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Itô’s Calculus and the Derivation of the Black–Scholes Option-Pricing Model

In: HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING

Author

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  • George Chalamandaris
  • A. G. Malliaris

Abstract

The purpose of this chapter is to develop certain relatively recent mathematical discoveries known generally as stochastic calculus, or more specifically as Itô’s Calculus and to also illustrate their application in the pricing of options. The mathematical methods of stochastic calculus are illustrated in alternative derivations of the celebrated Black–Scholes–Merton model. The topic is motivated by a desire to provide an intuitive understanding of certain probabilistic methods that have found significant use in financial economics.

Suggested Citation

  • George Chalamandaris & A. G. Malliaris, 2020. "Itô’s Calculus and the Derivation of the Black–Scholes Option-Pricing Model," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 27, pages 1025-1074, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811202391_0027
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    More about this item

    Keywords

    Financial Econometrics; Financial Mathematics; Financial Statistics; Financial Technology; Machine Learning; Covariance Regression; Cluster Effect; Option Bound; Dynamic Capital Budgeting; Big Data;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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