Geometric Lévy Process & MEMM] Pricing Model and Related Estimation Problems

Abstract

In this article the [Geometric Levy Process & MEMM] pricingmodel is proposed. This model is an option pricing model for theincomplete markets, and this model is based on the assumptions that theprice processes are geometric Levy processes and that the pricesof the options are determined by the minimal relative entropy methods.This model has many good points. For example, the theoretical part ofthe model is contained in the framework of the theory of Levyprocess (additive process). In fact the price process is also aLevy process (with changed Levy measure) under the minimalrelative entropy martingale measure (MEMM), and so the calculation ofthe prices of options are reduced to the computation of functionals ofLevy process. In previous papers, we have investigated thesemodels in the case of jump type geometric Levy processes. In thispaper we extend the previous results for more general type of geometricLevy processes. In order to apply this model to real optionpricing problems, we have to estimate the price process of theunderlying asset. This problem is reduced to the estimation problem ofthe characteristic triplet of Levy processes. We investigate thisproblem in the latter half of the paper.