The author proposes and analyses a novel fitted volume numerical method for a degenerate partial differential equation, Black-Scholes-type equation, governing option pricing. The fitting technique is based on the idea proposed by

*D. N. de G. Allen* and

*R. V. Southwell* [Q. J. Mech. Appl. Math. 8, 129–145 (1955;

Zbl 0064.19802)]. The author shows that the system matrix of the discretization scheme is an

$M$-matrix, so that the discretization is monotonic. Then it is formulated as a Petrov-Galerkin finite element method to establish the stability of the method with respect to a discrete energy norm. Author shows that the error of the numerical solution in the energy norm is bounded by

$O\left(h\right)$, where h denotes the mesh parameter. Numerical experiments are performed to demonstrate the effectiveness of the method.