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Minimizing Transaction Costs Of Option Hedging Strategies

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  • E. R. Grannan
  • G. H. Swindle

Abstract

This paper introduces a method for constructing option hedging strategies in the presence of transaction costs. the approach begins with the prescription of a large, but tractable class of strategies. A variational problem is constructed in which the expected square replication error is minimized subject to a fixed initial portfolio value from among the class of strategies. the solution of this variational problem results in a replicating strategy which simulations show outperforms strategies previously considered. We illustrate this method in a particular class of strategies which contains Leland's discrete time replication scheme. We show that a strategy which uses varying time intervals between hedging can significantly reduce replication error for a given initial wealth. We will also construct and assess strategies obtained by optimizing a mean-variance criterion. This methodology extends to other optimization problems involving initial portfolio value and expected square replication error, as well as to other classes of strategies. Copyright 1996 Blackwell Publishers.

Suggested Citation

  • E. R. Grannan & G. H. Swindle, 1996. "Minimizing Transaction Costs Of Option Hedging Strategies," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 341-364.
  • Handle: RePEc:bla:mathfi:v:6:y:1996:i:4:p:341-364
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9965.1996.tb00121.x
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    Citations

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    Cited by:

    1. repec:dau:papers:123456789/4654 is not listed on IDEAS
    2. 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.
    3. Emmanuel Denis & Yuri Kabanov, 2010. "Mean square error for the Leland–Lott hedging strategy: convex pay-offs," Finance and Stochastics, Springer, vol. 14(4), pages 625-667, December.
    4. Branger, Nicole & Mahayni, Antje, 2006. "Tractable hedging: An implementation of robust hedging strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 1937-1962, November.
    5. Fehle, Frank, 2004. "A note on transaction costs and the existence of derivatives markets," Journal of Economics and Business, Elsevier, vol. 56(1), pages 63-70.
    6. Jiatu Cai & Masaaki Fukasawa, 2016. "Asymptotic replication with modified volatility under small transaction costs," Finance and Stochastics, Springer, vol. 20(2), pages 381-431, April.
    7. Balder, Sven & Brandl, Michael & Mahayni, Antje, 2009. "Effectiveness of CPPI strategies under discrete-time trading," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 204-220, January.
    8. Jiatu Cai & Masaaki Fukasawa, 2014. "Asymptotic replication with modified volatility under small transaction costs," Papers 1408.5677, arXiv.org.
    9. repec:gam:jjrfmx:v:10:y:2017:i:3:p:16-:d:107638 is not listed on IDEAS
    10. Jacques, Sébastien & Lai, Van Son & Soumaré, Issouf, 2011. "Synthetizing a debt guarantee: Super-replication versus utility approach," International Review of Financial Analysis, Elsevier, vol. 20(1), pages 27-40, January.
    11. Bertsimas, Dimitris & Kogan, Leonid & Lo, Andrew W., 2000. "When is time continuous?," Journal of Financial Economics, Elsevier, vol. 55(2), pages 173-204, February.
    12. Nicole Branger & Antje Mahayni, 2011. "Tractable hedging with additional hedge instruments," Review of Derivatives Research, Springer, vol. 14(1), pages 85-114, April.
    13. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance,in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742 Elsevier.

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