Numerical solution of the Black-Scholes equation using finite element methods
| dc.contributor.author | Anderson, Tyler, author | |
| dc.contributor.author | Bangerth, Wolfgang, advisor | |
| dc.contributor.author | Aristoff, David, committee member | |
| dc.contributor.author | Wang, Tianyang, committee member | |
| dc.date.accessioned | 2023-06-01T17:27:05Z | |
| dc.date.available | 2023-06-01T17:27:05Z | |
| dc.date.issued | 2023 | |
| dc.description.abstract | The Black-Scholes model is a well known model for pricing financial options. This model takes the form of a partial differential equation (PDE) that, surprisingly, is deterministic. In the special case where the option only has one single underlying asset, what is called the one dimensional version of the Black-Scholes model, there exists an analytical solution. In higher dimensions, however, there is no such analytical solution. This higher dimensional version refers to what is called a Basket-Case Option. This means that to get a solution to this Basket-Case Option PDE, one must employ numerical methods. This thesis will first discuss the stochastic calculus theory necessary to derive the Black-Scholes model, then will explain in detail the time and space discretization used to solve the PDE using a Finite Element Method (FEM). Finally, this thesis will explain some of the results and convergence of this numerical solution. | |
| dc.format.medium | born digital | |
| dc.format.medium | masters theses | |
| dc.identifier | Anderson_colostate_0053N_17639.pdf | |
| dc.identifier.uri | https://hdl.handle.net/10217/236575 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2020- | |
| dc.rights | Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. | |
| dc.title | Numerical solution of the Black-Scholes equation using finite element methods | |
| dc.type | Text | |
| dcterms.rights.dpla | This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science (M.S.) |