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Book
Option prices as probabilities : a new look at generalized Black-Scholes formulae
Authors: --- ---
ISBN: 3642103944 9786612835346 3642103952 1282835343 Year: 2010 Publisher: Heidelberg ; New York : Springer,

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Abstract

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.


Digital
Option Prices as Probabilities : A New Look at Generalized Black-Scholes Formulae
Authors: --- ---
ISBN: 9783642103957 9783642103964 9783642103940 Year: 2010 Publisher: Berlin, Heidelberg Springer

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Abstract

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.


Digital
Peacocks and Associated Martingales, with Explicit Constructions
Authors: --- --- ---
ISBN: 9788847019089 Year: 2011 Publisher: Milano Springer Milan

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Book
Peacocks and Associated Martingales, with Explicit Constructions
Authors: --- --- --- ---
ISBN: 9788847019089 Year: 2011 Publisher: Milano Springer Milan

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Abstract

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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