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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60G15 Gaussian processes
- 90A09 Finance, portfolios, investment

**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*