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Asymptotic replication with modified volatility under small transaction costs

Author

Listed:
  • Jiatu Cai

    (Université Paris Diderot)

  • Masaaki Fukasawa

    (Osaka University)

Abstract

We consider the dynamic hedging of a European option under a general local volatility model with small proportional transaction costs. Extending the approach of Leland, we introduce a class of continuous strategies of finite cost that asymptotically (super-)replicate the payoff. An associated central limit theorem for the hedging error is proved. We also obtain an explicit trading strategy minimizing the asymptotic error variance.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:2:d:10.1007_s00780-016-0294-2
    DOI: 10.1007/s00780-016-0294-2
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    References listed on IDEAS

    as
    1. E. R. Grannan & G. H. Swindle, 1996. "Minimizing Transaction Costs Of Option Hedging Strategies," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 341-364, October.
    2. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    3. Dylan Possamai & H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs: the multidimensional case," Papers 1212.6275, arXiv.org, revised Jan 2013.
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    5. Masaaki Fukasawa, 2011. "Conservative delta hedging under transaction costs," Papers 1103.2013, arXiv.org, revised Jan 2012.
    6. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
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    8. 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.
    9. Jan Kallsen & Shen Li, 2013. "Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach," Papers 1309.3479, arXiv.org.
    10. Papavasiliou, A. & Pavliotis, G.A. & Stuart, A.M., 2009. "Maximum likelihood drift estimation for multiscale diffusions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3173-3210, October.
    11. Nicole El Karoui & Monique Jeanblanc‐Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126, April.
    12. Masaaki Fukasawa, 2012. "Conservative Delta Hedging under Transaction Costs," World Scientific Book Chapters, in: Akihiko Takahashi & Yukio Muromachi & Hidetaka Nakaoka (ed.), Recent Advances In Financial Engineering 2011, chapter 4, pages 55-72, World Scientific Publishing Co. Pte. Ltd..
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    14. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
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    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Cayé, Thomas & Herdegen, Martin & Muhle-Karbe, Johannes, 2020. "Scaling limits of processes with fast nonlinear mean reversion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1994-2031.

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    More about this item

    Keywords

    Leland’s strategy; Proportional transaction costs; Singular control; Homogenization; Central limit theorem;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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