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 |