Master’s dissertation (Dissertations and theses)
Analyse de l’intégration de produits dérivés dans un référentiel rendement-risque
Bodson, Laurent
2006
 

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Abstract :
[en] 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.
Disciplines :
Finance
Author, co-author :
Bodson, Laurent ;  Université de Liège - ULiège > HEC - École de gestion de l'ULiège > Gestion financière
Language :
English
Title :
Analyse de l’intégration de produits dérivés dans un référentiel rendement-risque
Defense date :
06 June 2006
Number of pages :
93
Institution :
ULiège - Université de Liège
Degree :
Grade d’ingénieur de gestion
Promotor :
Hübner, Georges  ;  Université de Liège - ULiège > HEC Recherche > HEC Recherche: Financial Management for the Future
Jury member :
Michel, Pierre-Armand ;  Université de Liège - ULiège > Ecole de Gestion de l'Université de Liège
Bourdoux, Jean-Michel
Available on ORBi :
since 30 March 2009

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