IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i3p279-d490266.html
   My bibliography  Save this article

The Lie Algebraic Approach for Determining Pricing for Trade Account Options

Author

Listed:
  • Shih-Hsien Tseng

    (Department of Industrial Management, National Taiwan University of Science and Technology, 43 Sec. 4 Keelung Road, Daan District, Taipei 106335, Taiwan)

  • Tien Son Nguyen

    (Institute of Industrial Management, National Central University, 300 Zhongda Road, Zhongli District, Taoyuan City 32001, Taiwan)

  • Ruei-Ci Wang

    (Minastir Asset Management AB, Quantitative Developer, Gottakrav. 28, 236 41 Hollviken, Sweden)

Abstract

In recent years, many advanced techniques have been applied to financial problems; however, very few scholars have used the Lie theory. The purpose of this study was to examine the options for a trade account through Lie symmetry analysis. According to our results, it is effective for determining analytical solutions for pricing issues and solving other partial differential equations. The proposed solution can be used by further researchers or practitioners in option pricing problems for better performance compared with the classical Black–Scholes model.

Suggested Citation

  • Shih-Hsien Tseng & Tien Son Nguyen & Ruei-Ci Wang, 2021. "The Lie Algebraic Approach for Determining Pricing for Trade Account Options," Mathematics, MDPI, vol. 9(3), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:279-:d:490266
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/3/279/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/3/279/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    2. A. Paliathanasis & K. Krishnakumar & K. M. Tamizhmani & P. G. L. Leach, 2015. "Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility," Papers 1508.06797, arXiv.org, revised May 2016.
    3. Steven E. Shreve & Jan Vecer, 2000. "Options on a traded account: Vacation calls, vacation puts and passport options," Finance and Stochastics, Springer, vol. 4(3), pages 255-274.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    6. Xiaolin Li & Weian Li & Yaowei Zhang, 2020. "Family Control, Political Connection, and Corporate Green Governance," Sustainability, MDPI, vol. 12(17), pages 1-18, August.
    7. Tristan Guillaume, 2019. "On the multidimensional Black–Scholes partial differential equation," Annals of Operations Research, Springer, vol. 281(1), pages 229-251, October.
    8. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    9. J. Vecer & J. Kampen & R. Navratil, 2020. "Options on a traded account: symmetric treatment of the underlying assets," Quantitative Finance, Taylor & Francis Journals, vol. 20(1), pages 37-47, January.
    10. 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.
    11. Nicolette C. Caister & John G. O'Hara & Keshlan S. Govinder, 2010. "Solving The Asian Option Pde Using Lie Symmetry Methods," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1265-1277.
    12. Konstantinos Mamais & Kleanthis Karvelas, 2020. "Feeling good, as a guide to performance: the impact of economic sentiment in financial market performance for Germany," Applied Economics, Taylor & Francis Journals, vol. 52(41), pages 4529-4541, September.
    13. Stephen Taylor & Scott Glasgow, 2009. "A Novel Reduction Of The Simple Asian Option And Lie-Group Invariant Solutions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(08), pages 1197-1212.
    14. Cristina Raluca Gh. Popescu & Gheorghe N. Popescu, 2019. "An Exploratory Study Based on a Questionnaire Concerning Green and Sustainable Finance, Corporate Social Responsibility, and Performance: Evidence from the Romanian Business Environment," JRFM, MDPI, vol. 12(4), pages 1-79, October.
    15. Petros Kalantonis & Sotiria Schoina & Spyros Missiakoulis & Constantin Zopounidis, 2020. "The Impact of the Disclosed R & D Expenditure on the Value Relevance of the Accounting Information: Evidence from Greek Listed Firms," Post-Print hal-02880138, HAL.
    16. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, 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. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    2. Cheng Few Lee & Yibing Chen & John Lee, 2020. "Alternative Methods to Derive Option Pricing Models: Review and Comparison," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 102, pages 3573-3617, World Scientific Publishing Co. Pte. Ltd..
    3. Henry Lam & Zhenming Liu, 2014. "From Black-Scholes to Online Learning: Dynamic Hedging under Adversarial Environments," Papers 1406.6084, arXiv.org.
    4. Boris Ter-Avanesov & Homayoon Beigi, 2024. "MLP, XGBoost, KAN, TDNN, and LSTM-GRU Hybrid RNN with Attention for SPX and NDX European Call Option Pricing," Papers 2409.06724, arXiv.org, revised Oct 2024.
    5. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    6. Michael C. Fu & Bingqing Li & Guozhen Li & Rongwen Wu, 2017. "Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions," Management Science, INFORMS, vol. 63(11), pages 3961-3977, November.
    7. repec:dau:papers:123456789/5374 is not listed on IDEAS
    8. Zafar Ahmad & Reilly Browne & Rezaul Chowdhury & Rathish Das & Yushen Huang & Yimin Zhu, 2023. "Fast American Option Pricing using Nonlinear Stencils," Papers 2303.02317, arXiv.org, revised Oct 2023.
    9. Ross A. Maller & Rosemary Tan & Mark Vyver, 2002. "How Might Companies Value ESOs?," Australian Accounting Review, CPA Australia, vol. 12(26), pages 11-24, March.
    10. Tim Leung & Marco Santoli, 2014. "Accounting for earnings announcements in the pricing of equity options," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 1-46.
    11. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.
    12. Dai, Min & Li, Peifan & Zhang, Jin E., 2010. "A lattice algorithm for pricing moving average barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 542-554, March.
    13. Peter Carr & John Crosby, 2010. "A class of Levy process models with almost exact calibration to both barrier and vanilla FX options," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1115-1136.
    14. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2020. "Early exercise boundaries for American-style knock-out options," European Journal of Operational Research, Elsevier, vol. 285(2), pages 753-766.
    15. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    16. Jun, Doobae & Ku, Hyejin, 2015. "Static hedging of chained-type barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 317-327.
    17. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    18. Robert C. Merton, 2006. "Paul Samuelson and Financial Economics," The American Economist, Sage Publications, vol. 50(2), pages 9-31, October.
    19. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2003. "Are convertible bonds underpriced? An analysis of the French market," Journal of Banking & Finance, Elsevier, vol. 27(4), pages 635-653, April.
    20. Kim, Amy M. & Li, Huanan, 2020. "Incorporating the impacts of climate change in transportation infrastructure decision models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 134(C), pages 271-287.
    21. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.

    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:jmathe:v:9:y:2021:i:3:p:279-:d:490266. 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.