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Cubature on Wiener Space for the Heath--Jarrow--Morton framework
Mälardalen University, School of Education, Culture and Communication.
2019 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

This thesis established the cubature method developed by Gyurkó & Lyons (2010) and Lyons & Victor (2004) for the Heath–Jarrow–Morton (HJM) model. The HJM model was first proposed by Heath, Jarrow, and Morton (1992) to model the evolution of interest rates through the dynamics of the forward rate curve. These dynamics are described by an infinite-dimensional stochastic equation with the whole forward rate curve as a state variable. To construct the cubature method, we first discretize the infinite dimensional HJM equation and thereafter apply stochastic Taylor expansion to obtain cubature formulae. We further used their results to construct cubature formulae to degree 3, 5, 7 and 9 in 1-dimensional space. We give, a considerable step by step calculation regarding construction of cubature formulae on Wiener space.

Place, publisher, year, edition, pages
2019. , p. 50
Keywords [en]
Heath–Jarrow–Morton model, stochastic Taylor expansion, Cubature formulae, Brownian signature, forward rate.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-42804OAI: oai:DiVA.org:mdh-42804DiVA, id: diva2:1292190
Subject / course
Mathematics/Applied Mathematics
Presentation
2019-02-01, U3-083, Västerås, 10:15 (English)
Supervisors
Examiners
Available from: 2019-02-28 Created: 2019-02-27 Last updated: 2019-02-28Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf