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Approximate hedging problem with transaction costs in stochastic volatility markets

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  • Huu Thai Nguyen

    ()
    (LMRS - Laboratoire de Mathématiques Raphaël Salem - CNRS : UMR6085 - Université de Rouen)

  • Serguei Pergamenchtchikov

    ()
    (LMRS - Laboratoire de Mathématiques Raphaël Salem - CNRS : UMR6085 - Université de Rouen)

Abstract

This paper investigates the problem of hedging European call options using Leland's strategy in stochastic volatility markets with transaction costs. Introducing a new form for the enlarged volatility in Leland's algorithm, we establish a limit theorem and determine a convergence rate for the hedging error. This provides a suggestion to release the underhedging property pointed out by Kabanov and Safarian (1997). Possibilities to improve the convergence rate and lower the option price inclusive transaction costs are also discussed.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number hal-00808608.

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Date of creation: 01 Nov 2012
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Handle: RePEc:hal:wpaper:hal-00808608

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Keywords: Leland strategy; transaction costs; quantile hedging; limit theorem;

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  1. Lépinette-Denis, Emmanuel & Kabanov, Yuri, 2010. "Mean square error for the Leland-Lott hedging strategy: convex pay-offs," Economics Papers from University Paris Dauphine 123456789/4654, Paris Dauphine University.
  2. Peter Grandits & Werner Schachinger, 2001. "Leland's Approach to Option Pricing: The Evolution of a Discontinuity," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 11(3), pages 347-355.
  3. Lépinette-Denis, Emmanuel, 2009. "Leland's Approximations for Concave Pay-Off Functions," Economics Papers from University Paris Dauphine 123456789/9304, Paris Dauphine University.
  4. Y. M. Kabanov & M. Safarian, 1995. "On Leland's Strategy of Option Pricing with Transaction Costs," SFB 373 Discussion Papers 1995,65, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  5. Hayne E. Leland., 1984. "Option Pricing and Replication with Transactions Costs," Research Program in Finance Working Papers, University of California at Berkeley 144, University of California at Berkeley.
  6. Michal Barski, 2010. "Quantile hedging for multiple assets derivatives," Papers 1010.5810, arXiv.org, revised Feb 2011.
  7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  8. Jaksa Cvitanić & Ioannis Karatzas, 1996. "HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH-super-2," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 6(2), pages 133-165.
  9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  10. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
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Cited by:
  1. Huu Thai Nguyen & Serguei Pergamenchtchikov, 2014. "Approximate hedging with proportional transaction costs in stochastic volatility models with jumps," Working Papers hal-00979199, HAL.

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