High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation
University of Konstanz Center of Finance and Econometrics Discussion Paper No. 01/07
28 Pages Posted: 26 Mar 2004
Date Written: November 24, 2001
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. In particular, the compact schemes of Rigal are generalized. 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, compact finite difference discretizations
JEL Classification: G13
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