Financial Phenomena," Journal of the History of Economic Thought, Cambridge University Press, vol. 39(4), pages 549-569, December.
    2. Markose, Sheri M & Alentorn, Amadeo, 2005. "The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing," Economics Discussion Papers 3726, University of Essex, Department of Economics.
    3. Joocheol Kim & HyunOh Kim, 2014. "Option Pricing with Generalized Logistic Distributions(published in:Global Economic Review, (2014) Vol.43, NO.3)," Working papers 2014rwp-66, Yonsei University, Yonsei Economics Research Institute.
    4. Sheri Markose & Amadeo Alentorn, 2005. "Option Pricing and the Implied Tail Index with the Generalized Extreme Value (GEV) Distribution," Computing in Economics and Finance 2005 397, Society for Computational Economics.
    5. repec:uts:finphd:40 is not listed on IDEAS
    6. Zhu, Ke & Ling, Shiqing, 2015. "Model-based pricing for financial derivatives," Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
    7. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.
    8. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    9. 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).
    10. Hardeep Singh Mundi, 2023. "Risk neutral variances to compute expected returns using data from S&P BSE 100 firms—a replication study," Management Review Quarterly, Springer, vol. 73(1), pages 215-230, February.
    11. Detlefsen, Kai & Härdle, Wolfgang Karl & Moro, Rouslan A., 2007. "Empirical pricing kernels and investor preferences," SFB 649 Discussion Papers 2007-017, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    12. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, Decembrie.
    13. Peter A. Abken & Saikat Nandi, 1996. "Options and volatility," Economic Review, Federal Reserve Bank of Atlanta, vol. 81(Dec), pages 21-35.
    14. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    15. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    16. Lasko Basnarkov & Viktor Stojkoski & Zoran Utkovski & Ljupco Kocarev, 2019. "Option Pricing With Heavy-Tailed Distributions Of Logarithmic Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-35, November.
    17. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, December.
    18. Geman, Hélyette, 2005. "From measure changes to time changes in asset pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2701-2722, November.
    19. 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.
    20. 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.
    21. Thomas Busch, 2008. "Testing the martingale restriction for option implied densities," Review of Derivatives Research, Springer, vol. 11(1), pages 61-81, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:yon:wpaper:2014rwp-73. 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: YERI (email available below). General contact details of provider: https://edirc.repec.org/data/eryonkr.html .

    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.