Fitted strong stability-preserving schemes for the Black-Scholes-Barenblatt equation

We solve numerically a fully nonlinear Black–Scholes problem of Bellman type. The algorithm is focused on the so-called Delta greek, the first spatial derivative of the option price. Since the elliptic operator degenerates on the boundary we use a fitted finite volume discretization in space. Strong stability-preserving time-marching is further applied in accordance to the nonlinear nature of the differential problem. Numerical experiments validate our considerations.