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The Black–Scholes–Merton Model as an Idealization of Discrete-Time Economies

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  • Kreps,David M.

Abstract

This book examines whether continuous-time models in frictionless financial economies can be well approximated by discrete-time models. It specifically looks to answer the question: in what sense and to what extent does the famous Black-Scholes-Merton (BSM) continuous-time model of financial markets idealize more realistic discrete-time models of those markets? While it is well known that the BSM model is an idealization of discrete-time economies where the stock price process is driven by a binomial random walk, it is less known that the BSM model idealizes discrete-time economies whose stock price process is driven by more general random walks. Starting with the basic foundations of discrete-time and continuous-time models, David M. Kreps takes the reader through to this important insight with the goal of lowering the entry barrier for many mainstream financial economists, thus bringing less-technical readers to a better understanding of the connections between BSM and nearby discrete-economies.

Suggested Citation

  • Kreps,David M., 2019. "The Black–Scholes–Merton Model as an Idealization of Discrete-Time Economies," Cambridge Books, Cambridge University Press, number 9781108707657.
    • Handle: RePEc:cup:cbooks:9781108707657
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    Cited by:

    1. Friedrich Hubalek & Walter Schachermayer, 2021. "Convergence of optimal expected utility for a sequence of binomial models," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1315-1331, October.

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