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Option Pricing and Replication with Transaction Costs and Dividends

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  • 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.

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Bibliographic Info

Paper provided by International Center for Financial Asset Management and Engineering in its series FAME Research Paper Series with number rp8.

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Date of creation: Jul 1999
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Handle: RePEc:fam:rpseri:rp8

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Keywords: Pricing; Transaction costs; American options; Dividends;

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References

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  1. Constantinides, George M, 1986. "Capital Market Equilibrium with Transaction Costs," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 842-62, August.
  2. 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.
  3. 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.
  4. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  5. 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 637-54, May-June.
  6. 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.
  7. 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 577-95, June.
  8. Perrakis, Stylianos & Lefoll, Jean, 1997. "Derivative Asset Pricing with Transaction Costs: An Extension," Computational Economics, Society for Computational Economics, vol. 10(4), pages 359-76, November.
  9. 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.
  10. Hayne E. Leland., 1984. "Option Pricing and Replication with Transactions Costs," Research Program in Finance Working Papers 144, University of California at Berkeley.
  11. 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(01), pages 117-138, March.
  12. Michael J. P. Selby & Stewart D. Hodges, 1987. "On the Evaluation of Compound Options," Management Science, INFORMS, vol. 33(3), pages 347-355, March.
  13. Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86.
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Citations

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Cited by:
  1. Nan Zhang & Alet Roux & Tomasz Zastawniak, 2011. "Parallel Binomial American Option Pricing with (and without) Transaction Costs," Papers 1110.2477, arXiv.org.
  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. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
  4. 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.

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