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Evaluation of Options using the Black-Scholes Methodology

Author

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  • Vasile BRÄ‚TIAN

    (Lucian Blaga University Sibiu, Romania)

Abstract

This paper discusses how to obtain the Black-Scholes equation to evaluate options and how to obtain explicit solutions for Call and Put. The Black-Scholes equation, which is the basis for determining explicit solutions for Call and Put, is a rather sophisticated equation. It is a partial differential equation of the second order, parabolic, similar to the heat equation. The terms of the equation express diffusion in a homogeneous environment, convection and reaction. The main objective of the paper is to present the Black-Scholes methodology and apply this methodology on the underlying asset of the nature of the listed stock on the Bucharest Stock Exchange. Also, a secondary objective is to compare the results obtained in this paper with our results in an article where we determined the values for Call and Put by Monte Carlo simulation.

Suggested Citation

  • Vasile BRÄ‚TIAN, 2019. "Evaluation of Options using the Black-Scholes Methodology," Expert Journal of Economics, Sprint Investify, vol. 7(2), pages 59-65.
    • Handle: RePEc:exp:econcs:v:7:y:2019:i:2:p:59-65
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    References listed on IDEAS

    as
    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    2. U. Çetin & R. Jarrow & P. Protter & M. Warachka, 2008. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 9, pages 185-221, World Scientific Publishing Co. Pte. Ltd..
    3. Nicole El Karoui & Monique Jeanblanc‐Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126, April.
    4. Haug, Espen Gaarder & Taleb, Nassim Nicholas, 2011. "Option traders use (very) sophisticated heuristics, never the Black-Scholes-Merton formula," Journal of Economic Behavior & Organization, Elsevier, vol. 77(2), pages 97-106, February.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. 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.
    7. MacBeth, James D & Merville, Larry J, 1979. "An Empirical Examination of the Black-Scholes Call Option Pricing Model," Journal of Finance, American Finance Association, vol. 34(5), pages 1173-1186, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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