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

David M. Kreps

• Publisher: Cambridge University Press
• Year: 2019
• Print ISBN: 9781108486361
• eBook ISBN: 9781108775502
• Topic: Economics
• Subtopic: Econometrics
• Index: Economics

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.

Table of contents

• Cover
• Half-title page
• Series page
• Title page
• Copyright page
• Contents
• Preface
• 1. Introduction
• 2. Finitely Many States and Times
• 3. Continuous Time and the Black–Scholes–Merton (BSM) Model
• 4. BSM as an Idealization of Binomial-Random-Walk Economies
• 5. General Random-Walk Models
• 6. Barlow’s Example
• 7. The Pötzelberger–Schlumprecht Example and Asymptotic Arbitrage
• 8. Concluding Remarks, Part 1: How Robust an Idealization is BSM?
• 9. Concluding Remarks, Part 2: Continuous-Time Models as Idealizations of Discrete Time
• Appendix
• References
• Author Index
• Subject Index