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

Examines whether continuous-time models in frictionless financial economies can be well approximated by discrete-time models.

David M. Kreps (Author)

9781108707657, Cambridge University Press

Paperback / softback, published 19 September 2019

214 pages, 7 b/w illus. 1 table
22.8 x 15.3 x 1.2 cm, 0.32 kg

'Continuous-time finance involves conceptual and technical complexities, which are often swept under the rug when the material is taught to economists. This book cuts through the complexities while providing excellent economic intuition and insight. It helps the reader develop a deeper appreciation of the foundations of modern finance theory, and of the connections between continuous- and discrete-time models in economics more generally.' Dimitri Vayanos, Professor of Finance, London School of Economics and Political Science

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.

Subject Areas: Finance & accounting [KF], Econometrics [KCH]