Analyse de l’intégration de produits dérivés dans un référentiel rendement-risque

We present a model which aims at integrating derivatives into a portfolio management tool, taking into account the first four moments of the distributions of the assets it analyzes. We propose a new approach by regarding any optional asset as a portfolio made up of four basic assets which duplicates perfectly its payments. In order to preserve the first four moments of the distributions of the basic assets, we build the quadrinomial trees of their future evolution. In addition to the tree of the underlying asset calibrated on its historical values and the tree of the riskless asset, we build the quadrinomial trees of two European-style puts to fill out our market (Ross, 1976). We force the risk-neutral probabilities to be nonnegative in order to correct the trees of the two additional options and exclude arbitrage opportunities created by their valuation using the Black and Scholes formula (1973). We build the quadrinomial tree of the optional asset according to these risk-neutral probabilities. We determine, starting from the trees produced, the sensitivities (deltas) of the optional asset with respect to each one of its basic assets over the first period of the tree. These values allow us to deduct the weight of each basic asset in the replication portfolio. We then obtain a linear function between the optional asset’s return and the returns of its basic assets. We calculate the moments and co-moments of the historical returns of each basic asset to establish the moments of the optional asset, and in addition its co-moments with the market. We then present a concrete implementation of the model and three of its potential applications: the calculation of the VaR of an optional asset, the creation of a portfolio with guaranteed capital and the integration of an optional asset into an unspecified portfolio.

Grantor dc:publisher

ULiège - Université de Liège

Year dc:date

2006

Author dc:creator

• Bodson, Laurent

Contributors dc:contributor

• Hübner, Georges

• Business & economic sciences
• Finance
• Sciences économiques & de gestion

Statement dc:rights

• restricted access
• info:eu-repo/semantics/restrictedAccess

Licence

• http://purl.org/coar/access_right/c_16ec

Language dc:language

en

Identifier

info:hdl:2268/9995

OAI identifier oai:identifier

oai:orbi.ulg.ac.be:2268/9995