IDEAS home Printed from https://ideas.repec.org/p/fip/fednrp/9501.html
   My bibliography  Save this paper

Taylor, Black and Scholes: series approximations and risk management pitfalls

Author

Listed:
  • Arturo Estrella

Abstract

Risk managers make frequent use of finite Taylor approximations to option pricing formulas, particularly of first and second order (delta and gamma). This paper shows that for a plausible range of parameter values, the Taylor series for the Black-Scholes formula diverges. Using a numerical technique developed in the paper, it is also shown that even when the series converges, finite approximations of very large order are generally necessary to achieve acceptable levels of accuracy. Implications for risk management and stress testing are discussed.

Suggested Citation

  • Arturo Estrella, 1995. "Taylor, Black and Scholes: series approximations and risk management pitfalls," Research Paper 9501, Federal Reserve Bank of New York.
    • Handle: RePEc:fip:fednrp:9501
    as

    Download full text from publisher

    File URL: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/research_papers/9501.pdf
    Download Restriction: no
    File URL: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/research_papers/9501.html
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. Patricia Jackson & David Maude & William Perraudin, 1998. "Bank Capital and Value at Risk," Bank of England working papers 79, Bank of England.
    2. P.J.G. Vlaar, 1996. "Methods to determine capital requirements for options," Banca Nazionale del Lavoro Quarterly Review, Banca Nazionale del Lavoro, vol. 49(198), pages 351-373.
    3. Matthew Pritsker, 1996. "Evaluating Value-at-Risk Methodologies: Accuracy versus Computational Time," Center for Financial Institutions Working Papers 96-48, Wharton School Center for Financial Institutions, University of Pennsylvania.
    4. Michel Aglietta, 1996. "Financial Market Failures and Systemic Risk," Working Papers 1996-01, CEPII research center.
    5. Giuseppe Di Graziano & Lorenzo Torricelli, 2012. "Target Volatility Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-17.
    6. Jean-Philippe Aguilar, 2018. "On expansions for the Black-Scholes prices and hedge parameters," Papers 1809.06736, arXiv.org, revised Jun 2019.
    7. Michele Mininni & Giuseppe Orlando & Giovanni Taglialatela, 2021. "Challenges in approximating the Black and Scholes call formula with hyperbolic tangents," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 73-100, June.

    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. Ben Abdallah, Skander & Lasserre, Pierre, 2016. "Asset retirement with infinitely repeated alternative replacements: Harvest age and species choice in forestry," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 144-164.
    2. Kau, James B. & Keenan, Donald C., 1999. "Patterns of rational default," Regional Science and Urban Economics, Elsevier, vol. 29(6), pages 765-785, November.
    3. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.
    4. William R. Morgan, 2023. "Finance Must Be Defended: Cybernetics, Neoliberalism and Environmental, Social, and Governance (ESG)," Sustainability, MDPI, vol. 15(4), pages 1-21, February.
    5. Filipe Fontanela & Antoine Jacquier & Mugad Oumgari, 2019. "A Quantum algorithm for linear PDEs arising in Finance," Papers 1912.02753, arXiv.org, revised Feb 2021.
    6. 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.
    7. Gordian Rättich & Kim Clark & Evi Hartmann, 2011. "Performance measurement and antecedents of early internationalizing firms: A systematic assessment," Working Papers 0031, College of Business, University of Texas at San Antonio.
    8. Paul Ormerod, 2010. "La crisis actual y la culpabilidad de la teoría macroeconómica," Revista de Economía Institucional, Universidad Externado de Colombia - Facultad de Economía, vol. 12(22), pages 111-128, January-J.
    9. An Chen & Thai Nguyen & Thorsten Sehner, 2022. "Unit-Linked Tontine: Utility-Based Design, Pricing and Performance," Risks, MDPI, vol. 10(4), pages 1-27, April.
    10. Kearney, Fearghal & Shang, Han Lin & Sheenan, Lisa, 2019. "Implied volatility surface predictability: The case of commodity markets," Journal of Banking & Finance, Elsevier, vol. 108(C).
    11. Álvarez Echeverría Francisco & López Sarabia Pablo & Venegas Martínez Francisco, 2012. "Valuación financiera de proyectos de inversión en nuevas tecnologías con opciones reales," Contaduría y Administración, Accounting and Management, vol. 57(3), pages 115-145, julio-sep.
    12. Vorst, A. C. F., 1988. "Option Pricing And Stochastic Processes," Econometric Institute Archives 272366, Erasmus University Rotterdam.
    13. Dybvig, Philip H. & Gong, Ning & Schwartz, Rachel, 2000. "Bias of Damage Awards and Free Options in Securities Litigation," Journal of Financial Intermediation, Elsevier, vol. 9(2), pages 149-168, April.
    14. Zhao, Zhibiao & Wu, Wei Biao, 2009. "Nonparametric inference of discretely sampled stable Lévy processes," Journal of Econometrics, Elsevier, vol. 153(1), pages 83-92, November.
    15. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
    16. Yonggu Kim & Keeyoung Shin & Joseph Ahn & Eul-Bum Lee, 2017. "Probabilistic Cash Flow-Based Optimal Investment Timing Using Two-Color Rainbow Options Valuation for Economic Sustainability Appraisement," Sustainability, MDPI, vol. 9(10), pages 1-16, October.
    17. Chen, Peimin & Wu, Chunchi, 2014. "Default prediction with dynamic sectoral and macroeconomic frailties," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 211-226.
    18. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    19. Robert C. Merton, 2006. "Paul Samuelson and Financial Economics," The American Economist, Sage Publications, vol. 50(2), pages 9-31, October.
    20. Nadia Saghi-Zedek & Amine Tarazi, 2015. "Droits de contrôle versus droits pécuniaires, crise financière et vulnérabilité des banques européennes," Revue économique, Presses de Sciences-Po, vol. 66(3), pages 527-535.

    More about this item

    Keywords

    options; Risk;

    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:fip:fednrp:9501. 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: Gabriella Bucciarelli (email available below). General contact details of provider: https://edirc.repec.org/data/frbnyus.html .

    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.