Variational inequalities applied to option market problem

Since the classic work of Black and Scholes [F. Black, M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973) 354–637] many techniques to calculate the value of European option have been developed. When we are interested in assessing the American option, these techniques must change to adapt to the early exercise possibility. To solve the American options problem, we obtain an inequality variational system and use numerical methods over it. This work aims to get the put American option price using the finite elements method and finite differences method. Numerical results are presented.