Monte Carlo Euler approximations of HJM term structure financial models

Handle URI:
http://hdl.handle.net/10754/562421
Title:
Monte Carlo Euler approximations of HJM term structure financial models
Authors:
Björk, Tomas; Szepessy, Anders; Tempone, Raul ( 0000-0003-1967-4446 ) ; Zouraris, Georgios E.
Abstract:
We present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on Itô stochastic differential equations in infinite dimensional spaces, and prove strong and weak error convergence estimates. The weak error estimates are based on stochastic flows and discrete dual backward problems, and they can be used to identify different error contributions arising from time and maturity discretization as well as the classical statistical error due to finite sampling. Explicit formulas for efficient computation of sharp error approximation are included. Due to the structure of the HJM models considered here, the computational effort devoted to the error estimates is low compared to the work to compute Monte Carlo solutions to the HJM model. Numerical examples with known exact solution are included in order to show the behavior of the estimates. © 2012 Springer Science+Business Media Dordrecht.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Stochastic Numerics Research Group
Publisher:
Springer Nature
Journal:
BIT Numerical Mathematics
Issue Date:
22-Nov-2012
DOI:
10.1007/s10543-012-0410-4
ARXIV:
arXiv:1204.1733
Type:
Article
ISSN:
00063835
Sponsors:
This work has been partially supported by: The Swedish National Network in Applied Mathematics (NTM) 'Numerical approximation of stochastic differential equations' (NADA, KTH), The EU-TMR project HCL # ERBFMRXCT960033, UdelaR and UdeM in Uruguay, The Swedish Research Council for Engineering Science (TFR) Grant#222-148, The VR project 'Effektiva numeriska metoder for stokastiska differentialekvationer med tillampningar' (NADA, KTH), the European Union's Seventh Framework Programme (FP7-REGPOT-2009-1) under grant agreement no. 245749 'Archimedes Center for Modeling, Analysis and Computation' (University of Crete, Greece), The University of Crete (Sabbatical Leave of the fourth author), and The King Abdullah University of Science and Technology (KAUST). The third author is a member of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.
Additional Links:
http://arxiv.org/abs/arXiv:1204.1733v1
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBjörk, Tomasen
dc.contributor.authorSzepessy, Andersen
dc.contributor.authorTempone, Raulen
dc.contributor.authorZouraris, Georgios E.en
dc.date.accessioned2015-08-03T10:37:36Zen
dc.date.available2015-08-03T10:37:36Zen
dc.date.issued2012-11-22en
dc.identifier.issn00063835en
dc.identifier.doi10.1007/s10543-012-0410-4en
dc.identifier.urihttp://hdl.handle.net/10754/562421en
dc.description.abstractWe present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on Itô stochastic differential equations in infinite dimensional spaces, and prove strong and weak error convergence estimates. The weak error estimates are based on stochastic flows and discrete dual backward problems, and they can be used to identify different error contributions arising from time and maturity discretization as well as the classical statistical error due to finite sampling. Explicit formulas for efficient computation of sharp error approximation are included. Due to the structure of the HJM models considered here, the computational effort devoted to the error estimates is low compared to the work to compute Monte Carlo solutions to the HJM model. Numerical examples with known exact solution are included in order to show the behavior of the estimates. © 2012 Springer Science+Business Media Dordrecht.en
dc.description.sponsorshipThis work has been partially supported by: The Swedish National Network in Applied Mathematics (NTM) 'Numerical approximation of stochastic differential equations' (NADA, KTH), The EU-TMR project HCL # ERBFMRXCT960033, UdelaR and UdeM in Uruguay, The Swedish Research Council for Engineering Science (TFR) Grant#222-148, The VR project 'Effektiva numeriska metoder for stokastiska differentialekvationer med tillampningar' (NADA, KTH), the European Union's Seventh Framework Programme (FP7-REGPOT-2009-1) under grant agreement no. 245749 'Archimedes Center for Modeling, Analysis and Computation' (University of Crete, Greece), The University of Crete (Sabbatical Leave of the fourth author), and The King Abdullah University of Science and Technology (KAUST). The third author is a member of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.en
dc.publisherSpringer Natureen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1204.1733v1en
dc.subjectA posteriori error estimatesen
dc.subjectA priori error estimatesen
dc.subjectBond marketen
dc.subjectHJM modelen
dc.subjectMonte Carlo methodsen
dc.subjectOption priceen
dc.subjectStochastic differential equationsen
dc.titleMonte Carlo Euler approximations of HJM term structure financial modelsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentStochastic Numerics Research Groupen
dc.identifier.journalBIT Numerical Mathematicsen
dc.contributor.institutionInstitutionen för Finansiell Ekonomi, Handelshögskolan, Box 6501, 11 383 Stockholm, Swedenen
dc.contributor.institutionMatematiska Institutionen, Kungl. Tekniska Högskolan, 100 44 Stockholm, Swedenen
dc.contributor.institutionDepartment of Mathematics, University of Crete, 714 09 Heraklion, Greeceen
dc.identifier.arxividarXiv:1204.1733en
kaust.authorTempone, Raulen
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