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

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

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  • ISBN:9781108707657
  • Editorial: Cambridge University Press
  • Fecha de la edición:
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  • Nº Pág.:214
  • Idiomas:Ingles

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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

1. Introduction
2. Finitely many states and dates
3. Countinuous time and the Black-Scholes-Merton (BSM) Model
4. BSM as an idealization of binomial-random-walk economies
5. Random walks that are not binomial
6. Barlow's example
7. The Pötzelberger-Schlumprecht example and asymptotic arbitrage
8. Concluding remarks, Part I: how robust an idealization is BSM?
9. Concluding remarks, Part II: continuous-time models as idealizations of discrete time
Appendix.

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