Computation and sensitivity analysis of the pricing of American call options

摘要

We present a new numerical scheme for the approximate solution of the Black–Scholes partial differential equation describing the pricing of American call options.The corresponding mathematical problem is a free boundary problem for a convection–diffusion equation. The concept of our numerical solution is suitable for sensitivity analysis with respect to all parameters, for which we have used automatic differentiation implemented in the ODE solver LSODA-C.