Study and Evaluation of a European Option by Heston Model

In this work we propose an approximate numerical method for an option pricing by the Heston model. First we prove the existence and uniqueness of the solution in a weighted Sobolev space, and then we propose the finite element and finite difference methods to solve the considered problem. Therefore, we compare the obtained results for the two approaches, with those by the Monte Carlo method in Broadie-Kaya. To show the efficiency of the numerical approaches, we use different values of the interest rate and show improvements in the results for the convergence and cputime