uu.seUppsala University Publications

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Accurate Finite Difference Methods for Option PricingPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2006 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### 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

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##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt446",{id:"formSmash:j_idt446",widgetVar:"widget_formSmash_j_idt446",multiple:true}); Available from: 2006-09-08 Created: 2006-09-08 Last updated: 2011-10-27Bibliographically approved
##### List of papers

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.

1. Pricing European multi-asset options using a space-time adaptive FD-method$(function(){PrimeFaces.cw("OverlayPanel","overlay72209",{id:"formSmash:j_idt495:0:j_idt499",widgetVar:"overlay72209",target:"formSmash:j_idt495:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Space-time adaptive finite difference method for European multi-asset options$(function(){PrimeFaces.cw("OverlayPanel","overlay38494",{id:"formSmash:j_idt495:1:j_idt499",widgetVar:"overlay38494",target:"formSmash:j_idt495:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. A highly accurate adaptive finite difference solver for the Black–Scholes equation$(function(){PrimeFaces.cw("OverlayPanel","overlay113829",{id:"formSmash:j_idt495:2:j_idt499",widgetVar:"overlay113829",target:"formSmash:j_idt495:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Improved radial basis function methods for multi-dimensional option pricing$(function(){PrimeFaces.cw("OverlayPanel","overlay39614",{id:"formSmash:j_idt495:3:j_idt499",widgetVar:"overlay39614",target:"formSmash:j_idt495:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Pricing turbo warrants$(function(){PrimeFaces.cw("OverlayPanel","overlay106837",{id:"formSmash:j_idt495:4:j_idt499",widgetVar:"overlay106837",target:"formSmash:j_idt495:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Pricing American options using a space-time adaptive finite difference method$(function(){PrimeFaces.cw("OverlayPanel","overlay51350",{id:"formSmash:j_idt495:5:j_idt499",widgetVar:"overlay51350",target:"formSmash:j_idt495:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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