Change search
ReferencesLink to record
Permanent link

Direct link
Spectral Discretizations of Option Pricing Models for European Put Options
Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Mathematical Sciences.
2014 (English)MasteroppgaveStudent thesis
Abstract [en]

The aim of this thesis is to solve option pricing models efficiently by using spectral methods. The option pricing models that will be solved are the Black-Scholes model and Heston's stochastic volatility model. We will restrict us to pricing European put options. We derive the partial differential equations governing the two models and their corresponding weak formulations. The models are then solved using both the spectral Galerkin method and a polynomial collocation method. The numerical solutions are compared to the exact solution. The exact solution is also used to study the numerical convergence. We compare the results from the two numerical methods, and look at the time consumptions of the different methods. Analysis of the methods are also given. This includes coercivity, continuity, stability and convergence estimates. For Black-Scholes equation, we study both the original equation and the log transformed equation, and we also compare the results to a solution obtained by using a finite element method solver.

Place, publisher, year, edition, pages
Institutt for matematiske fag , 2014. , 76 p.
URN: urn:nbn:no:ntnu:diva-26546Local ID: ntnudaim:11035OAI: diva2:748571
Available from: 2014-09-19 Created: 2014-09-19 Last updated: 2014-09-19Bibliographically approved

Open Access in DiVA

fulltext(935 kB)457 downloads
File information
File name FULLTEXT01.pdfFile size 935 kBChecksum SHA-512
Type fulltextMimetype application/pdf
cover(184 kB)5 downloads
File information
File name COVER01.pdfFile size 184 kBChecksum SHA-512
Type coverMimetype application/pdf

By organisation
Department of Mathematical Sciences

Search outside of DiVA

GoogleGoogle Scholar
Total: 457 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 36 hits
ReferencesLink to record
Permanent link

Direct link