| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: In the framework of a continuous-time Black-Scholes economy, the problem of static and dynamic hedging of path-dependent options is systematically studied by means of chaotic time space decompositions: in particular, the results of \cite{IOa}, \cite{IOb} and \cite{IOc} allow (i) to give a general characterization of trading strategies that replicate contingent claims with a given degree of path-dependency, and (ii) to obtain a closed expression for the quadratic risk faced by an investor who (statically) hedges the risk of a contract with a high degree of path-dependency (like a barrier option) merely by means of a portfolio of less complex contingent claims (like vanilla European options). The application of such results to other hedging problems in a Brownian setting is also discussed.
Mots Clés: Hedging ; Path-dependent options ; Quadratic risk ; Time space chaos ; Black-Scholes model
Date: 2001-06-21
Prépublication numéro: PMA-673