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Approximate hedging problem with transaction costs in stochastic volatility markets

Author

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  • Huu Thai Nguyen

    (LMRS - Laboratoire de Mathématiques Raphaël Salem - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université - CNRS - Centre National de la Recherche Scientifique)

  • Serguei Pergamenchtchikov

    (LMRS - Laboratoire de Mathématiques Raphaël Salem - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Huu Thai Nguyen & Serguei Pergamenchtchikov, 2012. "Approximate hedging problem with transaction costs in stochastic volatility markets," Working Papers hal-00808608, HAL.
    • Handle: RePEc:hal:wpaper:hal-00808608
    Note: View the original document on HAL open archive server: https://hal.science/hal-00808608v2
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    References listed on IDEAS

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    1. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    2. Yuri M. Kabanov & (*), Mher M. Safarian, 1997. "On Leland's strategy of option pricing with transactions costs," Finance and Stochastics, Springer, vol. 1(3), pages 239-250.
    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. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(4), pages 589-607, December.
    5. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    6. Micha{l} Barski, 2010. "Quantile hedging for basket derivatives," Papers 1010.5810, arXiv.org, revised Jan 2016.
    7. Peter Grandits & Werner Schachinger, 2001. "Leland's Approach to Option Pricing: The Evolution of a Discontinuity," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 347-355, July.
    8. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    9. repec:dau:papers:123456789/4654 is not listed on IDEAS
    10. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    11. Emmanuel Temam & Emmanuel Gobet, 2001. "Discrete time hedging errors for options with irregular payoffs," Finance and Stochastics, Springer, vol. 5(3), pages 357-367.
    12. repec:dau:papers:123456789/4055 is not listed on IDEAS
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    14. repec:dau:papers:123456789/9304 is not listed on IDEAS
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    1. repec:hal:wpaper:hal-03284655 is not listed on IDEAS
    2. Huu Thai Nguyen & Serguei Pergamenchtchikov, 2014. "Approximate hedging with proportional transaction costs in stochastic volatility models with jumps," Working Papers hal-00979199, HAL.
    3. Thai Huu Nguyen & Serguei Pergamenschchikov, 2015. "Approximate hedging with proportional transaction costs in stochastic volatility models with jumps," Papers 1505.02627, arXiv.org, revised Sep 2019.

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    Keywords

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