Christophe Profeta's Books

Option Prices as Probabilities

A New Look at Generalized Black-Scholes Formulae

By: Christophe Profeta,Bernard Roynette,Marc Yor

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Option Prices as Probabilities

A New Look at Generalized Black-Scholes Formulae

By: Christophe Profeta,Bernard Roynette,Marc Yor

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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282

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Springer Science & Business Media

Published Date

ISBN 10

3642103952

ISBN 13

9783642103957

Peacocks and Associated Martingales, with Explicit Constructions

By: Francis Hirsch,Christophe Profeta,Bernard Roynette,Marc Yor

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Peacocks and Associated Martingales, with Explicit Constructions

By: Francis Hirsch,Christophe Profeta,Bernard Roynette,Marc Yor

We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings. They are developed in eight chapters, with about a hundred of exercises.

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412

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Springer Science & Business Media

Published Date

ISBN 10

8847019087

ISBN 13

9788847019089

Option Prices as Probabilities

A New Look at Generalized Black-Scholes Formulae

By: Christophe Profeta,Bernard Roynette,Marc Yor

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Option Prices as Probabilities

A New Look at Generalized Black-Scholes Formulae

By: Christophe Profeta,Bernard Roynette,Marc Yor

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Page Count

282

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642103952

ISBN 13

9783642103957

Peacocks and Associated Martingales, with Explicit Constructions

By: Francis Hirsch,Christophe Profeta,Bernard Roynette,Marc Yor

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Peacocks and Associated Martingales, with Explicit Constructions

By: Francis Hirsch,Christophe Profeta,Bernard Roynette,Marc Yor

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412

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Springer Science & Business Media

Published Date

ISBN 10

8847019087

ISBN 13

9788847019089

Most Excellent Way

An Essay On

By: Christophe Chalamet

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Most Excellent Way

An Essay On

By: Christophe Chalamet

Faith, hope, and love are the three core realities of Christian existence. Reflecting on the meaning these three realities have for us today, Christophe Chalamet argues that we gain a deeper understanding of them as we consider them in their interrelation, rather than separately.

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196

Published Date

ISBN 10

1978707800

ISBN 13

9781978707801

Gospel

By: Jean-Christophe Chaumette

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Gospel

By: Jean-Christophe Chaumette

À la mort de son père, médecin dans le delta du Mississippi, un riche chirurgien hérite d'une valise remplie de notes et de bandes magnétiques, qui constituent divers témoignages sur l'existence des Noirs dans le Sud des États-Unis juste avant la Grande Dépression. De ces documents émerge la geste d'un chanteur et guitariste itinérant, interprète de blues et de spirituals. Trois hommes, un musicien, un pasteur et un talent scout employé par une maison de disques, racontent chacun à leur manière son histoire, que le chirurgien complètera lui-même en allant écouter une vieille femme noire dans une maison de retraite. Ainsi prend forme la vie de Manson, songster touché par la grâce, faiseur de miracles et ennemi des bien-pensants, dont nul ne sait rien avant la battle of songs qu'il remporte contre John le Baptiste. Autour de lui s’agrège un orchestre disparate qui sillonne les routes du delta. Certains de ses membres essaient simplement de survivre, d’autres rêvent de gloire et l’un d’entre eux voudrait bouleverser la société. Mais aucun ne comprend qui est réellement Manson ou ne distingue la voie sur laquelle il cherche à les guider, du moins jusqu’à l’achèvement de son destin. Chaque chapitre comporte une illustration noir et blanc et le livre est associé à une bande son que vous pouvez découvrir sur deezer. Cet epub est un peu lourd du fait de la présence des illustrations intérieures. Merci de votre compréhension.

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Page Count

141

Publisher

Editions Voy'el

Published Date

ISBN 10

2364752868

ISBN 13

9782364752863

Book's by Christophe Profeta

Option Prices as Probabilities

Option Prices as Probabilities

Peacocks and Associated Martingales, with Explicit Constructions

Peacocks and Associated Martingales, with Explicit Constructions

Option Prices as Probabilities

Option Prices as Probabilities

Peacocks and Associated Martingales, with Explicit Constructions

Peacocks and Associated Martingales, with Explicit Constructions

Most Excellent Way

Most Excellent Way

Gospel

Gospel

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