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Optimal Hedging of Options with Small but Arbitrary Transaction Cost Structure

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  • A.E. Whalley
  • P. Wilmott

Abstract

In this paper we consider the problem of hedging options in the presence of costs in trading the underlying asset. This work is an asymptotic analysis of a stochastic control problem, as in Hodges & Neuberger (1989) and Davis, Panas & Zariphopoulou (1993) . We derive a simple expression for the `hedging bandwidth' around the Black-Scholes delta; this is the region in which it is optimal not to rehedge. The effect of the costs on the value of the option, and on the width of this hedging band is of a significantly greater order of magnitude than the costs themselves. When costs are proportional to volume traded, rehedging should be done to the edge of this band; when there are fixed costs present, trading should be done to an optimal point in the interior of the no-transaction region.

Suggested Citation

  • A.E. Whalley & P. Wilmott, 1999. "Optimal Hedging of Options with Small but Arbitrary Transaction Cost Structure," OFRC Working Papers Series 1999mf09, Oxford Financial Research Centre.
    • Handle: RePEc:sbs:wpsefe:1999mf09
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    File URL: http://www.finance.ox.ac.uk/file_links/finecon_papers/1999mf09.pdf
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    Citations

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    Cited by:

    1. Hitoshi Imai & Naoyuki Ishimura & Ikumi Mottate & Masaaki Nakamura, 2006. "On the Hoggard–Whalley–Wilmott Equation for the Pricing of Options with Transaction Costs," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 315-326, December.
    2. Jochen Zahn, 2011. "Utility based pricing and hedging of jump diffusion processes with a view to applications," Papers 1106.1395, arXiv.org, revised Dec 2012.
    3. Masaaki Fukasawa, 2014. "Efficient discretization of stochastic integrals," Finance and Stochastics, Springer, vol. 18(1), pages 175-208, January.
    4. Fischer, Georg, 2019. "How dynamic hedging affects stock price movements: Evidence from German option and certificate markets," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe B-35-19, University of Passau, Faculty of Business and Economics.
    5. Naoyuki Ishimura, 2010. "Remarks on the Nonlinear Black-Scholes Equations with the Effect of Transaction Costs," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 17(3), pages 241-259, September.
    6. Mariano González-Sánchez & Eva M. Ibáñez Jiménez & Ana I. Segovia San Juan, 2021. "Market and Liquidity Risks Using Transaction-by-Transaction Information," Mathematics, MDPI, vol. 9(14), pages 1-14, July.
    7. Yingting Miao & Qiang Zhang, 2023. "Optimal Investment and Consumption Strategies with General and Linear Transaction Costs under CRRA Utility," Papers 2304.07672, arXiv.org.
    8. Samuel N. Cohen & Derek Snow & Lukasz Szpruch, 2021. "Black-box model risk in finance," Papers 2102.04757, arXiv.org.
    9. Shota Imaki & Kentaro Imajo & Katsuya Ito & Kentaro Minami & Kei Nakagawa, 2021. "No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging," Papers 2103.01775, arXiv.org.

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