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Simulations of transaction costs and optimal rehedging

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  • Benjamin Mohamed

Abstract

This paper addresses the issue of hedging options under proportional transaction costs. The Black-Scholes environment assumes frictionless markets in which one can replicate the option payoff exactly by continuous rehedging. However, when transaction costs are involved, frequent rehedging results in the accumulation of transaction costs. Conversely, infrequent hedging results in replication errors. This document attempts to evaluate several rehedging strategies by Monte Carlo simulations. The simulations are constructed so that hedging errors and transaction costs are separated permitting the relative trade-offs to be inspected. Results show that an analytic approximation to a utility maximization approach is both effective and simple to implement. The strategy results in the requirement to hedge to within a dynamic band around the Black-Scholes delta. The band is a function of the option's gamma.

Suggested Citation

  • Benjamin Mohamed, 1994. "Simulations of transaction costs and optimal rehedging," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(1), pages 49-62.
    • Handle: RePEc:taf:apmtfi:v:1:y:1994:i:1:p:49-62
    DOI: 10.1080/13504869400000003
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    References listed on IDEAS

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    1. Boyle, Phelim P. & Emanuel, David, 1980. "Discretely adjusted option hedges," Journal of Financial Economics, Elsevier, vol. 8(3), pages 259-282, September.
    2. 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.
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    Cited by:

    1. Zakamouline, Valeri I., 2006. "European option pricing and hedging with both fixed and proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 1-25, January.
    2. Johannes Gerer & Gregor Dorfleitner, 2016. "A Note On Utility Indifference Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-17, September.
    3. Valeri Zakamouline, 2003. "European Option Pricing and Hedging with both Fixed and Proportional Transaction Costs," Finance 0311009, University Library of Munich, Germany.
    4. Lai, Tze Leung & Lim, Tiong Wee, 2009. "Option hedging theory under transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1945-1961, December.
    5. Naio Ino & Afonso De Campos Pint, 2014. "Delta Hedge Com Custos Detransação: Uma Análise Comparativa," Anais do XLI Encontro Nacional de Economia [Proceedings of the 41st Brazilian Economics Meeting] 143, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    6. Lu, Xiaoping & Yan, Dong & Zhu, Song-Ping, 2022. "Optimal exercise of American puts with transaction costs under utility maximization," Applied Mathematics and Computation, Elsevier, vol. 415(C).

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