IDEAS home Printed from https://ideas.repec.org/a/ibf/beaccr/v5y2013i1p1-16.html

An Exposition On The Mathematics And Economics Of Option Pricing

Author

Listed:
  • Luke Miller
  • Mark Bertus

Abstract

The application of options pricing theory to value irreversible investment decisions has witnessed a marked increase over the last decade. For instructional and simplified applications, the Black-Scholes model is commonly demonstrated due to its tractability and acceptance in the finance community. This paper provides a detailed mathematical exposition of the Black-Scholes model. The main contribution of this paper is the step-by-step instructional account of the Black-Scholes model that can be used directly in the classroom to introduce stochastic calculus, arbitrage-free valuation, and option-pricing theory. In contrast with most Black-Scholes derivations found in the pedagogical literature, this paper develops the fair option price from an economic equilibrium perspective. Through this approach, it is hoped the reader will comprehend both the mathematics and economics underlying option pricing theory, as both are equally important.

Suggested Citation

  • Luke Miller & Mark Bertus, 2013. "An Exposition On The Mathematics And Economics Of Option Pricing," Business Education and Accreditation, The Institute for Business and Finance Research, vol. 5(1), pages 1-16.
    • Handle: RePEc:ibf:beaccr:v:5:y:2013:i:1:p:1-16
    as

    Download full text from publisher

    File URL: http://www.theibfr2.com/RePEc/ibf/beaccr/bea-v5n1-2013/BEA-V5N1-2013-1.pdf
    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. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893, January.
    3. repec:bla:jfinan:v:43:y:1988:i:5:p:1235-56 is not listed on IDEAS
    4. Fischer, Stanley, 1978. "Call Option Pricing when the Exercise Price Is Uncertain, and the Valuation of Index Bonds," Journal of Finance, American Finance Association, vol. 33(1), pages 169-176, March.
    5. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    6. Madan, Dilip B & Milne, Frank & Shefrin, Hersh, 1989. "The Multinomial Option Pricing Model and Its Brownian and Poisson Limits," The Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 251-265.
    7. 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..
    8. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    9. 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.
    10. 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.
    11. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    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. 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.
    2. 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.
    3. Yepes Rodri­guez, Ramón, 2008. "Real option valuation of free destination in long-term liquefied natural gas supplies," Energy Economics, Elsevier, vol. 30(4), pages 1909-1932, July.
    4. Otto Konstandatos & Timothy J Kyng, 2012. "Real Options Analysis for Commodity Based Mining Enterprises with Compound and Barrier Features," Published Paper Series 2012-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    5. Philipp N. Baecker, 2007. "Real Options and Intellectual Property," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-48264-2, March.
    6. Schachter, J.A. & Mancarella, P., 2016. "A critical review of Real Options thinking for valuing investment flexibility in Smart Grids and low carbon energy systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 56(C), pages 261-271.
    7. 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.
    8. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, March.
    9. 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, March.
    10. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," JRFM, MDPI, vol. 13(12), pages 1-33, December.
    11. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," Papers 2011.08343, arXiv.org.
    12. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    13. Kung, James J. & Lee, Lung-Sheng, 2009. "Option pricing under the Merton model of the short rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 378-386.
    14. Zmeskal, Zdenek, 2010. "Generalised soft binomial American real option pricing model (fuzzy-stochastic approach)," European Journal of Operational Research, Elsevier, vol. 207(2), pages 1096-1103, December.
    15. Akamatsu, Takashi & Nagae, Takeshi, 2011. "A network of options: Evaluating complex interdependent decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 714-729, May.
    16. Yoram Landskroner & Alon Raviv, 2008. "The valuation of inflation‐indexed and FX convertible bonds," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(7), pages 634-655, July.
    17. Raffaele Oriani & Luigi Sereno, 2011. "Advanced Valuation Methods: The Real Options Approach," Chapters, in: Federico Munari & Raffaele Oriani (ed.), The Economic Valuation of Patents, chapter 6, Edward Elgar Publishing.
    18. Zdenìk Zmeškal, 2008. "Application of the American Real Flexible Switch Options Methodology A Generalized Approach," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 58(05-06), pages 261-275, August.
    19. Scholes, Myron S, 1998. "Derivatives in a Dynamic Environment," American Economic Review, American Economic Association, vol. 88(3), pages 350-370, June.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • A22 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Undergraduate
    • A23 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Graduate
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G00 - Financial Economics - - General - - - General
    • M19 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Other

    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:ibf:beaccr:v:5:y:2013:i:1:p:1-16. 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: Mercedes Jalbert The email address of this maintainer does not seem to be valid anymore. Please ask Mercedes Jalbert to update the entry or send us the correct address (email available below). General contact details of provider: .

    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.