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Pricing and hedging of financial derivatives using a posteriori error estimates and adaptive methods for stochastic di¤erential equations.
2010 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 235, 563-592 p.Article in journal (Refereed) Published
Abstract [en]

The efficient and accurate calculation of sensitivities of the price of financial derivatives with respect to perturbations of the parameters in the underlying model, the so-called ‘Greeks’, remains a great practical challenge in the derivative industry. This is true regardless of whether methods for partial differential equations or stochastic differential equations (Monte Carlo techniques) are being used. The computation of the ‘Greeks’ is essential to risk management and to the hedging of financial derivatives and typically requires substantially more computing time as compared to simply pricing the derivatives. Any numerical algorithm (Monte Carlo algorithm) for stochastic differential equations produces a time-discretization error and a statistical error in the process of pricing financial derivatives and calculating the associated ‘Greeks’. In this article we show how a posteriori error estimates and adaptive methods for stochastic differential equations can be used to control both these errors in the context of pricing and hedging of financial derivatives. In particular, we derive expansions, with leading order terms which are computable in a posteriori form, of the time-discretization errors for the price and the associated ‘Greeks’. These expansions allow the user to simultaneously first control the time-discretization errors in an adaptive fashion, when calculating the price, sensitivities and hedging parameters with respect to a large number of parameters, and then subsequently to ensure that the total errors are, with prescribed probability, within tolerance.

Place, publisher, year, edition, pages
2010. Vol. 235, 563-592 p.
Keyword [en]
Sensitivity analysis; Parabolic partial differential equations; Stochastic differential equations; Euler scheme; A posteriori error estimate; Adaptive algorithms; Hedging; Financial derivatives
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-203799DOI: 10.1016/j.cam.2010.06.009OAI: oai:DiVA.org:kth-203799DiVA: diva2:1082593
Note

QC 20170405

Available from: 2017-03-17 Created: 2017-03-17 Last updated: 2017-11-29Bibliographically approved

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Önskog, Thomas
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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf