The damped Crank–Nicolson time-marching scheme for the adaptive solution of the Black–Scholes equation

Christian Goll and Rolf Rannacher and Winnifried Wollner

Journal of Computational Finance

Abstract: ABSTRACT This paper is concerned with the derivation of a residual-based a posteriori error estimator and mesh-adaptation strategies for the space-time finite element approximation of parabolic problems with irregular data. Typical applications arise in the field of mathematical finance, where the Black-Scholes equation is used for modeling the pricing of European options. A conforming finite element discretization in space is combined with second-order time discretization by a damped Crank-Nicolson scheme for coping with data irregularities in the model. The a posteriori error analysis is developed within the general framework of the dual weighted residual method for sensitivity-based, goal-oriented error estimation and mesh optimization. In particular, the correct form of the dual problem with damping is considered.

References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.risk.net/journal-of-computational-fina ... ack-scholes-equation (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:rsk:journ0:2406534

Access Statistics for this article

More articles in Journal of Computational Finance from Journal of Computational Finance
Bibliographic data for series maintained by Thomas Paine ().