uu.seUppsala universitets publikasjoner
Endre søk
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Radial basis function partition of unity methods for pricing vanilla basket options
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
2016 (engelsk)Inngår i: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 71, s. 185-200Artikkel i tidsskrift (Fagfellevurdert) Published
sted, utgiver, år, opplag, sider
2016. Vol. 71, s. 185-200
HSV kategori
Identifikatorer
URN: urn:nbn:se:uu:diva-272085DOI: 10.1016/j.camwa.2015.11.007ISI: 000369455000012OAI: oai:DiVA.org:uu-272085DiVA, id: diva2:892965
Prosjekter
eSSENCETilgjengelig fra: 2015-12-03 Laget: 2016-01-11 Sist oppdatert: 2017-11-30bibliografisk kontrollert
Inngår i avhandling
1. Radial basis function methods for pricing multi-asset options
Åpne denne publikasjonen i ny fane eller vindu >>Radial basis function methods for pricing multi-asset options
2016 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
Abstract [en]

The price of an option can under some assumptions be determined by the solution of the Black–Scholes partial differential equation. Often options are issued on more than one asset. In this case it turns out that the option price is governed by the multi-dimensional version of the Black–Scholes equation. Options issued on a large number of underlying assets, such as index options, are of particular interest, but pricing such options is a challenge due to the "curse of dimensionality". The multi-dimensional PDE turn out to be computationally expensive to solve accurately even in quite a low number of dimensions.

In this thesis we develop a radial basis function partition of unity method for pricing multi-asset options up to moderately high dimensions. Our approach requires the use of a lower number of node points per dimension than other standard PDE methods, such as finite differences or finite elements, thanks to a high order convergence rate. Our method shows good results for both European style options and American style options, which allow early exercise. For the options which do not allow early exercise, the method exhibits an exponential convergence rate under node refinement. For options that allow early exercise the option pricing problem becomes a free boundary problem. We incorporate two different approaches for handling the free boundary into the radial basis function partition of unity method: a penalty method, which leads to a nonlinear problem, and an operator splitting method, which leads to a splitting scheme. We show that both methods allow for locally high algebraic convergence rates, but it turns out that the operator splitting method is computationally more efficient than the penalty method. The main reason is that there is no need to solve a nonlinear problem, which is the case in the penalty formulation.

sted, utgiver, år, opplag, sider
Uppsala University, 2016
Serie
IT licentiate theses / Uppsala University, Department of Information Technology, ISSN 1404-5117 ; 2016-001
HSV kategori
Forskningsprogram
Beräkningsvetenskap med inriktning mot numerisk analys
Identifikatorer
urn:nbn:se:uu:diva-284306 (URN)
Veileder
Prosjekter
eSSENCE
Tilgjengelig fra: 2016-01-08 Laget: 2016-04-16 Sist oppdatert: 2017-08-31bibliografisk kontrollert
2. Localised Radial Basis Function Methods for Partial Differential Equations
Åpne denne publikasjonen i ny fane eller vindu >>Localised Radial Basis Function Methods for Partial Differential Equations
2018 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

Radial basis function methods exhibit several very attractive properties such as a high order convergence of the approximated solution and flexibility to the domain geometry. However the method in its classical formulation becomes impractical for problems with relatively large numbers of degrees of freedom due to the ill-conditioning and dense structure of coefficient matrix. To overcome the latter issue we employ a localisation technique, namely a partition of unity method, while the former issue was previously addressed by several authors and was of less concern in this thesis.

In this thesis we develop radial basis function partition of unity methods for partial differential equations arising in financial mathematics and glaciology. In the applications of financial mathematics we focus on pricing multi-asset equity and credit derivatives whose models involve several stochastic factors. We demonstrate that localised radial basis function methods are very effective and well-suited for financial applications thanks to the high order approximation properties that allow for the reduction of storage and computational requirements, which is crucial in multi-dimensional problems to cope with the curse of dimensionality. In the glaciology application we in the first place make use of the meshfree nature of the methods and their flexibility with respect to the irregular geometries of ice sheets and glaciers. Also, we exploit the fact that radial basis function methods are stated in strong form, which is advantageous for approximating velocity fields of non-Newtonian viscous liquids such as ice, since it allows to avoid a full coefficient matrix reassembly within the nonlinear iteration.

In addition to the applied problems we develop a least squares radial basis function partition of unity method that is robust with respect to the node layout. The method allows for scaling to problem sizes of a few hundred thousand nodes without encountering the issue of large condition numbers of the coefficient matrix. This property is enabled by the possibility to control the coefficient matrix condition number by the rate of oversampling and the mode of refinement.

sted, utgiver, år, opplag, sider
Uppsala: Acta Universitatis Upsaliensis, 2018. s. 54
Serie
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1600
Emneord
Radial basis function, Partition of unity, Computational finance, Option pricing, Credit default swap, Glaciology, Fluid dynamics, Non-Newtonian flow, Anisotropic RBF
HSV kategori
Forskningsprogram
Beräkningsvetenskap med inriktning mot numerisk analys
Identifikatorer
urn:nbn:se:uu:diva-332715 (URN)978-91-513-0157-0 (ISBN)
Disputas
2018-01-19, ITC 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 10:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2017-12-14 Laget: 2017-11-21 Sist oppdatert: 2018-03-08

Open Access i DiVA

fulltext(613 kB)135 nedlastinger
Filinformasjon
Fil FULLTEXT01.pdfFilstørrelse 613 kBChecksum SHA-512
7081780c3b6d47813a0ad397b343e4d6f74e6f81b728bdfc628e28ef9567d962f70bb280b6949422aedf70abae2d83c35cc8d50759b5264024c6814e960b0139
Type fulltextMimetype application/pdf

Andre lenker

Forlagets fulltekst

Personposter BETA

Shcherbakov, VictorLarsson, Elisabeth

Søk i DiVA

Av forfatter/redaktør
Shcherbakov, VictorLarsson, Elisabeth
Av organisasjonen
I samme tidsskrift
Computers and Mathematics with Applications

Søk utenfor DiVA

GoogleGoogle Scholar
Totalt: 135 nedlastinger
Antall nedlastinger er summen av alle nedlastinger av alle fulltekster. Det kan for eksempel være tidligere versjoner som er ikke lenger tilgjengelige

doi
urn-nbn

Altmetric

doi
urn-nbn
Totalt: 439 treff
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf