IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1705.00212.html
   My bibliography  Save this paper

Option pricing: A yet simpler approach

Author

Listed:
  • Jarno Talponen
  • Minna Turunen

Abstract

We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox-Ross-Rubinstein (CRR) pricing model. The main tool used in the paper for cleaning up the reasoning is applying static hedging arguments. This can be accomplished by taking various routes through some auxiliary considerations, namely Arrow-Debreu securities, digital options or backward random processes. In the last case the CRR model is extended to an infinite state space which leads to an interesting new phenomenon not present in the classical CRR model. At the end we discuss the paradox involving the drift parameter $\mu$ in the BSM model pricing. We provide sensitivity analysis and the speed of converge for the asymptotically vanishing drift.

Suggested Citation

  • Jarno Talponen & Minna Turunen, 2017. "Option pricing: A yet simpler approach," Papers 1705.00212, arXiv.org, revised Mar 2018.
    • Handle: RePEc:arx:papers:1705.00212
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1705.00212
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(1), pages 1-12, March.
    2. 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..
    3. 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.
    4. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    5. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    6. Brown, Donald J & Ross, Stephen A, 1991. "Spanning, Valuation and Options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 3-12, January.
    7. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    8. 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.
    9. Babbs, Simon, 2000. "Binomial valuation of lookback options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1499-1525, October.
    10. Sanjiv R. Das & Rangarajan K. Sundaram, 2007. "An Integrated Model for Hybrid Securities," Management Science, INFORMS, vol. 53(9), pages 1439-1451, September.
    11. Andrea Gamba & Lenos Trigeorgis, 2007. "An Improved Binomial Lattice Method for Multi-Dimensional Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 453-475.
    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. Jarno Talponen & Minna Turunen, 2022. "Option pricing: a yet simpler approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 57-81, June.
    2. 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.
    3. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    4. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, December.
    5. Felipe Isaza Cuervo & Sergio Botero Boterob, 2014. "Aplicación de las opciones reales en la toma de decisiones en los mercados de electricidad," Estudios Gerenciales, Universidad Icesi, November.
    6. Vipul Kumar Singh, 2016. "Pricing and hedging competitiveness of the tree option pricing models: Evidence from India," Journal of Asset Management, Palgrave Macmillan, vol. 17(6), pages 453-475, October.
    7. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    8. Kyoung-Sook Moon & Hongjoong Kim, 2013. "A multi-dimensional local average lattice method for multi-asset models," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 873-884, May.
    9. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    10. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "When Is Time Continuous?," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 3, pages 71-102, World Scientific Publishing Co. Pte. Ltd..
    11. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "American options with stochastic dividends and volatility: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 53-92.
    12. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    13. Constantinides, George M. & Jackwerth, Jens Carsten & Perrakis, Stylianos, 2005. "Option pricing: Real and risk-neutral distributions," CoFE Discussion Papers 05/06, University of Konstanz, Center of Finance and Econometrics (CoFE).
    14. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, May.
    15. 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..
    16. Carlos Andrés Zapata Quimbayo, 2020. "OPCIONES REALES Una guía teórico-práctica para la valoración de inversiones bajo incertidumbre mediante modelos en tiempo discreto y simulación de Monte Carlo," Books, Universidad Externado de Colombia, Facultad de Finanzas, Gobierno y Relaciones Internacionales, number 138, April.
    17. Ruas, João Pedro & Dias, José Carlos & Vidal Nunes, João Pedro, 2013. "Pricing and static hedging of American-style options under the jump to default extended CEV model," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4059-4072.
    18. Barr, Kanlaya Jintanakul, 2009. "The implied volatility bias and option smile: is there a simple explanation?," ISU General Staff Papers 200901010800002026, Iowa State University, Department of Economics.
    19. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
    20. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.

    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:1705.00212. 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.