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Calibration de modèles financiers par minimisation d'entropie relative et modèles avec sauts

Laurent Nguyen 
Abstract : The smile observed in option markets is the evidence of the deficiency of the Black and Scholes model. With the necessity to find a more relevant model of financial assets comes the requirement of its calibration. This is the subjetc of the present work.
A calibration technique of financial models, based on the minimization of relative entropy, has been recently suggested in the framework of Monte carlo. We have proved the convergence and stability of this technique and extended the results to criteria more general than relative entropy. The martingale constraint on the underlying necessary to insure No Free Lunch has been examined from the point of view of moment problems.
In the second part we have considered a simple model of crashes by introducing jumps in the volatily process. The quadratic risk has benn computed and approximate close formulae of the smile have been obtained for the calibration.
Finally we have used the relative entropy criterion to calibrate the jump intensity of a jump diffusion model. The stability of this method has been proved by means of optimal control techniques combined with the implicit function theorem.
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Submitted on : Monday, April 5, 2004 - 6:02:32 PM
Last modification on : Monday, March 21, 2016 - 5:49:44 PM
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  • HAL Id : tel-00005766, version 1



Laurent Nguyen. Calibration de modèles financiers par minimisation d'entropie relative et modèles avec sauts. Modélisation et simulation. Ecole des Ponts ParisTech, 2003. Français. ⟨tel-00005766⟩



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