Numerical solution of generalized Black-Scholes model

This paper presents a numerical scheme that approximates the option prices for different option styles, governed by the generalized Black-Scholes equation in its degenerate form. The proposed method uses the HODIE scheme in the spacial direction and the two-step backward differentiation formula in the temporal direction. It is proved that the method has second order convergence in space as well as in time. Numerical experiments validate the theoretical results.