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Comparative Analysis of Root Finding Algorithms for Implied Volatility Estimation of Ethereum Options

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  • S. Sapna

    (National Institute of Technology Karnataka)

  • Biju R. Mohan

    (National Institute of Technology Karnataka)

Abstract

In this paper, a comparative analysis of traditional and hybrid root finding algorithms is performed in estimating implied volatility for Ethereum Options using the Black–Scholes model. Results indicate the efficiency of Newton–Raphson method in terms of algorithmic convergence as well as computational time. Since Newton–Raphson method may not always lead to convergence, the best approximation technique is chosen from the convergent bracketed methods. The hybrid Bisection–Regula Falsi method serves as the best choice for root estimation among the bracketed methods under consideration.

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  • S. Sapna & Biju R. Mohan, 2024. "Comparative Analysis of Root Finding Algorithms for Implied Volatility Estimation of Ethereum Options," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 515-550, July.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:1:d:10.1007_s10614-023-10446-8
    DOI: 10.1007/s10614-023-10446-8
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    References listed on IDEAS

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    1. Pierre J. Venter & Eben Mare & Edson Pindza & David McMillan, 2020. "Price discovery in the cryptocurrency option market: A univariate GARCH approach," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1803524-180, January.
    2. Elsayed Badr & Sultan Almotairi & Abdallah El Ghamry, 2021. "A Comparative Study among New Hybrid Root Finding Algorithms and Traditional Methods," Mathematics, MDPI, vol. 9(11), pages 1-15, June.
    3. Chaman Lal Sabharwal, 2019. "Blended Root Finding Algorithm Outperforms Bisection and Regula Falsi Algorithms," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    4. Fan Fang & Carmine Ventre & Michail Basios & Leslie Kanthan & David Martinez-Rego & Fan Wu & Lingbo Li, 2022. "Cryptocurrency trading: a comprehensive survey," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-59, December.
    5. Pierre J. Venter & Eben Maré, 2021. "Univariate and Multivariate GARCH Models Applied to Bitcoin Futures Option Pricing," JRFM, MDPI, vol. 14(6), pages 1-14, June.
    6. Chi, Yeguang & Hao, Wenyan, 2021. "Volatility models for cryptocurrencies and applications in the options market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 75(C).
    7. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    8. Ai Jun Hou & Weining Wang & Cathy Y H Chen & Wolfgang Karl Härdle, 2020. "Pricing Cryptocurrency Options," Journal of Financial Econometrics, Oxford University Press, vol. 18(2), pages 250-279.
    9. Ryno du Plooy & Pierre J. Venter & David McMillan, 2021. "Pricing vanilla options using artificial neural networks: Application to the South African market," Cogent Economics & Finance, Taylor & Francis Journals, vol. 9(1), pages 1914285-191, January.
    10. Fabian Woebbeking, 2021. "Cryptocurrency volatility markets," Digital Finance, Springer, vol. 3(3), pages 273-298, December.
    11. 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.
    12. Katsiampa, Paraskevi, 2017. "Volatility estimation for Bitcoin: A comparison of GARCH models," Economics Letters, Elsevier, vol. 158(C), pages 3-6.
    13. James S. Ang & Gwoduan David Jou & Tsong-Yue Lai, 2009. "Alternative Formulas to Compute Implied Standard Deviation," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 159-176.
    14. Akanksha Jalan & Roman Matkovskyy & Saqib Aziz, 2021. "The Bitcoin options market: A first look at pricing and risk," Applied Economics, Taylor & Francis Journals, vol. 53(17), pages 2026-2041, April.
    15. Giancarlo Giudici & Alistair Milne & Dmitri Vinogradov, 2020. "Cryptocurrencies: market analysis and perspectives," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 47(1), pages 1-18, March.
    16. 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.
    17. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    18. 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.
    19. Fan Fang & Carmine Ventre & Michail Basios & Leslie Kanthan & Lingbo Li & David Martinez-Regoband & Fan Wu, 2020. "Cryptocurrency Trading: A Comprehensive Survey," Papers 2003.11352, arXiv.org, revised Jan 2022.
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