uu.seUppsala universitets publikationer
Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Radial basis function generated finite differences for option pricing problems
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.ORCID-id: 0000-0003-3164-5242
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.
2018 (Engelska)Ingår i: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 75, s. 1462-1481Artikel i tidskrift (Refereegranskat) Published
Ort, förlag, år, upplaga, sidor
2018. Vol. 75, s. 1462-1481
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
URN: urn:nbn:se:uu:diva-336813DOI: 10.1016/j.camwa.2017.11.015ISI: 000428100600024OAI: oai:DiVA.org:uu-336813DiVA, id: diva2:1167155
Projekt
eSSENCETillgänglig från: 2017-12-01 Skapad: 2017-12-18 Senast uppdaterad: 2018-08-21Bibliografiskt granskad
Ingår i avhandling
1. Radial Basis Function generated Finite Difference Methods for Pricing of Financial Derivatives
Öppna denna publikation i ny flik eller fönster >>Radial Basis Function generated Finite Difference Methods for Pricing of Financial Derivatives
2018 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

The purpose of this thesis is to present state of the art in radial basis function generated finite difference (RBF-FD) methods for pricing of financial derivatives. This work provides a detailed overview of RBF-FD properties and challenges that arise when the RBF-FD methods are used in financial applications.

Across the financial markets of the world, financial derivatives such as futures, options, and others, are traded in substantial volumes. Knowing the prices of those financial instruments at any given time is of utmost importance. Many of the theoretical pricing models for financial derivatives can be represented using multidimensional PDEs, which are in most cases analytically unsolvable.

We present RBF-FD as a recent numerical method with the potential to efficiently approximate solutions of PDEs in finance. As its name suggests, the RBF-FD method is of a finite difference (FD) type, from the radial basis function (RBF) group of methods. When used to approximate differential operators, the method is featured with a sparse differentiation matrix, and it is relatively simple to implement — like the standard FD methods. Moreover, the method is mesh-free, meaning that it does not require a structured discretization of the computational domain, and it is of a customizable order of accuracy — which are the features it inherits from the global RBF approximations.

The results in this thesis demonstrate how to successfully apply RBF-FD to different pricing problems by studying the effects of RBF shape parameters for Gaussian RBF-FD approximations, improving the approximation of differential operators in multiple dimensions by using polyharmonic splines augmented with polynomials, constructing suitable node layouts, and smoothing of the initial data to enable high order convergence of the method. Finally, we compare RBF-FD with other available methods on a plethora of pricing problems to form an objective image of the method’s performance.

Future development of RBF-FD is expected to result in a solid mesh-free high order method for multi-dimensional PDEs, that can be used together with dimension reduction techniques to efficiently solve problems of high dimensionality that we often encounter in finance.

Ort, förlag, år, upplaga, sidor
Uppsala: Acta Universitatis Upsaliensis, 2018. s. 63
Serie
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1702
Nyckelord
Radial basis function, Finite difference, Computational finance, Pricing of financial derivatives, Option pricing, Partial differential equation
Nationell ämneskategori
Beräkningsmatematik
Forskningsämne
Beräkningsvetenskap med inriktning mot numerisk analys
Identifikatorer
urn:nbn:se:uu:diva-357220 (URN)978-91-513-0403-8 (ISBN)
Disputation
2018-09-28, ITC 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 10:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2018-09-06 Skapad: 2018-08-14 Senast uppdaterad: 2018-10-02

Open Access i DiVA

Fulltext saknas i DiVA

Övriga länkar

Förlagets fulltext

Personposter BETA

Milovanović, Slobodanvon Sydow, Lina

Sök vidare i DiVA

Av författaren/redaktören
Milovanović, Slobodanvon Sydow, Lina
Av organisationen
Avdelningen för beräkningsvetenskapNumerisk analys
I samma tidskrift
Computers and Mathematics with Applications
Beräkningsmatematik

Sök vidare utanför DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetricpoäng

doi
urn-nbn
Totalt: 221 träffar
RefereraExporteraLänk till posten
Permanent länk

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