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Asymptotic replication with modified volatility under small transaction costs

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  • Jiatu Cai
  • Masaaki Fukasawa

Abstract

Dynamic hedging of an European option under a general local volatility model with small linear transaction costs is studied. A continuous control version of Leland's strategy that asymptotically replicates the payoff is constructed. An associated central limit theorem of hedging error is proved. The asymptotic error variance is minimized by an explicit trading strategy.

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  • Jiatu Cai & Masaaki Fukasawa, 2014. "Asymptotic replication with modified volatility under small transaction costs," Papers 1408.5677, arXiv.org.
    • Handle: RePEc:arx:papers:1408.5677
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    References listed on IDEAS

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    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.
    4. 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.
    5. 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.
    6. 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..
    7. H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs," Papers 1202.6131, arXiv.org, revised Jun 2013.
    8. repec:dau:papers:123456789/4654 is not listed on IDEAS
    9. Masaaki Fukasawa, 2011. "Conservative delta hedging under transaction costs," Papers 1103.2013, arXiv.org, revised Jan 2012.
    10. Toft, Klaus Bjerre, 1996. "On the Mean-Variance Tradeoff in Option Replication with Transactions Costs," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(2), pages 233-263, June.
    11. 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.
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