IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1404.3160.html
   My bibliography  Save this paper

Pricing of Basket Options Using Polynomial Approximations

Author

Listed:
  • Pablo Olivares

Abstract

In this paper we use Bernstein and Chebyshev polynomials to approximate the price of some basket options under a bivariate Black-Scholes model. The method consists in expanding the price of a univariate related contract after conditioning on the remaining underlying assets and calculating the mixed exponential-power moments of a Gaussian distribution that arise as a consequence of such approximation. Our numerical implementation on spread contracts shows the method is as accurate as a standard Monte Carlo approach at considerable lesser computational effort.

Suggested Citation

  • Pablo Olivares, 2014. "Pricing of Basket Options Using Polynomial Approximations," Papers 1404.3160, arXiv.org.
    • Handle: RePEc:arx:papers:1404.3160
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1404.3160
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Minqiang Li & Jieyun Zhou & Shi-Jie Deng, 2010. "Multi-asset spread option pricing and hedging," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 305-324.
    2. 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.
    3. Pablo Olivares & Alexander Alvarez, 2014. "A Note on the Pricing of Basket Options Using Taylor Approximations," Papers 1404.3229, arXiv.org.
    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. Damir Filipovi'c & Martin Larsson, 2017. "Polynomial Jump-Diffusion Models," Papers 1711.08043, arXiv.org, revised Jul 2019.
    2. H. Peter Boswijk & Roger J. A. Laeven & Evgenii Vladimirov, 2022. "Estimating Option Pricing Models Using a Characteristic Function-Based Linear State Space Representation," Papers 2210.06217, arXiv.org.
    3. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    4. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
    5. Juan Arismendi, 2014. "A Multi-Asset Option Approximation for General Stochastic Processes," ICMA Centre Discussion Papers in Finance icma-dp2014-03, Henley Business School, University of Reading.
    6. Pablo Olivares & Alexander Alvarez, 2014. "A Note on the Pricing of Basket Options Using Taylor Approximations," Papers 1404.3229, arXiv.org.
    7. Andrey Itkin, 2023. "The ATM implied skew in the ADO-Heston model," Papers 2309.15044, arXiv.org.
    8. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
    9. Eudald Romo & Luis Ortiz-Gracia, 2021. "SWIFT calibration of the Heston model," Papers 2103.01570, arXiv.org.
    10. Brignone, Riccardo & Gonzato, Luca & Lütkebohmert, Eva, 2023. "Efficient Quasi-Bayesian Estimation of Affine Option Pricing Models Using Risk-Neutral Cumulants," Journal of Banking & Finance, Elsevier, vol. 148(C).
    11. Adam Aleksander Majewski & Giacomo Bormetti & Fulvio Corsi, 2014. "Smile from the Past: A general option pricing framework with multiple volatility and leverage components," Papers 1404.3555, arXiv.org.
    12. Xie, Jiayi & Zhang, Zhimin, 2020. "Statistical estimation for some dividend problems under the compound Poisson risk model," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 101-115.
    13. 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).
    14. Hanwen Zhang & Duy-Minh Dang, 2023. "A monotone numerical integration method for mean-variance portfolio optimization under jump-diffusion models," Papers 2309.05977, arXiv.org.
    15. Evgenii Vladimirov, 2023. "iCOS: Option-Implied COS Method," Papers 2309.00943, arXiv.org, revised Feb 2024.
    16. Pellegrino, Tommaso & Sabino, Piergiacomo, 2014. "On the use of the moment-matching technique for pricing and hedging multi-asset spread options," Energy Economics, Elsevier, vol. 45(C), pages 172-185.
    17. 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.
    18. Rong Du & Duy-Minh Dang, 2023. "Fourier Neural Network Approximation of Transition Densities in Finance," Papers 2309.03966, arXiv.org, revised May 2024.
    19. Ziming Dong & Dan Tang & Xingchun Wang, 2023. "Pricing vulnerable basket spread options with liquidity risk," Review of Derivatives Research, Springer, vol. 26(1), pages 23-50, April.
    20. João Pedro Vidal Nunes & Tiago Ramalho Viegas Alcaria, 2016. "Valuation of forward start options under affine jump-diffusion models," Quantitative Finance, Taylor & Francis Journals, vol. 16(5), pages 727-747, May.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:1404.3160. 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.