In this paper, we consider as an inverse problem the simultaneous estimation
of the five parameters of a jump diffusion process from return observations of a
price trajectory. We show that there occur some ill-posedness phenomena in the
parameter estimation problem, because the forward operator fails to be injective
and small perturbations in the data may lead to large changes in the solution. We
illustrate the instability effect by a numerical case study. To overcome the difficulty
coming from ill-posedness we use a multi-parameter regularization approach that
finds a trade-off between a least-squares approach based on empircal densities and
a fitting of semi-invariants. In this context, a fixed point iteration is proposed that
provides good results for the example under consideration in the case study.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18198 |
| Date | 25 August 2004 |
| Creators | Düvelmeyer, Dana, Hofmann, Bernd |
| Publisher | Technische Universität Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:lecture, info:eu-repo/semantics/lecture, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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