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An Exposition On The Mathematics And Economics Of Option Pricing

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  • 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
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    References listed on IDEAS

    as
    1. repec:bla:jfinan:v:43:y:1988:i:5:p:1235-56 is not listed on IDEAS
    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. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    4. 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.
    5. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    6. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893, September.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    More about this item

    Keywords

    Options Pricing; Black-Scholes Model; Stochastic Calculus; Pedagogy;
    All these 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

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