The Black–Scholes–Merton model as an idealization of discrete-time economies/ David M Kreps

Includes bibliographical references and index

1 - Introduction -- 2 - Finitely Many States and Times -- 3 - Countinuous 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

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.