15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien


Sektion 10 - Angewandte Mathematik, Industrie- und Finanzmathematik
Montag, 17. September 2001, 16.30, Hörsaal 42

 

High Order Compact Schemes for a Nonlinear Black-Scholes equation

Bertram Düring, Universität Konstanz (Koautoren: M. Fournie, A. Jüngel)

Option pricing in markets with transaction costs lead to fully nonlinear Black-Scholes equations with nonlinear volatilities depending on the second derivative of the option price (the 'Gamma'), derived by Barles and Soner in 1998 [1]. The corresponding parabolic problem is solved using high order compact finite difference schemes by extending the compact schemes proposed by Rigal. The compact schemes are compared with classical finite difference schemes (explicit, semi-implicit, Dufort-Frankel), and their properties (stability, non-oscillations) are studied theoretically and numerically. It turns out that the proposed compact scheme is stable and non-oscillatory for a wide range of parameters and gives significantly better accuracy than the other schemes with comparable CPU times.

[1] G. Barles, H.M. Soner: Option Pricing with transaction costs and a nonlinear Black-Scholes equation, Finance Stochast. 2, 369-397, 1998.

E-Mail: Bertram.Duering@uni-konstanz.de
Homepage: www.mathe.uni-konstanz.de/~juengel/team/duering.html


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