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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. This volume gives a representation of the Black-Scholes formula in terms of Brownian last passages times.
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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.
Reading the Black-Scholes Formula in Terms of First and Last Passage Times.- Generalized Black-Scholes Formulae for Martingales, in Terms of Last Passage Times.- Representation of some particular Azéma supermartingales.- An Interesting Family of Black-Scholes Perpetuities.- Study of Last Passage Times up to a Finite Horizon.- Put Option as Joint Distribution Function in Strike and Maturity.- Existence and Properties of Pseudo-Inverses for Bessel and Related Processes.- Existence of Pseudo-Inverses for Diffusions.
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- EditoreSpringer
- Data di pubblicazione2010
- ISBN 10 3642103944
- ISBN 13 9783642103940
- RilegaturaCopertina flessibile
- Numero edizione1
- Numero di pagine292
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Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae (Springer Finance) by Profeta, Christophe [Paperback ]
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Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae (Springer Finance)
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Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae (Springer Finance)
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Descrizione libro Condizione: New. pp. 294. Codice articolo 261375801
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Option Prices as Probabilities
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Springer Berlin Heidelberg Feb 2010
(2010)
ISBN 10: 3642103944
ISBN 13: 9783642103940
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Descrizione libro Taschenbuch. Condizione: 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. Codice articolo 9783642103940
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Option Prices As Probabilities: A New Look at Generalized Black-scholes Formulae
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ISBN 13: 9783642103940
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Descrizione libro Paperback. Condizione: Brand New. 1st edition. 270 pages. 9.25x6.25x0.50 inches. In Stock. Codice articolo x-3642103944
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Descrizione libro Condizione: New. pp. 294 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam. Codice articolo 6504934
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Option Prices as Probabilities : A New Look at Generalized Black-Scholes Formulae
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(2010)
ISBN 10: 3642103944
ISBN 13: 9783642103940
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Descrizione libro Taschenbuch. Condizione: 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. Codice articolo 9783642103940
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