IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v17y2024i10p436-d1488913.html
   My bibliography  Save this article

Bayesian Lower and Upper Estimates for Ether Option Prices with Conditional Heteroscedasticity and Model Uncertainty

Author

Listed:
  • Tak Kuen Siu

    (Department of Actuarial Studies and Business Analytics, Macquarie Business School, Macquarie University, Sydney, NSW 2109, Australia)

Abstract

This paper aims to leverage Bayesian nonlinear expectations to construct Bayesian lower and upper estimates for prices of Ether options, that is, options written on Ethereum, with conditional heteroscedasticity and model uncertainty. Specifically, a discrete-time generalized conditional autoregressive heteroscedastic (GARCH) model is used to incorporate conditional heteroscedasticity in the logarithmic returns of Ethereum, and Bayesian nonlinear expectations are adopted to introduce model uncertainty, or ambiguity, about the conditional mean and volatility of the logarithmic returns of Ethereum. Extended Girsanov’s principle is employed to change probability measures for introducing a family of alternative GARCH models and their risk-neutral counterparts. The Bayesian credible intervals for “uncertain” drift and volatility parameters obtained from conjugate priors and residuals obtained from the estimated GARCH model are used to construct Bayesian superlinear and sublinear expectations giving the Bayesian lower and upper estimates for the price of an Ether option, respectively. Empirical and simulation studies are provided using real data on Ethereum in AUD. Comparisons with a model incorporating conditional heteroscedasticity only and a model capturing ambiguity only are presented.

Suggested Citation

  • Tak Kuen Siu, 2024. "Bayesian Lower and Upper Estimates for Ether Option Prices with Conditional Heteroscedasticity and Model Uncertainty," JRFM, MDPI, vol. 17(10), pages 1-32, September.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:10:p:436-:d:1488913
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/17/10/436/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1911-8074/17/10/436/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Dilip B. Madan, 2016. "Benchmarking in two price financial markets," Annals of Finance, Springer, vol. 12(2), pages 201-219, May.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Dilip Madan, 2015. "Asset pricing theory for two price economies," Annals of Finance, Springer, vol. 11(1), pages 1-35, February.
    5. 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.
    6. Hsieh, David A, 1991. "Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-1877, December.
    7. V. Lucic & A. Sepp, 2024. "Valuation and hedging of cryptocurrency inverse options," Quantitative Finance, Taylor & Francis Journals, vol. 24(7), pages 851-869, July.
    8. Yao, Qiwei & Tong, Howell, 1998. "A bootstrap detection for operational determinism," LSE Research Online Documents on Economics 6697, London School of Economics and Political Science, LSE Library.
    9. Gael M. Martin & Catherine S. Forbes & Vance L. Martin, 2005. "Implicit Bayesian Inference Using Option Prices," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 437-462, May.
    10. Shu Wing Ho & Alan Lee & Alastair Marsden, 2011. "Use of Bayesian Estimates to determine the Volatility Parameter Input in the Black-Scholes and Binomial Option Pricing Models," JRFM, MDPI, vol. 4(1), pages 1-23, December.
    11. Yao, Qiwei & Tong, Howell, 1994. "Quantifying the influence of initial values on nonlinear prediction," LSE Research Online Documents on Economics 19426, London School of Economics and Political Science, LSE Library.
    12. F. Douglas Foster & Charles H. Whiteman, 1999. "An Application of Bayesian Option Pricing to the Soybean Market," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(3), pages 722-727.
    13. Tak Kuen Siu & Robert J. Elliott, 2021. "Bitcoin option pricing with a SETAR-GARCH model," The European Journal of Finance, Taylor & Francis Journals, vol. 27(6), pages 564-595, April.
    14. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
    15. Paul Wilmott & Asli Oztukel, 1998. "Uncertain Parameters, an Empirical Stochastic Volatility Model and Confidence Limits," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 175-189.
    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. Tak Kuen Siu, 2023. "Bayesian nonlinear expectation for time series modelling and its application to Bitcoin," Empirical Economics, Springer, vol. 64(1), pages 505-537, January.
    2. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    3. Dutta, Shantanu & Essaddam, Naceur & Kumar, Vinod & Saadi, Samir, 2017. "How does electronic trading affect efficiency of stock market and conditional volatility? Evidence from Toronto Stock Exchange," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 867-877.
    4. John T. Barkoulas & Christopher F. Baum & Joseph Onochie, 1997. "A nonparametric investigation of the 90‐day t‐bill rate," Review of Financial Economics, John Wiley & Sons, vol. 6(2), pages 187-198.
    5. Dilip B. Madan, 2018. "Financial equilibrium with non-linear valuations," Annals of Finance, Springer, vol. 14(2), pages 211-221, May.
    6. Wolff Rodney & Yao Qiwei & Tong Howell, 2004. "Statistical Tests for Lyapunov Exponents of Deterministic Systems," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-19, May.
    7. Verhoeven, Peter & McAleer, Michael, 2004. "Fat tails and asymmetry in financial volatility models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(3), pages 351-361.
    8. Stavros Degiannakis & Evdokia Xekalaki, 2007. "Assessing the performance of a prediction error criterion model selection algorithm in the context of ARCH models," Applied Financial Economics, Taylor & Francis Journals, vol. 17(2), pages 149-171.
    9. Brini, Alessio & Lenz, Jimmie, 2024. "Pricing cryptocurrency options with machine learning regression for handling market volatility," Economic Modelling, Elsevier, vol. 136(C).
    10. repec:wyi:journl:002128 is not listed on IDEAS
    11. Pezzo, Rosanna & Uberti, Mariacristina, 2006. "Approaches to forecasting volatility: Models and their performances for emerging equity markets," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 556-565.
    12. Robert J. Elliott & Dilip B. Madan & Tak Kuen Siu, 2021. "Two price economic equilibria and financial market bid/ask prices," Annals of Finance, Springer, vol. 17(1), pages 27-43, March.
    13. Claudeci Da Silva & Hugo Agudelo Murillo & Joaquim Miguel Couto, 2014. "Early Warning Systems: Análise De Ummodelo Probit De Contágio De Crise Dos Estados Unidos Para O Brasil(2000-2010)," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 110, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    14. Florence Guillaume & Gero Junike & Peter Leoni & Wim Schoutens, 2019. "Implied liquidity risk premia in option markets," Annals of Finance, Springer, vol. 15(2), pages 233-246, June.
    15. Coronado-Ramírez, Semei L. & Porras-Serrano, Jesús & Venegas-Martínez, Francisco, 2011. "Estructuras no lineales en mercados eficientes: el caso IBEX-35," Sección de Estudios de Posgrado e Investigación de la Escuela Superios de Economía del Instituto Politécnico Nacional, in: Perrotini-Hernández, Ignacio (ed.), Economía: Teoría y Métodos, volume 1, chapter 8, pages 116-129, Escuela Superior de Economía, Instituto Politécnico Nacional.
    16. Robert J Bianchi & Adam E Clements & Michael E Drew, 2009. "HACking at Non-linearity: Evidence from Stocks and Bonds," School of Economics and Finance Discussion Papers and Working Papers Series 244, School of Economics and Finance, Queensland University of Technology.
    17. Fernando Fernandez-Rodriguez & Simon Sosvilla-Rivero & Maria Dolores Garcia-Artiles, 1997. "Using nearest neighbour predictors to forecast the Spanish stock market," Investigaciones Economicas, Fundación SEPI, vol. 21(1), pages 75-91, January.
    18. Yi-Ting Chen & Chung-Ming Kuan, 2002. "Time irreversibility and EGARCH effects in US stock index returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 565-578.
    19. An-Sing Chen, 1997. "The square compass rose: the evidence from Taiwan," Journal of Multinational Financial Management, Elsevier, vol. 7(2), pages 127-144, June.
    20. R. P. Brito & H. Sebastião & P. Godinho, 2017. "Portfolio choice with high frequency data: CRRA preferences and the liquidity effect," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 16(2), pages 65-86, August.
    21. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, July.

    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:17:y:2024:i:10:p:436-:d:1488913. 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.