High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation

Bertram Düring, Michel Fournié () and Ansgar Jüngel ()
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Michel Fournié: UMR-CNRS 5640, Laboratoire MIP, Université Paul Sabatier, Toulouse 3, 31062 Toulouse Cedex, France
Ansgar Jüngel: Fachbereich Mathematik und Informatik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2003, vol. 06, issue 07, 767-789

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.

Keywords: Option pricing; transaction costs; parabolic equations; high order; compact finite difference discretizations (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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Working Paper: High order compact finite difference schemes for a nonlinear Black-Scholes equation (2001)
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DOI: 10.1142/S0219024903002183

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