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dc.contributor.authorBjörk, Tomas
dc.contributor.authorSzepessy, Anders
dc.contributor.authorTempone, Raul
dc.contributor.authorZouraris, Georgios E.
dc.date.accessioned2015-08-03T10:37:36Z
dc.date.available2015-08-03T10:37:36Z
dc.date.issued2012-11-22
dc.identifier.citationBjörk, T., Szepessy, A., Tempone, R., & Zouraris, G. E. (2012). Monte Carlo Euler approximations of HJM term structure financial models. BIT Numerical Mathematics. doi:10.1007/s10543-012-0410-4
dc.identifier.issn00063835
dc.identifier.doi10.1007/s10543-012-0410-4
dc.identifier.urihttp://hdl.handle.net/10754/562421
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.
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.
dc.publisherSpringer Nature
dc.relation.urlhttp://arxiv.org/abs/arXiv:1204.1733v1
dc.subjectA posteriori error estimates
dc.subjectA priori error estimates
dc.subjectBond market
dc.subjectHJM model
dc.subjectMonte Carlo methods
dc.subjectOption price
dc.subjectStochastic differential equations
dc.titleMonte Carlo Euler approximations of HJM term structure financial models
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStochastic Numerics Research Group
dc.identifier.journalBIT Numerical Mathematics
dc.contributor.institutionInstitutionen för Finansiell Ekonomi, Handelshögskolan, Box 6501, 11 383 Stockholm, Sweden
dc.contributor.institutionMatematiska Institutionen, Kungl. Tekniska Högskolan, 100 44 Stockholm, Sweden
dc.contributor.institutionDepartment of Mathematics, University of Crete, 714 09 Heraklion, Greece
dc.identifier.arxivid1204.1733
kaust.personTempone, Raul
dc.versionv1
dc.date.posted2012-04-08


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