[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.
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- [Geometric Lévy Process & MEMM] Pricing Model and Related Estimation Problems
Asia-Pacific Financial Markets
Volume 8, Issue 1 , pp 45-60
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- estimation of stochastic process
- geometric Lévy process
- incomplete markets
- minimal entropy martingale measure
- pricing model
- Industry Sectors
- Yoshio Miyahara (1)
- Author Affiliations
- 1. Faculty of Economics, Nagoya City University, Mizuhochou, Mizuhoku, Nagoya, 467-8501, Japan