[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v28y2019icp185-190.html
   My bibliography  Save this article

Enhancing binomial and trinomial equity option pricing models

Author

Listed:
  • Kim, Young Shin
  • Stoyanov, Stoyan
  • Rachev, Svetlozar
  • Fabozzi, Frank J.
Abstract
We extend the classical Cox–Ross–Rubinstein binomial model in two ways. We first develop a binomial model with time-dependent parameters that equate all moments of the pricing tree increments with the corresponding moments of the increments of the limiting Itô price process. Second, we introduce a new trinomial model in the natural (historical) world, again fitting all moments of the pricing tree increments to the corresponding geometric Brownian motion. We introduce the risk-neutral trinomial tree and derive a hedging strategy based on an additional perpetual derivative used as a second asset for hedging at any node of the trinomial pricing tree.

Suggested Citation

  • Kim, Young Shin & Stoyanov, Stoyan & Rachev, Svetlozar & Fabozzi, Frank J., 2019. "Enhancing binomial and trinomial equity option pricing models," Finance Research Letters, Elsevier, vol. 28(C), pages 185-190.
    • Handle: RePEc:eee:finlet:v:28:y:2019:i:c:p:185-190
    DOI: 10.1016/j.frl.2018.04.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1544612317307572
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.frl.2018.04.022?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(2), pages 153-164, June.
    2. Steve Heston & Guofu Zhou, 2000. "On the Rate of Convergence of Discrete‐Time Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 53-75, January.
    3. Dietmar Leisen & Matthias Reimer, 1996. "Binomial models for option valuation - examining and improving convergence," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 319-346.
    4. Figlewski, Stephen & Gao, Bin, 1999. "The adaptive mesh model: a new approach to efficient option pricing," Journal of Financial Economics, Elsevier, vol. 53(3), pages 313-351, September.
    5. Kim, Y.S. & Stoyanov, S. & Rachev, S. & Fabozzi, F., 2016. "Multi-purpose binomial model: Fitting all moments to the underlying geometric Brownian motion," Economics Letters, Elsevier, vol. 145(C), pages 225-229.
    6. 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.
    7. Davydov, Youri & Rotar, Vladimir, 2008. "On a non-classical invariance principle," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2031-2038, October.
    8. Madan, Dilip B & Milne, Frank & Shefrin, Hersh, 1989. "The Multinomial Option Pricing Model and Its Brownian and Poisson Limits," The Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 251-265.
    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. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," JRFM, MDPI, vol. 13(12), pages 1-33, December.
    2. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," Papers 2011.08343, arXiv.org.
    3. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev, 2022. "ESG-valued discrete option pricing in complete markets," Papers 2209.06276, arXiv.org.
    4. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2021. "Market Complete Option Valuation using a Jarrow-Rudd Pricing Tree with Skewness and Kurtosis," Papers 2106.09128, arXiv.org.
    5. Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    6. 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.
    7. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.

    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. Andrea Gamba & Lenos Trigeorgis, 2007. "An Improved Binomial Lattice Method for Multi-Dimensional Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 453-475.
    2. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," JRFM, MDPI, vol. 13(12), pages 1-33, December.
    3. Kyoung-Sook Moon & Hongjoong Kim, 2013. "A multi-dimensional local average lattice method for multi-asset models," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 873-884, May.
    4. San-Lin Chung & Pai-Ta Shih, 2007. "Generalized Cox-Ross-Rubinstein Binomial Models," Management Science, INFORMS, vol. 53(3), pages 508-520, March.
    5. Mark Broadie & Jérôme Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    6. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," Papers 2011.08343, arXiv.org.
    7. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    8. Dong An & Noah Linden & Jin-Peng Liu & Ashley Montanaro & Changpeng Shao & Jiasu Wang, 2020. "Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance," Papers 2012.06283, arXiv.org, revised Jun 2021.
    9. 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.
    10. Qianru Shang & Brian Byrne, 2021. "American option pricing: Optimal Lattice models and multidimensional efficiency tests," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(4), pages 514-535, April.
    11. Katarzyna Toporek, 2012. "Simple is better. Empirical comparison of American option valuation methods," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 29.
    12. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    13. H'el`ene Halconruy, 2021. "The insider problem in the trinomial model: a discrete-time jump process approach," Papers 2106.15208, arXiv.org, revised Sep 2023.
    14. Mattia Fabbri & Pier Giuseppe Giribone, 2020. "Design, implementation and validation of advanced lattice techniques for pricing EAKO — European American Knock-Out option," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 1-26, February.
    15. Shvimer, Yossi & Herbon, Avi, 2020. "Comparative empirical study of binomial call-option pricing methods using S&P 500 index data," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    16. Ghafarian, Bahareh & Hanafizadeh, Payam & Qahi, Amir Hossein Mortazavi, 2018. "Applying Greek letters to robust option price modeling by binomial-tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 632-639.
    17. Svetlozar Rachev & Stoyan Stoyanov & Frank J. Fabozzi, 2017. "Behavioral Finance Option Pricing Formulas Consistent with Rational Dynamic Asset Pricing," Papers 1710.03205, arXiv.org.
    18. Jean-Christophe Breton & Youssef El-Khatib & Jun Fan & Nicolas Privault, 2021. "A q-binomial extension of the CRR asset pricing model," Papers 2104.10163, arXiv.org, revised Feb 2023.
    19. Leisen, Dietmar P. J., 1999. "The random-time binomial model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1355-1386, September.
    20. Josheski Dushko & Apostolov Mico, 2020. "A Review of the Binomial and Trinomial Models for Option Pricing and their Convergence to the Black-Scholes Model Determined Option Prices," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 24(2), pages 53-85, June.

    More about this item

    Keywords

    Cox-Ross-Rubinstein binomial model; geometric Brownian motion; Poisson process; Itô price process; trinomial model;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:eee:finlet:v:28:y:2019:i:c:p:185-190. 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/locate/frl .

    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.