Fast computational approach to the Delta Greek of non-linear Black-Scholes equations

In this paper, we consider a class of non-linear option pricing models. The focus is on the numerical investigation of Delta equation, where the unknown solution is the first spatial derivative of the option value. We construct and analyze monotone and sign-preserving finite difference schemes for the problems. Newton's and Picard's iterative procedures for solving the non-linear systems of algebraic equations are proposed. On this base, in order to improve the computational efficiency, we develop fast two-grid algorithms. Numerical experiments, using also Richardson extrapolation in time, are discussed in terms of accuracy, convergence and efficiency.