Abstract

In this article the [Geometric L\'evy Process \& MEMM] pricing model is proposed. This model is an option pricing model for the incomplete markets, and this model is based on the assumptions that the price processes are geometric L\'evy  processes and that the prices of the options are determined by the minimal relative entropy methods. 
 
  This model has many good points. For example, the theoretical part of the model is contained in the framework of the theory of L\'evy process (additive process). In fact the price process is also a L\'evy process (with changed L\'evy measure) under the minimal relative entropy martingale measure (MEMM), and so the calculation of the prices of options are reduced to the computation of functionals of L\'evy process. 
  
  In previous papers, we have investigated these models in the case of jump type geometric L\'evy  processes. In this paper we extend the previous results for more general type of geometric L\'evy  processes. 
  

In order to apply this model to real option pricing problems, we have to estimate the price process of the underlying asset. This problem is reduced to the estimation problem of the characteristic triplet of L\'evy processes. We investigate this problem in the latter half of the paper.

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Key words: incomplete markets, pricing model, geometric L\'evy process, minimal entropy martingale measure, estimation of stochastic process.