A novel numerical scheme for a time fractional Black–Scholes equation

This paper consists of two parts. On one hand, the regularity of the solution of the time-fractional Black–Scholes equation is investigated. On the other hand, to overcome the difficulty of initial layer, a modified L 1 time discretization is presented based on a change of variable. And the spatial discretization is done by using the Chebyshev Galerkin method. Optimal error estimates of the fully-discrete scheme are obtained. Finally, several numerical results are given to confirm the theoretical results.