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

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. INDICE: 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.

• ISBN: 978-1-108-48636-1
• Editorial: Cambridge University Press
• Encuadernacion: Cartoné
• Páginas: 214
• Fecha Publicación: 19/09/2019
• Nº Volúmenes: 1
• Idioma: Inglés