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Finite-dimensional Markovian realizations for stochastic volatility forward-rate models
KTH, Superseded Departments, Mathematics.
2004 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 460, no 2041, 53-83 p.Article in journal (Refereed) Published
Abstract [en]

We consider forward-rate models of Heath-Jarrow-Morton type, as well as more general infinite-dimensional stochastic differential equations, where the volatility-diffusion term is stochastic in the sense of being driven by a separate hidden Markov process. Within this framework, we use the previously developed Hilbert-space-realization theory in order to provide general necessary and sufficient conditions for the existence of a finite-dimensional Markovian realization for the stochastic volatility models. We illustrate the theory by analysing a number of concrete examples.

Place, publisher, year, edition, pages
2004. Vol. 460, no 2041, 53-83 p.
Keyword [en]
HJM models, stochastic volatility, factor models, forward rates, state, space models, Markovian realizations, interest-rate dynamics, term structure, existence
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-23086DOI: 10.1098/rspa.2003.1235ISI: 000187988200004Scopus ID: 2-s2.0-12144289724OAI: oai:DiVA.org:kth-23086DiVA: diva2:341784
Note
QC 20100525 QC 20111031Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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