The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model

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dc.availability.bitstreamopenaccess
dc.contributor.advisorKelly, Conallen
dc.contributor.authorMaulana, Heru
dc.contributor.funderIndonesia Endowment Fund for Education (LPDP)en
dc.date.accessioned2022-09-12T13:14:43Z
dc.date.available2022-09-12T13:14:43Z
dc.date.issued2022-07-04
dc.date.submitted2022-07-04
dc.description.abstractWe demonstrate the effectiveness of an adaptive explicit Euler method for the approximate solution of the Cox-Ingersoll-Ross model. This relies on a class of path-bounded timestepping strategies which work by reducing the stepsize as solutions approach a neighbourhood of zero. The method is hybrid in the sense that a convergent backstop method is invoked if the timestep becomes too small, or to prevent solutions from overshooting zero and becoming negative. Under parameter constraints that imply Feller’s condition, we prove that such a scheme is strongly convergent, of order at least 1/2. Control of the strong error is important for multi-level Monte Carlo techniques. Under Feller’s condition we also prove that the probability of ever needing the backstop method to prevent a negative value can be made arbitrarily small. Numerically, we compare this adaptive method to fixed step implicit and explicit schemes, and a novel semi-implicit adaptive variant. We observe that the adaptive approach leads to methods that are competitive in a domain that extends beyond Feller’s condition, indicating suitability for the modelling of stochastic volatility in Heston-type asset models.en
dc.description.statusNot peer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationMaulana, H. 2022. The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model. PhD Thesis, University College Cork.en
dc.identifier.endpage48en
dc.identifier.urihttps://hdl.handle.net/10468/13582
dc.language.isoenen
dc.publisherUniversity College Corken
dc.rights© 2022, Heru Maulana.en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectCox–Ingersoll–Ross modelen
dc.subjectAdaptive timesteppingen
dc.subjectExplicit Euler–Maruyama methoden
dc.subjectStrong convergenceen
dc.subjectPositivityen
dc.titleThe role of adaptivity in a numerical method for the Cox-Ingersoll-Ross modelen
dc.typeDoctoral thesisen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD - Doctor of Philosophyen
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