The Black–Scholes–Merton Model as an Idealization of Discrete-Time Economies (Econometric Society Monographs, Series Number 63)

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. Cover Front Matter Econometric Society Monograph Series The Black–Scholes–Merton Modelas an Idealization of Discrete-Time Economies Copyright 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 P ̈otzelberger–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. Two Equivalent Ways to Represent a Field of Events for a Finite State Space References Author Index Subject Index Econometric Society Monograph Series (continued from page ii) "I began this monograph (which, at the time, was a nascent paper) with the objective of understandinghow and how well continuous-time models of economic phenomena - and in particular models that employ Brownian motion - relate to "near by" discrete-time models. We know by examples that the connections are sometimes not altogether obvious; see, for instance, Fudenberg and Levine (2009) and Sadzik and Stacchetti (2015). So, it seemed to me, a general theory connecting the two types of models ought to be available"-- Provided by publisher This book examines whether continuous-time models in frictionless financial economies can be well approximated by discrete-time models. Mainstream financial economists and economic theorists who want to understand important ideas and results from the highly mathematical literature of financial mathematics will find this book an invaluable aid.