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Bernstein’s inequalities and their extensions for getting the Black–Scholes option pricing formula

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  • Glazyrina, Anna
  • Melnikov, Alexander

Abstract

In this paper we show how the results of Bernstein (1943) and recent results of Zubkov and Serov (2012) on the normal approximation to the binomial distribution lead to an alternative derivation of the Black–Scholes formula from a binomial option pricing model.

Suggested Citation

  • Glazyrina, Anna & Melnikov, Alexander, 2016. "Bernstein’s inequalities and their extensions for getting the Black–Scholes option pricing formula," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 86-92.
    • Handle: RePEc:eee:stapro:v:111:y:2016:i:c:p:86-92
    DOI: 10.1016/j.spl.2016.01.002
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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. San-Lin Chung & Pai-Ta Shih, 2007. "Generalized Cox-Ross-Rubinstein Binomial Models," Management Science, INFORMS, vol. 53(3), pages 508-520, March.
    3. Lo-Bin Chang & Ken Palmer, 2007. "Smooth convergence in the binomial model," Finance and Stochastics, Springer, vol. 11(1), pages 91-105, January.
    4. 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.
    5. 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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