IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/36127.html
   My bibliography  Save this paper

The vanna - volga method for derivatives pricing

Author

Listed:
  • Janek, Agnieszka

Abstract

This Master thesis highlights some basic features and applications of the vanna-volga method and its accuracy when pricing plain vanillas and simple barrier options. In the paper we derive formulas for premiums of vanilla FX options using two versions of the vanna-volga method – the exact vanna-volga method and the simplified vanna-volga method. We review a very common vanna-volga variation used to price the first-generation exotics and the application of the vanna-volga method to construct the implied volatility surface. Furthermore, we briefly discuss a popular stochastic volatility model that aims to take the smile effect into account – the Heston model. Its accuracy and efficiency is further compared with that of the vanna-volga method. In the part of the thesis, which is devoted to calibration results, we compare the results obtained by the exact vanna-volga method, the simplified vanna-volga method and the Heston model. We also investigate the accuracy of the vanna-volga method applied to barrier options. All the plots and graphs in this thesis were produced by programs implemented by the author in MATLAB. These programs are available on request.

Suggested Citation

  • Janek, Agnieszka, 2011. "The vanna - volga method for derivatives pricing," MPRA Paper 36127, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:36127
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/36127/1/MPRA_paper_36127.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wystup, Uwe, 2008. "Foreign exchange symmetries," CPQF Working Paper Series 9, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    2. Janek, Agnieszka & Kluge, Tino & Weron, Rafał & Wystup, Uwe, 2010. "FX smile in the Heston model," SFB 649 Discussion Papers 2010-047, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. 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.
    5. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    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. Alessandro Gnoatto, 2017. "Coherent Foreign Exchange Market Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-29, February.
    2. Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
    3. 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.
    4. Ying Jiao & Chunhua Ma & Simone Scotti & Chao Zhou, 2021. "The Alpha‐Heston stochastic volatility model," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 943-978, July.
    5. Bo, Lijun & Wang, Yongjin & Yang, Xuewei, 2010. "Markov-modulated jump-diffusions for currency option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 461-469, June.
    6. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, August.
    7. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, June.
    8. Bo, Lijun, 2011. "Exponential change of measure applied to term structures of interest rates and exchange rates," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 216-225, September.
    9. Branger, Nicole & Herold, Michael & Muck, Matthias, 2021. "International stochastic discount factors and covariance risk," Journal of Banking & Finance, Elsevier, vol. 123(C).
    10. Sanjay K. Nawalkha & Xiaoyang Zhuo, 2022. "A Theory of Equivalent Expectation Measures for Contingent Claim Returns," Journal of Finance, American Finance Association, vol. 77(5), pages 2853-2906, October.
    11. Janek, Agnieszka & Kluge, Tino & Weron, Rafał & Wystup, Uwe, 2010. "FX smile in the Heston model," SFB 649 Discussion Papers 2010-047, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    12. De Col, Alvise & Gnoatto, Alessandro & Grasselli, Martino, 2013. "Smiles all around: FX joint calibration in a multi-Heston model," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3799-3818.
    13. Thomas Kokholm & Martin Stisen, 2015. "Joint pricing of VIX and SPX options with stochastic volatility and jump models," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 16(1), pages 27-48, January.
    14. Darren Shannon & Grigorios Fountas, 2021. "Extending the Heston Model to Forecast Motor Vehicle Collision Rates," Papers 2104.11461, arXiv.org, revised May 2021.
    15. Cui, Yiran & del Baño Rollin, Sebastian & Germano, Guido, 2017. "Full and fast calibration of the Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 263(2), pages 625-638.
    16. Yang, Nian & Chen, Nan & Wan, Xiangwei, 2019. "A new delta expansion for multivariate diffusions via the Itô-Taylor expansion," Journal of Econometrics, Elsevier, vol. 209(2), pages 256-288.
    17. Almeida, Thiago Ramos, 2024. "Estimating time-varying factors’ variance in the string-term structure model with stochastic volatility," Research in International Business and Finance, Elsevier, vol. 70(PA).
    18. Chenxu Li, 2014. "Closed-Form Expansion, Conditional Expectation, and Option Valuation," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 487-516, May.
    19. Levendorskii, Sergei, 2004. "Consistency conditions for affine term structure models," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 225-261, February.
    20. O. Samimi & Z. Mardani & S. Sharafpour & F. Mehrdoust, 2017. "LSM Algorithm for Pricing American Option Under Heston–Hull–White’s Stochastic Volatility Model," Computational Economics, Springer;Society for Computational Economics, vol. 50(2), pages 173-187, August.

    More about this item

    Keywords

    vanna- volga method; implied volatility; volatility smile; Heston model;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

    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:pra:mprapa:36127. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.