IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1505.02546.html
   My bibliography  Save this paper

Approximate hedging problem with transaction costs in stochastic volatility markets

Author

Listed:
  • Thai Huu Nguyen
  • Serguei Pergamenshchikov

Abstract

This paper studies the problem of option replication in general stochastic volatility markets with transaction costs, using a new specification for the volatility adjustment in Leland's algorithm \cite{Leland}. We prove several limit theorems for the normalized replication error of Leland's strategy, as well as that of the strategy suggested by L\'epinette. The asymptotic results obtained not only generalize the existing results, but also enable us to fix the under-hedging property pointed out by Kabanov and Safarian. We also discuss possible methods to improve the convergence rate and to reduce the option price inclusive of transaction costs.

Suggested Citation

  • Thai Huu Nguyen & Serguei Pergamenshchikov, 2015. "Approximate hedging problem with transaction costs in stochastic volatility markets," Papers 1505.02546, arXiv.org.
    • Handle: RePEc:arx:papers:1505.02546
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1505.02546
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Huyěn Pham & Nizar Touzi, 1996. "Equilibrium State Prices In A Stochastic Volatility Model1," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 215-236, April.
    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. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huu Thai Nguyen & Serguei Pergamenchtchikov, 2012. "Approximate hedging problem with transaction costs in stochastic volatility markets," Working Papers hal-00808608, HAL.
    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. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    4. 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.
    5. Gabriele Fiorentini & Angel León & Gonzalo Rubio, "undated". "Short-term options with stochastic volatility: Estimation and empirical performance," Studies on the Spanish Economy 02, FEDEA.
    6. Joel Vanden, 2006. "Exact Superreplication Strategies for a Class of Derivative Assets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 61-87.
    7. Fathi Abid & Wafa Abdelmalek & Sana Ben Hamida, 2020. "Dynamic Hedging using Generated Genetic Programming Implied Volatility Models," Papers 2006.16407, arXiv.org.
    8. Serguei Pergamenchtchikov & Alena Shishkova, 2020. "Hedging problems for Asian options with transactions costs," Papers 2001.01443, arXiv.org.
    9. J. S. Kennedy & P. A. Forsyth & K. R. Vetzal, 2009. "Dynamic Hedging Under Jump Diffusion with Transaction Costs," Operations Research, INFORMS, vol. 57(3), pages 541-559, June.
    10. Stoyan V. Stoyanov & Yong Shin Kim & Svetlozar T. Rachev & Frank J. Fabozzi, 2017. "Option pricing for Informed Traders," Papers 1711.09445, arXiv.org.
    11. Wang, Xiao-Tian & Li, Zhe & Zhuang, Le, 2017. "Risk preference, option pricing and portfolio hedging with proportional transaction costs," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 111-130.
    12. Virginia R. Young, 2004. "Pricing In An Incomplete Market With An Affine Term Structure," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 359-381, July.
    13. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    14. Jacquier, Antoine & Roome, Patrick, 2016. "Large-maturity regimes of the Heston forward smile," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1087-1123.
    15. Christian Gouriéroux & Joann Jasiak & Peng Xu, 2013. "Non-tradable S&P 500 Index and the Pricing of Its Traded Derivatives," Working Papers 2013-05, Center for Research in Economics and Statistics.
    16. Lin, Zih-Ying & Chang, Chuang-Chang & Wang, Yaw-Huei, 2018. "The impacts of asymmetric information and short sales on the illiquidity risk premium in the stock option market," Journal of Banking & Finance, Elsevier, vol. 94(C), pages 152-165.
    17. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    18. Recchioni, M.C. & Sun, Y., 2016. "An explicitly solvable Heston model with stochastic interest rate," European Journal of Operational Research, Elsevier, vol. 249(1), pages 359-377.
    19. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    20. Baule, Rainer & Münchhalfen, Patrick & Shkel, David & Tallau, Christian, 2023. "Fair-washing in the market for structured retail products? Voluntary self-regulation versus government regulation," Journal of Banking & Finance, Elsevier, vol. 148(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1505.02546. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.