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Accurate Finite Difference Methods for Option Pricing
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (ndim)
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Stock options are priced numerically using space- and time-adaptive finite difference methods. European options on one and several underlying assets are considered. These are priced with adaptive numerical algorithms including a second order method and a more accurate method. For American options we use the adaptive technique to price options on one stock with and without stochastic volatility. In all these methods emphasis is put on the control of errors to fulfill predefined tolerance levels. The adaptive second order method is compared to an alternative discretization technique using radial basis functions. This method is not adaptive but shows potential in option pricing for one and several underlying assets. A finite difference method and a Monte Carlo method are applied to a new financial contract called Turbo warrant. A comparison of these two methods shows that for the case considered the finite difference method is superior.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2006. , p. 70
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 206
Keywords [en]
Finite differences, Option pricing, Adaptive methods
National Category
Computational Mathematics
Research subject
Numerical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-7097ISBN: 91-554-6627-3 (print)OAI: oai:DiVA.org:uu-7097DiVA, id: diva2:168713
Public defence
2006-09-29, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2006-09-08 Created: 2006-09-08 Last updated: 2011-10-27Bibliographically approved
List of papers
1. Pricing European multi-asset options using a space-time adaptive FD-method
Open this publication in new window or tab >>Pricing European multi-asset options using a space-time adaptive FD-method
2007 (English)In: Computing and Visualization in Science, ISSN 1432-9360, E-ISSN 1433-0369, Vol. 10, p. 173-183Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-44304 (URN)10.1007/s00791-007-0072-y (DOI)
Available from: 2007-07-06 Created: 2007-09-05 Last updated: 2018-01-11Bibliographically approved
2. Space-time adaptive finite difference method for European multi-asset options
Open this publication in new window or tab >>Space-time adaptive finite difference method for European multi-asset options
2007 (English)In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 53, p. 1159-1180Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-10726 (URN)10.1016/j.camwa.2006.09.014 (DOI)000247425100001 ()
Available from: 2007-04-09 Created: 2007-05-19 Last updated: 2018-01-12Bibliographically approved
3. A highly accurate adaptive finite difference solver for the Black–Scholes equation
Open this publication in new window or tab >>A highly accurate adaptive finite difference solver for the Black–Scholes equation
2009 (English)In: International Journal of Computer Mathematics, ISSN 0020-7160, E-ISSN 1029-0265, Vol. 86, p. 2104-2121Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-85675 (URN)10.1080/00207160802140023 (DOI)000273521800008 ()
Available from: 2008-10-14 Created: 2008-10-29 Last updated: 2018-01-13Bibliographically approved
4. Improved radial basis function methods for multi-dimensional option pricing
Open this publication in new window or tab >>Improved radial basis function methods for multi-dimensional option pricing
2008 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 222, p. 82-93Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-11845 (URN)10.1016/j.cam.2007.10.038 (DOI)000260709500007 ()
Available from: 2007-10-26 Created: 2008-10-01 Last updated: 2018-01-12Bibliographically approved
5. Pricing turbo warrants
Open this publication in new window or tab >>Pricing turbo warrants
2006 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2006-015
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-78924 (URN)
Available from: 2007-09-18 Created: 2007-09-18 Last updated: 2011-11-18Bibliographically approved
6. Pricing American options using a space-time adaptive finite difference method
Open this publication in new window or tab >>Pricing American options using a space-time adaptive finite difference method
2007 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2007-004
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-23576 (URN)
Available from: 2007-02-01 Created: 2009-01-28 Last updated: 2018-01-12Bibliographically approved

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