A Class of Financial Products and Models Where Super-replication Prices are Explicit

L. Carassus, E. Gobet and E. Temam
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L. Carassus: Laboratoire de Probabilités et Modèles Aléatoires - Université Paris 7 - Denis Diderot - Case 7012 - 2, place Jussieu - 75251 Paris cedex 05, France
E. Gobet: Laboratoire Jean Kuntzman - ENSIMAG INP Grenoble - BP 53 - 38041 Grenoble cedex 09, France
E. Temam: Laboratoire de Probabilités et Modèles Aléatoires - Université Paris 7 - Denis Diderot - Case 7012 - 2, place Jussieu - 75251 Paris cedex 05, France

Chapter 4 in Stochastic Processes and Applications to Mathematical Finance, 2007, pp 67-84 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe consider a multidimensional financial model with mild conditions on the underlying asset price process. The trading is only allowed at some fixed discrete times and the strategy is constrained to lie in a closed convex cone. We show how the minimal cost of a super hedging strategy can be easily computed by a backward recursive scheme. As an application, when the underlying asset follows a stochastic differential equation including stochastic volatility or Poisson jumps, we compute those super-replication prices for a range of European and American style options, including Asian, Lookback or Barrier Options. We also perform some multidimensional computations.

Keywords: Stochastic Calculus; Mathematical Finance; Insider Trading; Stochastic Control; Real Options; Filtering Model of Credit Risks; Stochastic Growth Models (search for similar items in EconPapers)
Date: 2007
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