IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2301.00648.html
   My bibliography  Save this paper

Fast Barrier Option Pricing by the COS BEM Method in Heston Model

Author

Listed:
  • A. Aimi
  • C. Guardasoni
  • L. Ortiz-Gracia
  • S. Sanfelici

Abstract

In this work, the Fourier-cosine series (COS) method has been combined with the Boundary Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its use in the Black and Scholes (BS) model, the focus of the paper is on the application of the proposed methodology to the barrier option evaluation in the Heston model, where its contribution is fundamental to improve computational efficiency and to make BEM appealing among Finance practitioners as a valid alternative to Monte Carlo (MC) or other more traditional approaches. An error analysis is provided on the number of terms used in the Fourier-cosine series expansion, where the error bound estimation is based on the characteristic function of the log-asset price process.

Suggested Citation

  • A. Aimi & C. Guardasoni & L. Ortiz-Gracia & S. Sanfelici, 2023. "Fast Barrier Option Pricing by the COS BEM Method in Heston Model," Papers 2301.00648, arXiv.org, revised Jan 2023.
    • Handle: RePEc:arx:papers:2301.00648
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2301.00648
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. A. Golbabai & L. Ballestra & D. Ahmadian, 2014. "A Highly Accurate Finite Element Method to Price Discrete Double Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 44(2), pages 153-173, August.
    2. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
    3. Paul Glasserman & Jeremy Staum, 2001. "Conditioning on One-Step Survival for Barrier Option Simulations," Operations Research, INFORMS, vol. 49(6), pages 923-937, December.
    4. 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).
    5. Gero Junike & Konstantin Pankrashkin, 2021. "Precise option pricing by the COS method--How to choose the truncation range," Papers 2109.01030, arXiv.org, revised Jan 2022.
    6. Nico Achtsis & Ronald Cools & Dirk Nuyens, 2012. "Conditional sampling for barrier option pricing under the Heston model," Papers 1207.6566, arXiv.org, revised Dec 2012.
    7. Simona Sanfelici, 2004. "Galerkin infinite element approximation for pricing barrier options and options with discontinuous payoff," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(2), pages 125-151, December.
    8. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    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. Alexander Lipton & Artur Sepp, 2022. "Toward an efficient hybrid method for pricing barrier options on assets with stochastic volatility," Papers 2202.07849, 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. Gero Junike, 2023. "On the number of terms in the COS method for European option pricing," Papers 2303.16012, arXiv.org, revised Mar 2024.

    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. Li, Hongshan & Huang, Zhongyi, 2020. "An iterative splitting method for pricing European options under the Heston model☆," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    2. Hongshan Li & Zhongyi Huang, 2020. "An iterative splitting method for pricing European options under the Heston model," Papers 2003.12934, arXiv.org.
    3. Hongshan Li & Zhongyi Huang, 2019. "Artificial boundary method for the solution of pricing European options under the Heston model," Papers 1912.00691, arXiv.org.
    4. Tobias Behrens & Gero Junike, 2023. "Greeks' pitfalls for the COS method in the Laplace model," Papers 2306.08421, arXiv.org, revised Jul 2023.
    5. Kontosakos, Vasileios E. & Mendonca, Keegan & Pantelous, Athanasios A. & Zuev, Konstantin M., 2021. "Pricing discretely-monitored double barrier options with small probabilities of execution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 313-330.
    6. Li, Zhe & Zhang, Weiguo & Zhang, Yue & Yi, Zhigao, 2019. "An analytical approximation approach for pricing European options in a two-price economy," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    7. Carl Chiarella & Boda Kang & Gunter H. Meyer, 2010. "The Evaluation Of Barrier Option Prices Under Stochastic Volatility," Research Paper Series 266, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. repec:qut:auncer:2013_02 is not listed on IDEAS
    9. Chen, Ding & Härkönen, Hannu J. & Newton, David P., 2014. "Advancing the universality of quadrature methods to any underlying process for option pricing," Journal of Financial Economics, Elsevier, vol. 114(3), pages 600-612.
    10. repec:uts:finphd:41 is not listed on IDEAS
    11. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
    12. A S Hurn & Kenenth A Lindsay & Andrew McClelland, 2013. "On the Efficacy of Fourier Series Approximations for Pricing European and Digital Options," NCER Working Paper Series 90, National Centre for Econometric Research.
    13. Michael Samet & Christian Bayer & Chiheb Ben Hammouda & Antonis Papapantoleon & Ra'ul Tempone, 2022. "Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in L\'evy Models," Papers 2203.08196, arXiv.org, revised Oct 2023.
    14. Augustyniak, Maciej & Badescu, Alexandru & Bégin, Jean-François, 2023. "A discrete-time hedging framework with multiple factors and fat tails: On what matters," Journal of Econometrics, Elsevier, vol. 232(2), pages 416-444.
    15. Chan, Tat Lung (Ron), 2019. "Efficient computation of european option prices and their sensitivities with the complex fourier series method," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    16. Jean-Philippe Aguilar & Jan Korbel & Nicolas Pesci, 2021. "On the Quantitative Properties of Some Market Models Involving Fractional Derivatives," Mathematics, MDPI, vol. 9(24), pages 1-24, December.
    17. Dilip B. Madan & Wim Schoutens, 2019. "Arbitrage Free Approximations to Candidate Volatility Surface Quotations," JRFM, MDPI, vol. 12(2), pages 1-21, April.
    18. Laurens Van Mieghem & Antonis Papapantoleon & Jonas Papazoglou-Hennig, 2023. "Machine learning for option pricing: an empirical investigation of network architectures," Papers 2307.07657, arXiv.org.
    19. Ballestra, Luca Vincenzo & Cecere, Liliana, 2016. "A numerical method to estimate the parameters of the CEV model implied by American option prices: Evidence from NYSE," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 100-106.
    20. Karl Friedrich Hofmann & Thorsten Schulz, 2016. "A General Ornstein–Uhlenbeck Stochastic Volatility Model With Lévy Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-23, December.
    21. Patrik Karlsson, 2018. "Finite element based Monte Carlo simulation of options on Lévy driven assets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-23, March.
    22. Grzelak, Lech & Oosterlee, Kees, 2009. "On The Heston Model with Stochastic Interest Rates," MPRA Paper 20620, University Library of Munich, Germany, revised 18 Jan 2010.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:2301.00648. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.