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

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

A time-space hedging theory


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