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On the term structure of forwards, futures and interest rates
KTH, Superseded Departments, Mathematics.
2001 (English)Doctoral thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH , 2001. , x, 20 p.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 01-OS-01
Keyword [en]
Term structure, Markovian realizations, affine term structures.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-3086ISBN: 993-435766-6 OAI: oai:DiVA.org:kth-3086DiVA: diva2:8839
Public defence
2001-02-16, 00:00 (English)
Note
QC 20100505Available from: 2001-02-14 Created: 2001-02-14 Last updated: 2010-05-05Bibliographically approved
List of papers
1. Bond pricing in a hidden Markov model of the short rate
Open this publication in new window or tab >>Bond pricing in a hidden Markov model of the short rate
2000 (English)In: Finance and Stochastics, ISSN 0949-2984, E-ISSN 1432-1122, Vol. 4, no 4, 371-389 p.Article in journal (Refereed) Published
Abstract [en]

We consider a diffusion type model for the short rate, where the drift and diffusion parameters are modulated by an underlying Markov process. The underlying Markov process is assumed to have a stochastic differential driven by Wiener processes and a marked point process. The model for the short rate thus falls within the category of hidden Markov models. For this model we look at the bond pricing problem. In order to obtain more concrete results we introduce the notion of a semi-affine term structure and give sufficient conditions for the existence of such a term structure. For a special case, when the underlying process is a Markov chain with only two states, we obtain a closed form expression for bond prices. Furthermore we consider the pricing problem when the modulating process can not be directly observed. It turns out that pricing in this context may be viewed as a filtering problem.

Keyword
Bond market, term structure of interest rates, regime shifts, hidden Markov model
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-12540 (URN)10.1007/PL00013526 (DOI)
Note
QC 20100505Available from: 2010-05-05 Created: 2010-05-05 Last updated: 2017-12-12Bibliographically approved
2. Spot price realizations of futures price term structures
Open this publication in new window or tab >>Spot price realizations of futures price term structures
2000 (English)In: AMS Scand 2000: First AMS-Scandinavian International Mathematics Meeting, XXIII Scandinavian Congress of Mathematicians, June 13-16, WMY 2000, Odense, Denmark : Abstracts., Odense: Syddansk Universitet , 2000Conference paper, Published paper (Other academic)
Place, publisher, year, edition, pages
Odense: Syddansk Universitet, 2000
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-12541 (URN)
Note
QC 20100505Available from: 2010-05-05 Created: 2010-05-05 Last updated: 2010-05-05Bibliographically approved
3. On the Term Structure of Futures and Forward Prices
Open this publication in new window or tab >>On the Term Structure of Futures and Forward Prices
2002 (English)In: Mathematical Finance - Bachelier Congress 2000 / [ed] Geman, Helyette, Madan, Dilip, Pliska, Stanley, Vorst, Ton, Springer-Verlag , 2002, 111-150 p.Conference paper, Published paper (Other academic)
Abstract [en]

We investigate the term structure of forward and futures prices for models where the price processes are allowed to be driven by a general marked point process as well as by a multidimensional Wiener process. Within an infinite dimensional HJM-type model for futures and forwards we study the properties of futures and forward convenience yield rates. For finite dimensional factor models, we develop a theory of affine term structures, which is shown to include almost all previously known models. We also derive two general pricing formulas for futures options. Finally we present an easily applicable sufficient condition for the possibility of fitting a finite dimensional futures price model to an arbitrary initial futures price curve, by introducing a time dependent function in the drift term.

Place, publisher, year, edition, pages
Springer-Verlag, 2002
National Category
Mathematics Economics and Business
Identifiers
urn:nbn:se:kth:diva-12542 (URN)
Conference
Mathematical Finance - Bachelier Congress 2000
Note
QC 20100505Available from: 2010-05-05 Created: 2010-05-05 Last updated: 2012-02-14Bibliographically approved
4. On the construction of finite dimensional realizations for nonlinear forward rate models
Open this publication in new window or tab >>On the construction of finite dimensional realizations for nonlinear forward rate models
2002 (English)In: Finance and Stochastics, ISSN 0949-2984, E-ISSN 1432-1122, Vol. 6, no 3, 303-331 p.Article in journal (Refereed) Published
Abstract [en]

We consider interest rate models of Heath-Jarrow-Morton type where the forward rates are driven by a multidimensional Wiener process, and where the volatility structure is allowed to be a smooth functional of the present forward rate curve. In a recent paper [3], Björk and Svensson give necessary and sufficient conditions for the existence of a finite dimensional Markovian state space realization (FDR) for such a forward rate model, and in the present paper we provide a general method for the actual construction of an FDR. We illustrate the method by constructing FDR:s for a number of concrete models. These FDR:s generalize previous results by allowing for a more general volatility structure. Furthermore the dimension of the realizations obtained by using our method is typically smaller than that of the corresponding previously known realizations.

Keyword
HJM models, factor models, forward rates, state space models, Markovian realizations
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-12543 (URN)10.1007/s007800100060 (DOI)
Note
QC 20100505Available from: 2010-05-05 Created: 2010-05-05 Last updated: 2017-12-12Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • de-DE
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  • fi-FI
  • nn-NO
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  • sv-SE
  • Other locale
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Output format
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  • text
  • asciidoc
  • rtf