| 书目名称 | Option Prices as Probabilities | | 副标题 | A New Look at Genera | | 编辑 | Cristophe Profeta,Bernard Roynette,Marc Yor | | 视频video | | | 概述 | To the best of our knowledge this book discusses in a unique way last passage times.Includes supplementary material: | | 丛书名称 | Springer Finance | | 图书封面 |  | | 描述 | Discovered in the seventies, Black-Scholes formula continues to play a central role in Mathematical Finance. We recall this formula. Let (B ,t? 0; F ,t? 0, P) - t t note a standard Brownian motion with B = 0, (F ,t? 0) being its natural ?ltra- 0 t t tion. Let E := exp B? ,t? 0 denote the exponential martingale associated t t 2 to (B ,t? 0). This martingale, also called geometric Brownian motion, is a model t to describe the evolution of prices of a risky asset. Let, for every K? 0: + ? (t) :=E (K?E ) (0.1) K t and + C (t) :=E (E?K) (0.2) K t denote respectively the price of a European put, resp. of a European call, associated with this martingale. Let N be the cumulative distribution function of a reduced Gaussian variable: x 2 y 1 ? 2 ? N (x) := e dy. (0.3) 2? ?? The celebrated Black-Scholes formula gives an explicit expression of? (t) and K C (t) in terms ofN : K ? ? log(K) t log(K) t ? (t)= KN ? + ?N ? ? (0.4) K t 2 t 2 and ? ? | | 出版日期 | Book 2010 | | 关键词 | Azéma supermartingale; Black-Scholes; Black-Scholes Formulae; Finite Horizon; Last passages times; Martin | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-10395-7 | | isbn_softcover | 978-3-642-10394-0 | | isbn_ebook | 978-3-642-10395-7Series ISSN 1616-0533 Series E-ISSN 2195-0687 | | issn_series | 1616-0533 | | copyright | Springer-Verlag Berlin Heidelberg 2010 |
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发表于 2025-3-21 17:22:13
