The Black–Scholes–Merton Model as an Idealization of Discrete-Time Economies: 63 (Econometric Society Monographs)
Cambridge University Press, 9/19/2019
EAN 9781108486361, ISBN10: 1108486363
Hardcover, 214 pages, 22.9 x 15.2 x 1.6 cm
Language: English
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.