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Derivative Asset Pricing with Transaction Costs: An Extension

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  • Perrakis, Stylianos
  • Lefoll, Jean

Abstract

This paper examines the optimal perfect hedging (super-replication) of an option by a cash-plus-riskless asset portfolio within the context of the binomial model. The cases discussed here were not covered by the earlier studies of Boyle and Vorst (1992) and Bensaid, Lesne, Pages and Scheinkman (1992). It is argued that these cases are empirically important, and that there is some indication that they are encountered very often in practice in the Swiss options market. A new algorithm is developed to compute the option price lower bound (bid price) for such cases. It is then shown that, for most such cases, the portfolio hedging the short call when replication is not optimal coincides with the Merton (1973) lower bound. Citation Copyright 1997 by Kluwer Academic Publishers.

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  • 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.
    • Handle: RePEc:kap:compec:v:10:y:1997:i:4:p:359-76
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    Cited by:

    1. 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.
    2. 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.
    3. Alet Roux & Tomasz Zastawniak, 2016. "Game options with gradual exercise and cancellation under proportional transaction costs," Papers 1612.02312, arXiv.org.
    4. Constantinides, George M. & Perrakis, Stylianos, 2002. "Stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1323-1352, July.
    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. Alet Roux & Zhikang Xu, 2019. "Optimal investment and contingent claim valuation with exponential disutility under proportional transaction costs," Papers 1909.06260, arXiv.org, revised May 2021.
    8. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
    9. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    10. Andreas Lohne & Birgit Rudloff, 2011. "An algorithm for calculating the set of superhedging portfolios in markets with transaction costs," Papers 1107.5720, arXiv.org, revised Dec 2013.
    11. Zachary Feinstein & Birgit Rudloff, 2013. "A comparison of techniques for dynamic multivariate risk measures," Papers 1305.2151, arXiv.org, revised Jan 2015.

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