IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v53y2019i4d10.1007_s10614-018-9819-4.html
   My bibliography  Save this article

Efficient Semi-Discretization Techniques for Pricing European and American Basket Options

Author

Listed:
  • Fazlollah Soleymani

    (Institute for Advanced Studies in Basic Sciences)

Abstract

This paper studies the valuation of option pricing problem in the presence of several assets. European- and American-style options are dealt with using high order semi-discretization techniques. We integrate the resulting system of semi-discretized ODEs in time with several time-stepping schemes such as explicit Euler method, explicit Runge–Kutta method, and the Runge–Kutta method with adaptive variable step sizes. Numerical results demonstrate that employing higher order semi-discretizations improves the computational performance of the multi-asset option pricing problems.

Suggested Citation

  • Fazlollah Soleymani, 2019. "Efficient Semi-Discretization Techniques for Pricing European and American Basket Options," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1487-1508, April.
    • Handle: RePEc:kap:compec:v:53:y:2019:i:4:d:10.1007_s10614-018-9819-4
    DOI: 10.1007/s10614-018-9819-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-018-9819-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-018-9819-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhongdi Cen & Anbo Le & Aimin Xu, 2012. "A Second-Order Difference Scheme for the Penalized Black–Scholes Equation Governing American Put Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 49-62, June.
    2. Darae Jeong & Minhyun Yoo & Junseok Kim, 2018. "Finite Difference Method for the Black–Scholes Equation Without Boundary Conditions," Computational Economics, Springer;Society for Computational Economics, vol. 51(4), pages 961-972, April.
    3. Kamille Sofie Tågholt Gad & Jesper Lund Pedersen, 2015. "Rationality Parameter for Exercising American Put," Risks, MDPI, vol. 3(2), pages 1-9, May.
    4. Rambeerich, N. & Tangman, D.Y. & Lollchund, M.R. & Bhuruth, M., 2013. "High-order computational methods for option valuation under multifactor models," European Journal of Operational Research, Elsevier, vol. 224(1), pages 219-226.
    5. Egorova, Yana, 2017. "Инвестирование Денежных Средств В Условиях Экономического Кризиса В 2017 Году," MPRA Paper 77648, University Library of Munich, Germany.
    6. Xianming Sun & Siqing Gan, 2014. "An Efficient Semi-Analytical Simulation for the Heston Model," Computational Economics, Springer;Society for Computational Economics, vol. 43(4), pages 433-445, April.
    7. Rafael Company & Vera Egorova & Lucas J'odar & Fazlollah Soleymani, 2017. "Computing stable numerical solutions for multidimensional American option pricing problems: a semi-discretization approach," Papers 1701.08545, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dilan Ahmed & Mudhafar Hama & Karwan Hama Faraj Jwamer & Stanford Shateyi, 2019. "A Seventh-Order Scheme for Computing the Generalized Drazin Inverse," Mathematics, MDPI, vol. 7(7), pages 1-10, July.

    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. Rafael Company & Vera Egorova & Lucas J'odar & Fazlollah Soleymani, 2017. "Computing stable numerical solutions for multidimensional American option pricing problems: a semi-discretization approach," Papers 1701.08545, arXiv.org.
    2. Louis Bhim & Reiichiro Kawai, 2018. "Smooth Upper Bounds For The Price Function Of American Style Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-38, February.
    3. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.
    4. Kirkby, J. Lars & Nguyen, Dang H. & Nguyen, Duy, 2020. "A general continuous time Markov chain approximation for multi-asset option pricing with systems of correlated diffusions," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    5. Galina S. TIMOKHINA, 2019. "Behaviour of high-income consumers: Results of research of the private banking services market in Russia," Upravlenets, Ural State University of Economics, vol. 10(4), pages 85-97, September.
    6. Jin-Yu Zhang & Wen-Bo Wu & Yong Li & Zhu-Sheng Lou, 2021. "Pricing Exotic Option Under Jump-Diffusion Models by the Quadrature Method," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 867-884, October.
    7. Darae Jeong & Minhyun Yoo & Changwoo Yoo & Junseok Kim, 2019. "A Hybrid Monte Carlo and Finite Difference Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 111-124, January.
    8. Stephan Barisitz & Alice Radzyner, 2017. "The New Silk Road, part I: a stocktaking and economic assessment," Focus on European Economic Integration, Oesterreichische Nationalbank (Austrian Central Bank), issue Q3/17, pages 8-30.
    9. Mohammad Mehdizadeh Khalsaraei & Ali Shokri & Higinio Ramos & Zahra Mohammadnia & Pari Khakzad, 2022. "A Positivity-Preserving Improved Nonstandard Finite Difference Method to Solve the Black-Scholes Equation," Mathematics, MDPI, vol. 10(11), pages 1-16, May.
    10. Company, Rafael & Egorova, Vera N. & Jódar, Lucas, 2021. "A front-fixing ETD numerical method for solving jump–diffusion American option pricing problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 189(C), pages 69-84.
    11. Vladimir V. Gromov & Nikolaj S. Milogolov, 2019. "Simplified Taxation System and Unified Tax on Imputed Income: Objectives, Problems, Long-term Vision," Finansovyj žhurnal — Financial Journal, Financial Research Institute, Moscow 125375, Russia, issue 2, pages 9-21, April.
    12. Radhakrishnan, Rokesh & Patra, Pradipta & Das, Manali & Ghosh, Amit, 2021. "Recent advancements in the ionic liquid mediated lignin valorization for the production of renewable materials and value-added chemicals," Renewable and Sustainable Energy Reviews, Elsevier, vol. 149(C).
    13. Kim, Junseok & Kim, Taekkeun & Jo, Jaehyun & Choi, Yongho & Lee, Seunggyu & Hwang, Hyeongseok & Yoo, Minhyun & Jeong, Darae, 2016. "A practical finite difference method for the three-dimensional Black–Scholes equation," European Journal of Operational Research, Elsevier, vol. 252(1), pages 183-190.
    14. Dina Kabdullinovna Tanatova* & Irina Vladimirovna Dolgorukova & Vardres Grigorevich Pogosyan & Tatiana Mihailovna Bormotova & Evgeniy Aleksandrovich Lidzer, 2018. "Youth Entrepreneurship: Social Practices and Risks," The Journal of Social Sciences Research, Academic Research Publishing Group, pages 348-353:3.
    15. Karakaya, Emrah, 2016. "Finite Element Method for forecasting the diffusion of photovoltaic systems: Why and how?," Applied Energy, Elsevier, vol. 163(C), pages 464-475.
    16. Jed O. Kaplan & Kristen M. Krumhardt & Marie-José Gaillard & Shinya Sugita & Anna-Kari Trondman & Ralph Fyfe & Laurent Marquer & Florence Mazier & Anne Birgitte Nielsen, 2017. "Constraining the Deforestation History of Europe: Evaluation of Historical Land Use Scenarios with Pollen-Based Land Cover Reconstructions," Land, MDPI, vol. 6(4), pages 1-20, December.
    17. Arkadii A. Simdiankin & Pavel S. Probin & Larisa N. Gerasimova & Zhanna Kevorkova & Vadim A. Dikikh & Aslan O. Nurmanov, 2020. "Method for evaluating the possibility of cluster forming," Entrepreneurship and Sustainability Issues, VsI Entrepreneurship and Sustainability Center, vol. 7(4), pages 3145-3157, June.
    18. Daria M. Arkhipova & Vadim V. Ermolaev & Vasili A. Miluykov & Farida G. Valeeva & Gulnara A. Gaynanova & Lucia Ya. Zakharova & Mikhail E. Minyaev & Valentine P. Ananikov, 2021. "Tri- tert -butyl( n -alkyl)phosphonium Ionic Liquids: Structure, Properties and Application as Hybrid Catalyst Nanomaterials," Sustainability, MDPI, vol. 13(17), pages 1-19, September.
    19. S. Egorova E. & L. Yudanova A. & V. Budasova A. & С. Егорова Е. & Л. Юданова А. & В. Будасова А., 2019. "Проблемы и особенности бюджетирования деятельности в социально-ориентированных некоммерческих организациях // Problems and Peculiarities of Budgeting the Activities in Socially Oriented Non-profit Org," Учет. Анализ. Аудит // Accounting. Analysis. Auditing, ФГОБУВО "Финансовый университет при Правительстве Российской Федерации" // Financial University under The Government of Russian Federation, vol. 6(4), pages 32-41.
    20. Molina-Muñoz, Jesús & Mora-Valencia, Andrés & Perote, Javier, 2020. "Market-crash forecasting based on the dynamics of the alpha-stable distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).

    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:kap:compec:v:53:y:2019:i:4:d:10.1007_s10614-018-9819-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.