[Geometric Lévy Process & MEMM] Pricing Model and Related Estimation Problems
 Yoshio Miyahara
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In this article the [Geometric Lévy 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 Lévy 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 Lévyprocess (additive process). In fact the price process is also aLévy process (with changed Lévy measure) under the minimalrelative entropy martingale measure (MEMM), and so the calculation ofthe prices of options are reduced to the computation of functionals ofLévy process. In previous papers, we have investigated thesemodels in the case of jump type geometric Lévy processes. In thispaper we extend the previous results for more general type of geometricLévy 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 Lévy processes. We investigate thisproblem in the latter half of the paper.
 Title
 [Geometric Lévy Process & MEMM] Pricing Model and Related Estimation Problems
 Journal

AsiaPacific Financial Markets
Volume 8, Issue 1 , pp 4560
 Cover Date
 200103
 DOI
 10.1023/A:1011445109763
 Print ISSN
 13872834
 Online ISSN
 15736946
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 estimation of stochastic process
 geometric Lévy process
 incomplete markets
 minimal entropy martingale measure
 pricing model
 Industry Sectors
 Authors

 Yoshio Miyahara ^{(1)}
 Author Affiliations

 1. Faculty of Economics, Nagoya City University, Mizuhochou, Mizuhoku, Nagoya, 4678501, Japan