IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v14y2007i1p1-17.html
   My bibliography  Save this article

Option Pricing with a Pentanomial Lattice Model that Incorporates Skewness and Kurtosis

Author

Listed:
  • James Primbs
  • Muruhan Rathinam
  • Yuji Yamada

Abstract

This paper analyzes a pentanomial lattice model for option pricing that incorporates skewness and kurtosis of the underlying asset. The lattice is constructed using a moment matching procedure, and explicit positivity conditions for branch probabilities are provided in terms of skewness and kurtosis. We also explore the limiting distribution of this lattice, which is compound Poisson, and give a Fourier transform based formula that can be used to more efficiently price European call and put options. An example illustrates some of the features of this model in capturing volatility smiles and smirks.

Suggested Citation

  • James Primbs & Muruhan Rathinam & Yuji Yamada, 2007. "Option Pricing with a Pentanomial Lattice Model that Incorporates Skewness and Kurtosis," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 1-17.
    • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:1:p:1-17
    DOI: 10.1080/13504860600659172
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600659172
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/13504860600659172?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Charles J. Corrado & Tie Su, 1996. "S&P 500 index option tests of Jarrow and Rudd's approximate option valuation formula," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 16(6), pages 611-629, September.
    2. C. J. Corrado & Tie Su, 1997. "Implied volatility skews and stock return skewness and kurtosis implied by stock option prices," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 73-85, March.
    3. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(1), pages 1-12, March.
    4. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    5. Amin, Kaushik I, 1993. "Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    6. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    7. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    8. Rendleman, Richard J, Jr & Bartter, Brit J, 1979. "Two-State Option Pricing," Journal of Finance, American Finance Association, vol. 34(5), pages 1093-1110, December.
    9. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    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. Bowei Chen & Jun Wang, 2014. "A lattice framework for pricing display advertisement options with the stochastic volatility underlying model," Papers 1409.0697, arXiv.org, revised Dec 2015.
    2. Arturo Leccadito & Pietro Toscano & Radu S. Tunaru, 2012. "Hermite Binomial Trees: A Novel Technique For Derivatives Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-36.
    3. Muroi, Yoshifumi & Suda, Shintaro, 2022. "Binomial tree method for option pricing: Discrete cosine transform approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 312-331.
    4. Ivivi J. Mwaniki, 2017. "On skewed, leptokurtic returns and pentanomial lattice option valuation via minimal entropy martingale measure," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1358894-135, January.

    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. 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.
    2. Felipe Isaza Cuervo & Sergio Botero Boterob, 2014. "Aplicación de las opciones reales en la toma de decisiones en los mercados de electricidad," Estudios Gerenciales, Universidad Icesi, November.
    3. Capelle-Blancard, G. & Jurczenko, E., 1999. "Une application de la formule de Jarrow et Rudd aux options sur indice CAC 40," Papiers d'Economie Mathématique et Applications 2000.05, Université Panthéon-Sorbonne (Paris 1).
    4. Yuji Yamada & James Primbs, 2004. "Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 335-365, September.
    5. Constantinides, George M. & Jackwerth, Jens Carsten & Perrakis, Stylianos, 2005. "Option pricing: Real and risk-neutral distributions," CoFE Discussion Papers 05/06, University of Konstanz, Center of Finance and Econometrics (CoFE).
    6. Bogdan Negrea & Bertrand Maillet & Emmanuel Jurczenko, 2002. "Revisited Multi-moment Approximate Option," FMG Discussion Papers dp430, Financial Markets Group.
    7. Seiji Harikae & James S. Dyer & Tianyang Wang, 2021. "Valuing Real Options in the Volatile Real World," Production and Operations Management, Production and Operations Management Society, vol. 30(1), pages 171-189, January.
    8. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    9. Shi-jie Jiang & Mujun Lei & Cheng-Huang Chung, 2018. "An Improvement of Gain-Loss Price Bounds on Options Based on Binomial Tree and Market-Implied Risk-Neutral Distribution," Sustainability, MDPI, vol. 10(6), pages 1-17, June.
    10. Ghaffari, Reza & Venkatesh, Bala, 2015. "Network constrained model for options based reserve procurement by wind generators using binomial tree," Renewable Energy, Elsevier, vol. 80(C), pages 348-358.
    11. Hadjiyannakis, Steve & Culumovic, Louis & Welch, Robert L., 1998. "The relative mispricing of the constant variance American put model," International Review of Economics & Finance, Elsevier, vol. 7(2), pages 149-171.
    12. Marin Bozic, 2010. "Pricing Options on Commodity Futures: The Role of Weather and Storage," Working Papers 1003, The Institute of Economics, Zagreb.
    13. Guidolin, Massimo & Timmermann, Allan, 2003. "Option prices under Bayesian learning: implied volatility dynamics and predictive densities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 717-769, March.
    14. Jondeau, Eric & Rockinger, Michael, 2000. "Reading the smile: the message conveyed by methods which infer risk neutral densities," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 885-915, December.
    15. Benhamou, Eric & Duguet, Alexandre, 2003. "Small dimension PDE for discrete Asian options," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11), pages 2095-2114.
    16. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
    17. Siddiqi, Hammad, 2014. "The Financial Market Consequences of Growing Awareness: The Case of Implied Volatiltiy Skew," Risk and Sustainable Management Group Working Papers 162568, University of Queensland, School of Economics.
    18. Davide Lauria & W. Brent Lindquist & Svetlozar T. Rachev & Yuan Hu, 2023. "Unifying Market Microstructure and Dynamic Asset Pricing," Papers 2304.02356, arXiv.org, revised Feb 2024.
    19. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "American options with stochastic dividends and volatility: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 53-92.
    20. Jarno Talponen & Minna Turunen, 2022. "Option pricing: a yet simpler approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 57-81, June.

    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:taf:apmtfi:v:14:y:2007:i:1:p:1-17. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    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.