IDEAS home Printed from https://ideas.repec.org/a/taf/apeclt/v16y2009i16p1657-1663.html
   My bibliography  Save this article

Accurate approximation formulas for stock options with discrete dividends

Author

Listed:
  • Tian-Shyr Dai
  • Yuh-Dauh Lyuu

Abstract

Pricing options on a stock that pays discrete dividends has not been satisfactorily settled in the literature. Frishling (2002) shows that there are three different models to model stock price with discrete dividends, but only one of these models is close to reality and generates consistent option prices. We follow Frishling (2002) by calling this model Model 3. Unfortunately, there is no analytical option pricing formula for Model 3, and many popular numerical methods such as trees are inefficient when used to implement Model 3. A new stock price model is proposed in this article. To guarantee that the option prices generated by this new model are close to those generated by Model 3, the distributions of the new model at exdividend dates and maturity approximate the distributions of Model 3 at those dates. To achieve this, a discrete dividend in Model 3 is replaced by a continuous dividend yield that can be represented as a function of discrete dividends and stock returns in the new model. Thus, the new model follows a lognormal diffusion process and the analytical option pricing formulas can be easily derived. Numerical experiments show that our analytical pricing formulas provide accurate pricing results.

Suggested Citation

  • Tian-Shyr Dai & Yuh-Dauh Lyuu, 2009. "Accurate approximation formulas for stock options with discrete dividends," Applied Economics Letters, Taylor & Francis Journals, vol. 16(16), pages 1657-1663.
    • Handle: RePEc:taf:apeclt:v:16:y:2009:i:16:p:1657-1663
    DOI: 10.1080/13504850701604078
    as

    Download full text from publisher

    File URL: http://www.informaworld.com/openurl?genre=article&doi=10.1080/13504850701604078&magic=repec&7C&7C8674ECAB8BB840C6AD35DC6213A474B5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/13504850701604078?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. Whaley, Robert E., 1982. "Valuation of American call options on dividend-paying stocks : Empirical tests," Journal of Financial Economics, Elsevier, vol. 10(1), pages 29-58, March.
    2. Carr, Peter, 1998. "Randomization and the American Put," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
    3. Roll, Richard, 1977. "An analytic valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 5(2), pages 251-258, November.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Geske, Robert & Shastri, Kuldeep, 1985. "Valuation by Approximation: A Comparison of Alternative Option Valuation Techniques," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(1), pages 45-71, March.
    6. Mark Shackleton & Rafal Wojakowski, 2001. "On the expected payoff and true probability of exercise of European options," Applied Economics Letters, Taylor & Francis Journals, vol. 8(4), pages 269-271.
    7. Chiras, Donald P. & Manaster, Steven, 1978. "The information content of option prices and a test of market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 213-234.
    8. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    9. San-Lin Chung & Mark Shackleton, 2003. "The simplest American and Real Option approximations: Geske-Johnson interpolation in maturity and yield," Applied Economics Letters, Taylor & Francis Journals, vol. 10(11), pages 709-716.
    10. Geske, Robert, 1979. "A note on an analytical valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 7(4), pages 375-380, December.
    11. David C. Heath & Robert A. Jarrow, 2008. "Ex-Dividend Stock Price Behavior and Arbitrage Opportunities," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 3, pages 47-60, World Scientific Publishing Co. Pte. Ltd..
    12. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    13. 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.
    14. Whaley, Robert E., 1981. "On the valuation of American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 9(2), pages 207-211, June.
    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. Tian-Shyr Dai & Chun-Yuan Chiu, 2013. "Pricing barrier stock options with discrete dividends by approximating analytical formulae," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1367-1382, October.
    2. Xing Gao & Daniel Ladley, 2022. "Noise trading and market stability," The European Journal of Finance, Taylor & Francis Journals, vol. 28(13-15), pages 1283-1301, October.
    3. Ma, Jingtang & Fan, Jiacheng, 2016. "Convergence rates of recombining trees for pricing options on stocks under GBM and regime-switching models with known cash dividends," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 128-147.
    4. 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.

    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. Tian-Shyr Dai, 2009. "Efficient option pricing on stocks paying discrete or path-dependent dividends with the stair tree," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 827-838.
    2. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    3. 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.
    4. 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.
    5. Mark Broadie & Jérôme Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    6. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, August.
    7. Linda S. Klein & David R. Peterson, 1988. "Investor Expectations Of Volatility Increases Around Large Stock Splits As Implied In Call Option Premia," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 11(1), pages 71-80, March.
    8. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    9. Andrew Ziogas, 2005. "Pricing American Options Using Fourier Analysis," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2005, January-A.
    10. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    11. Pool, Veronika Krepely & Stoll, Hans R. & Whaley, Robert E., 2008. "Failure to exercise call options: An anomaly and a trading game," Journal of Financial Markets, Elsevier, vol. 11(1), pages 1-35, February.
    12. Roland Mallier & Ghada Alobaidi, 2000. "Laplace transforms and American options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(4), pages 241-256.
    13. Andrew Ziogas, 2005. "Pricing American Options Using Fourier Analysis," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 29, July-Dece.
    14. Ma, Jingtang & Fan, Jiacheng, 2016. "Convergence rates of recombining trees for pricing options on stocks under GBM and regime-switching models with known cash dividends," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 128-147.
    15. Veld, C.H., 1991. "Warrant pricing : A review of theoretical and empirical research," Other publications TiSEM ac252bad-d1c0-45d6-832a-f, Tilburg University, School of Economics and Management.
    16. Tian-Shyr Dai & Chun-Yuan Chiu, 2013. "Pricing barrier stock options with discrete dividends by approximating analytical formulae," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1367-1382, October.
    17. Gukhal, C.R.Chandrasekhar Reddy, 2004. "The compound option approach to American options on jump-diffusions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 2055-2074, September.
    18. Engstrom, Malin & Norden, Lars, 2000. "The early exercise premium in American put option prices," Journal of Multinational Financial Management, Elsevier, vol. 10(3-4), pages 461-479, December.
    19. Robert L. Brown & Dominique Achour, 1984. "The Pricing of Land Options," Urban Studies, Urban Studies Journal Limited, vol. 21(3), pages 317-323, August.
    20. In oon Kim & Bong-Gyu Jang & Kyeong Tae Kim, 2013. "A simple iterative method for the valuation of American options," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 885-895, May.

    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:taf:apeclt:v:16:y:2009:i:16:p:1657-1663. 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/RAEL20 .

    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.