Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Closed Formulae for Super-Replication Prices with Discrete Time Strategies


Code(s) de Classification MSC:

Résumé: We consider a financial model with mild conditions on the dynamic of the underlying asset. The trading is only allowed at some fixed discrete times and the strategy is constrained to lie in a closed convex cone. In this context, we derive closed formulae to compute the super-replication prices of any contingent claim which depends on the values of the underlying at the discrete times above. As an application, when the underlying 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.

Mots Clés: Closed formula for Super-replication cost ; convex cone constraints on portfolio ; exotic European and American options

Date: 2001-10-16

Prépublication numéro: PMA-693

Postscript file : PMA-693.ps

Pdf file : PMA-693.pdf