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Titlebook: Option Prices as Probabilities; A New Look at Genera Cristophe Profeta,Bernard Roynette,Marc Yor Book 2010 Springer-Verlag Berlin Heidelber

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書目名稱Option Prices as Probabilities
副標(biāo)題A New Look at Genera
編輯Cristophe Profeta,Bernard Roynette,Marc Yor
視頻videohttp://file.papertrans.cn/704/703373/703373.mp4
概述To the best of our knowledge this book discusses in a unique way last passage times.Includes supplementary material:
叢書名稱Springer Finance
圖書封面Titlebook: Option Prices as Probabilities; A New Look at Genera Cristophe Profeta,Bernard Roynette,Marc Yor Book 2010 Springer-Verlag Berlin Heidelber
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
關(guān)鍵詞Azéma supermartingale; Black-Scholes; Black-Scholes Formulae; Finite Horizon; Last passages times; Martin
版次1
doihttps://doi.org/10.1007/978-3-642-10395-7
isbn_softcover978-3-642-10394-0
isbn_ebook978-3-642-10395-7Series ISSN 1616-0533 Series E-ISSN 2195-0687
issn_series 1616-0533
copyrightSpringer-Verlag Berlin Heidelberg 2010
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Existence and Properties of Pseudo-Inverses for Bessel and Related Processes,ework, starting with the case of Bessel (and some related) processes. We show in particular that the tail probabilities of a Bessel process of index .≥1/2 increase with respect to time; in fact it is the distribution function of a random time which is related to first and last passage times of Besse
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Existence of Pseudo-Inverses for Diffusions,We shall focus here on increasing pseudo-inverses, and we shall deal with two cases: . More precisely, we shall prove that, to a positive diffusion . starting from 0, we can associate another diffusion . such that the tail probabilities of . are the distribution functions of the last passage times o
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Book 2010t? 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
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Book 2010p. 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 ? ?
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Study of Last Passage Times up to a Finite Horizon,the ?.-measurable random time: . and write the analogues of formulae (1.20) and (1.21) for these times .. This will lead us to the interesting notion of past-future martingales, which we shall study in details in Section 5.2.
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