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Option Pricing and Replication with Transaction Costs and Dividends

Author

Listed:
  • Stylianos PERRAKIS

    (University of Ottawa)

  • Jean LEFOLL

    (University of Geneva)

Abstract
This paper derives optimal perfect hedging portfolios in the presence of transaction costs within the binomial model of stock returns, for a market maker that establishes bid and ask prices for American call options on stocks paying dividends prior to expiration. It is shown that, while the option holder's optimal exercise policy at the ex-dividend date varies according to the stock price, there are intervals of values for such a price where the optimal policy would depend on the holder's preferences. Nonetheless, the perfect hedging assumption still allows the derivation of optimal hedging portfolios for both long and short positions of a market maker on the option.

Suggested Citation

  • Stylianos PERRAKIS & Jean LEFOLL, 1999. "Option Pricing and Replication with Transaction Costs and Dividends," FAME Research Paper Series rp8, International Center for Financial Asset Management and Engineering.
    • Handle: RePEc:fam:rpseri:rp8
    as

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    References listed on IDEAS

    as
    1. Perrakis, Stylianos & Lefoll, Jean, 2000. "Option pricing and replication with transaction costs and dividends," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1527-1561, October.
    2. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    3. Omberg, Edward, 1987. "A Note on the Convergence of Binomial-Pricing and Compound-Option," Journal of Finance, American Finance Association, vol. 42(2), pages 463-469, June.
    4. Edirisinghe, Chanaka & Naik, Vasanttilak & Uppal, Raman, 1993. "Optimal Replication of Options with Transactions Costs and Trading Restrictions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(1), pages 117-138, March.
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    6. 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..
    7. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    8. Perrakis, Stylianos & Lefoll, Jean, 1997. "Derivative Asset Pricing with Transaction Costs: An Extension," Computational Economics, Springer;Society for Computational Economics, vol. 10(4), pages 359-376, November.
    9. 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.
    10. 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.
    11. 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.
    12. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 7, pages 207-227, World Scientific Publishing Co. Pte. Ltd..
    13. 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.
    14. 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.
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    16. Dumas, Bernard & Luciano, Elisa, 1991. "An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-595, June.
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    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. 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.
    2. Tokarz, Krzysztof & Zastawniak, Tomasz, 2006. "American contingent claims under small proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 65-85, December.
    3. Perrakis, Stylianos & Lefoll, Jean, 2000. "Option pricing and replication with transaction costs and dividends," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1527-1561, October.
    4. George M. Constantinides & Michal Czerwonko & Stylianos Perrakis, 2020. "Mispriced index option portfolios," Financial Management, Financial Management Association International, vol. 49(2), pages 297-330, June.
    5. Perrakis, Stylianos & Lefoll, Jean, 2004. "The American put under transactions costs," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 915-935, February.
    6. Nan Zhang & Alet Roux & Tomasz Zastawniak, 2011. "Parallel Binomial American Option Pricing with (and without) Transaction Costs," Papers 1110.2477, arXiv.org.
    7. Martin ZIEGELBAECK & Guenther BREUER, 2014. "The role of market makers in the Euronext milling wheat contract," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 60(4), pages 183-187.
    8. Pedro Polvora & Daniel Sevcovic, 2021. "Utility indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation," Papers 2108.12598, arXiv.org.
    9. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.

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    More about this item

    Keywords

    Pricing; Transaction costs; American options; Dividends;
    All these keywords.

    JEL classification:

    • G3 - Financial Economics - - Corporate Finance and Governance

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