IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v12y2009i02ns021902490900518x.html
   My bibliography  Save this article

Implied Volatility From Asian Options Via Monte Carlo Methods

Author

Listed:
  • ZHAOJUN YANG

    (School of Economics and Trade, Hunan University, 410079, Changsha, China)

  • CHRISTIAN-OLIVER EWALD

    (School of Mathematical Science, University College Cork, Cork, Ireland;
    Centre for Dynamic Macroeconomic Analysis, University of St. Andrews, St. Andrews, KY16 9AL, UK)

  • YAJUN XIAO

    (Department of Economics and Finance, Goethe University of Frankfurt, Merton Str. 17/21, 60054 Frankfurt, Germany)

Abstract

We discuss how implied volatilities for OTC traded Asian options can be computed by combining Monte Carlo techniques with the Newton method in order to solve nonlinear equations. The method relies on accurate and fast computation of the corresponding vegas of the option. In order to achieve this we propose the use of logarithmic derivatives instead of the classical approach. Our simulations document that the proposed method shows far better results than the classical approach. Furthermore we demonstrate how numerical results can be improved by localization.

Suggested Citation

  • Zhaojun Yang & Christian-Oliver Ewald & Yajun Xiao, 2009. "Implied Volatility From Asian Options Via Monte Carlo Methods," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 153-178.
    • Handle: RePEc:wsi:ijtafx:v:12:y:2009:i:02:n:s021902490900518x
    DOI: 10.1142/S021902490900518X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021902490900518X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S021902490900518X?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Higham,Desmond J., 2004. "An Introduction to Financial Option Valuation," Cambridge Books, Cambridge University Press, number 9780521547574, September.
    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. Michael Giles & Desmond Higham & Xuerong Mao, 2009. "Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff," Finance and Stochastics, Springer, vol. 13(3), pages 403-413, September.
    2. Kyoung-Sook Moon & Yunju Jeong & Hongjoong Kim, 2016. "An Efficient Binomial Method for Pricing Asian Options," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(2), pages 151-164.
    3. Somayeh Abdi-Mazraeh & Ali Khani & Safar Irandoust-Pakchin, 2020. "Multiple Shooting Method for Solving Black–Scholes Equation," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 723-746, December.
    4. Rambeerich, N. & Tangman, D.Y. & Lollchund, M.R. & Bhuruth, M., 2013. "High-order computational methods for option valuation under multifactor models," European Journal of Operational Research, Elsevier, vol. 224(1), pages 219-226.
    5. Geon Lee & Tae-Kyoung Kim & Hyun-Gyoon Kim & Jeonggyu Huh, 2022. "Newton Raphson Emulation Network for Highly Efficient Computation of Numerous Implied Volatilities," Papers 2210.15969, arXiv.org.
    6. Ömür Ugur, 2008. "An Introduction to Computational Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p556, February.
    7. Avner Engel & Tyson R. Browning, 2008. "Designing systems for adaptability by means of architecture options," Systems Engineering, John Wiley & Sons, vol. 11(2), pages 125-146, June.
    8. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1, July-Dece.
    9. Abhishek Kumar & Ashwin Waikos & Siddhartha P. Chakrabarty, 2011. "Pricing of average strike Asian call option using numerical PDE methods," Papers 1106.1999, arXiv.org.
    10. Xiang Wang & Jessica Li & Jichun Li, 2023. "A Deep Learning Based Numerical PDE Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 149-164, June.
    11. Melek AKSU & Şakir SAKARYA, 2018. "Pricing of Covered Warrants: An Analysis on Borsa İstanbul," Sosyoekonomi Journal, Sosyoekonomi Society.
    12. Geon Lee & Tae-Kyoung Kim & Hyun-Gyoon Kim & Jeonggyu Huh, 2022. "Newton–Raphson Emulation Network for Highly Efficient Computation of Numerous Implied Volatilities," JRFM, MDPI, vol. 15(12), pages 1-8, December.
    13. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
    14. Qi Tang & Danni Yan, 2010. "Autoregressive trending risk function and exhaustion in random asset price movement," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 465-470, November.
    15. Foad Shokrollahi, 2017. "Fractional delta hedging strategy for pricing currency options with transaction costs," Papers 1702.00037, arXiv.org.
    16. Desmond J. Higham, 2015. "An Introduction to Multilevel Monte Carlo for Option Valuation," Papers 1505.00965, arXiv.org.
    17. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2007, January-A.

    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:wsi:ijtafx:v:12:y:2009:i:02:n:s021902490900518x. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.