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Option replication with large transactions costs

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  • Reiß, Ariane

Abstract

In this paper we addressed the problem of determining the optimal replicating strategy for a European call option under differential transactions costs. We derived an upper boundary for the cost factor in a market where all Investors face the same factor. This upper boundary ensures the efficiency of the stock price as well as the bond price process. It turned out that exact replication is optimal in the presence of only one transactions cost factor. Hence, the option is redundant. Nevertheless the bid price is below the ask price with prices in this ränge being arbitrage-free. With an increasingly finer partition of the binomial tree the condition of dominance becomes more stringent, so that the cost factor must be rather small. Furthermore, the bid price increases and the ask price decreases with a finer partition.

Suggested Citation

  • Reiß, Ariane, 1997. "Option replication with large transactions costs," Tübinger Diskussionsbeiträge 106, University of Tübingen, School of Business and Economics.
    • Handle: RePEc:zbw:tuedps:106
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    References listed on IDEAS

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    1. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    2. 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.
    3. 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..
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    5. Gould, J. P. & Galai, D., 1974. "Transactions costs and the relationship between put and call prices," Journal of Financial Economics, Elsevier, vol. 1(2), pages 105-129, July.
    6. Boyle, Phelim P & Vorst, Ton, 1992. "Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-293, March.
    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.
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