Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae (Springer Finance Lecture Notes) - Softcover

Profeta, Christophe; Roynette, Bernard; Yor, Marc

9783642103940: Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae (Springer Finance Lecture Notes)

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ISBN 10: 3642103944 ISBN 13: 9783642103940

Verlag: Springer, 2010

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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 ? ?

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The Black-Scholes formula plays a central role in Mathematical Finance; it gives the right price at which buyer and seller can agree with, in the geometric Brownian framework, when strike K and maturity T are given. This yields an explicit well-known formula, obtained by Black and Scholes in 1973.

The present volume gives another representation of this formula in terms of Brownian last passages times, which, to our knowledge, has never been made in this sense.

The volume is devoted to various extensions and discussions of features and quantities stemming from the last passages times representation in the Brownian case such as: past-future martingales, last passage times up to a finite horizon, pseudo-inverses of processes... They are developed in eight chapters, with complements, appendices and exercises.

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Verlag: Springer
Erscheinungsdatum: 2010
Sprache: Englisch
ISBN 10: 3642103944
ISBN 13: 9783642103940
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Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae (Springer Finance)

Yor, Marc

Verlag: Springer, 2010

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Paperback. Zustand: Very Good. The book has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains undamaged. Bestandsnummer des Verk�ufers GOR014317756

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Option Prices as Probabilities

Christophe Profeta|Bernard Roynette|Marc Yor

Verlag: Springer Berlin Heidelberg, 2010

ISBN 10: 3642103944 ISBN 13: 9783642103940

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Kartoniert / Broschiert. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. To the best of our knowledge this book discusses in a unique way last passage timesDiscovered 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 . Bestandsnummer des Verk�ufers 5049227

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Option Prices as Probabilities : A New Look at Generalized Black-Scholes Formulae

Christophe Profeta

Verlag: Springer Berlin Heidelberg, 2010

ISBN 10: 3642103944 ISBN 13: 9783642103940

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Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Bestandsnummer des Verk�ufers 9783642103940

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Option Prices as Probabilities

Christophe Profeta

Verlag: Springer Berlin Heidelberg, Springer Berlin Heidelberg Feb 2010, 2010

ISBN 10: 3642103944 ISBN 13: 9783642103940

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Taschenbuch. Zustand: Neu. Neuware -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 Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 292 pp. Englisch. Bestandsnummer des Verk�ufers 9783642103940

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Option Prices as Probabilities

Christophe Profeta

Verlag: Springer Berlin Heidelberg Feb 2010, 2010

ISBN 10: 3642103944 ISBN 13: 9783642103940

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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 292 pp. Englisch. Bestandsnummer des Verk�ufers 9783642103940

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