High order compact finite difference schemes for a nonlinear Black-Scholes equation - Bertram Düring; Michel Fournié; Ansgar Jüngel (University of Konstanz, Center of Finance and Econometrics (CoFE), 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 e±cient than the considered classical schemes.
urn:nbn:de:bsz:352-opus-7191
Keywords: 330; Option pricing; transaction costs; parabolic equations; compact finite difference discretizations; Black-Scholes-Modell; Nichtlineare Optimierung; Hedging; Transaktionskosten; Theorie