A Monte Carlo approach to American options pricing including counterparty risk

In this work, we propose a numerical technique to compute the total value adjustment for the pricing of American options when considering counterparty risk. Several linear and nonlinear mathematical models, associated to different choices of the mark-to-market value at default, are deduced and numerically solved, thus leading to approximations of the option price with counterparty risk. The methodology is based on Monte Carlo simulations combined with a dynamic programming strategy. At each time step, an optimal stopping criterion is applied and the decision on either exercising or not the option is taken. We present some numerical tests to illustrate the behaviour of the proposed method.