IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v15y2022i12p616-d1007258.html
   My bibliography  Save this article

Newton–Raphson Emulation Network for Highly Efficient Computation of Numerous Implied Volatilities

Author

Listed:
  • Geon Lee

    (Department of Mathematics, Chonnam National University & Statistics, Gwangju 61186, Republic of Korea)

  • Tae-Kyoung Kim

    (Asset Management Department, KB Kookmin Bank, Seoul 07328, Republic of Korea)

  • Hyun-Gyoon Kim

    (Department of Mathematics, Yonsei University, Seoul 03722, Republic of Korea)

  • Jeonggyu Huh

    (Department of Statistics, Chonnam National University, Gwangju 61186, Republic of Korea)

Abstract

In finance, implied volatility is an important indicator that reflects the market situation immediately. Many practitioners estimate volatility by using iteration methods, such as the Newton–Raphson (NR) method. However, if numerous implied volatilities must be computed frequently, the iteration methods easily reach the processing speed limit. Therefore, we emulate the NR method as a network by using PyTorch, a well-known deep learning package, and optimize the network further by using TensorRT, a package for optimizing deep learning models. Comparing the optimized emulation method with the benchmarks, implemented in two popular Python packages, we demonstrate that the emulation network is up to 1000 times faster than the benchmark functions.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jjrfmx:v:15:y:2022:i:12:p:616-:d:1007258
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/15/12/616/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1911-8074/15/12/616/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Corrado, Charles J. & Miller, Thomas Jr., 1996. "A note on a simple, accurate formula to compute implied standard deviations," Journal of Banking & Finance, Elsevier, vol. 20(3), pages 595-603, April.
    2. Shuaiqiang Liu & Cornelis W. Oosterlee & Sander M. Bohte, 2019. "Pricing Options and Computing Implied Volatilities using Neural Networks," Risks, MDPI, vol. 7(1), pages 1-22, February.
    3. Higham,Desmond J., 2004. "An Introduction to Financial Option Valuation," Cambridge Books, Cambridge University Press, number 9780521547574, October.
    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. 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.
    2. Michele Mininni & Giuseppe Orlando & Giovanni Taglialatela, 2021. "Challenges in approximating the Black and Scholes call formula with hyperbolic tangents," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 73-100, June.
    3. Noshaba Zulfiqar & Saqib Gulzar, 2021. "Implied volatility estimation of bitcoin options and the stylized facts of option pricing," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-30, December.
    4. 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.
    5. Timothy DeLise, 2021. "Neural Options Pricing," Papers 2105.13320, arXiv.org.
    6. Patrick Büchel & Michael Kratochwil & Maximilian Nagl & Daniel Rösch, 2022. "Deep calibration of financial models: turning theory into practice," Review of Derivatives Research, Springer, vol. 25(2), pages 109-136, July.
    7. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
    8. Yibing Chen & Cheng-Few Lee & John Lee & Jow-Ran Chang, 2018. "Alternative Methods to Estimate Implied Variance: Review and Comparison," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-28, December.
    9. Junike, Gero & Pankrashkin, Konstantin, 2022. "Precise option pricing by the COS method—How to choose the truncation range," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    10. Sangseop Lim & Chang-hee Lee & Won-Ju Lee & Junghwan Choi & Dongho Jung & Younghun Jeon, 2022. "Valuation of the Extension Option in Time Charter Contracts in the LNG Market," Energies, MDPI, vol. 15(18), pages 1-14, September.
    11. 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.
    12. 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.
    13. Lokeshwar, Vikranth & Bharadwaj, Vikram & Jain, Shashi, 2022. "Explainable neural network for pricing and universal static hedging of contingent claims," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    14. Dan Stefanica & Radoš Radoičić, 2016. "A sharp approximation for ATM-forward option prices and implied volatilites," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-24, March.
    15. Sarit Maitra & Vivek Mishra & Goutam Kr. Kundu & Kapil Arora, 2023. "Integration of Fractional Order Black-Scholes Merton with Neural Network," Papers 2310.04464, arXiv.org, revised Oct 2023.
    16. 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.
    17. 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.
    18. Nikita Medvedev & Zhiguang Wang, 2022. "Multistep forecast of the implied volatility surface using deep learning," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(4), pages 645-667, April.
    19. Giacomo Morelli & Lea Petrella, 2021. "Option Pricing, Zero Lower Bound, and COVID-19," Risks, MDPI, vol. 9(9), pages 1-13, September.
    20. 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.

    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:gam:jjrfmx:v:15:y:2022:i:12:p:616-:d:1007258. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.