High-order compact finite difference schemes for a nonlinear Black-Scholes equation

Düring, Bertram, Fournié, Michel and Jüngel, Ansgar (2003) High-order compact finite difference schemes for a nonlinear Black-Scholes equation. International Journal of Theoretical and Applied Finance, 6 (7). pp. 767-789. ISSN 0219-0249

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Abstract

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Bertram During
Date Deposited: 06 Feb 2012 21:03
Last Modified: 27 Apr 2012 10:15
URI: http://sro.sussex.ac.uk/id/eprint/29281
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