adaptive monte carlo algorithm‎ finite difference method‎ black– scholes model‎

In this paper, a new adaptive Monte Carlo algorithm is proposed to solve ‎the ‎systems ‎of ‎linear ‎algebraic ‎equations ‎arising ‎from‎ the Black–Scholes model ‎to ‎price‎ European and American options. The proposed algorithm offers several advantages over the conventional and previous adaptive Monte Carlo algorithms. The corresponding properties of the algorithm ‎and ‎Convergence ‎theories‎ are discussed and numerical experiments are presented which demonstrate the computational efficiency of the proposed algorithm.‎‎ The results are also compared with other methods.