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A derivation of the Black-Scholes option pricing model using a central limit theorem argument

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Listed:
  • Rajeshwari Majumdar
  • Phanuel Mariano
  • Lowen Peng
  • Anthony Sisti

Abstract

The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most well-known formulas in mathematical finance. For their discovery, Merton and Scholes have been awarded the 1997 Nobel prize in Economics. The standard method of deriving the Black-Scholes European call option pricing formula involves stochastic differential equations. This approach is out of reach for most students learning the model for the first time. We provide an alternate derivation using the Lindeberg-Feller central limit theorem under suitable assumptions. Our approach is elementary and can be understood by undergraduates taking a standard undergraduate course in probability.

Suggested Citation

  • Rajeshwari Majumdar & Phanuel Mariano & Lowen Peng & Anthony Sisti, 2018. "A derivation of the Black-Scholes option pricing model using a central limit theorem argument," Papers 1804.03290, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1804.03290
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    References listed on IDEAS

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    1. 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..
    2. 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.
    3. Ross,Sheldon M., 2011. "An Elementary Introduction to Mathematical Finance," Cambridge Books, Cambridge University Press, number 9780521192538.
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