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.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-7097 |
| Date | January 2006 |
| Creators | Persson, Jonas |
| Publisher | Uppsala universitet, Avdelningen för teknisk databehandling, Uppsala universitet, Numerisk analys, Uppsala : Acta Universitatis Upsaliensis |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Doctoral thesis, comprehensive summary, info:eu-repo/semantics/doctoralThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, 1651-6214 ; 206 |
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