Valuation of American passport option using a three-time level scheme

An American passport option whose contingent claim is dependent on the balance of a trading account can be valued by solving a Hamilton-Jacobi-Bellman equation with free boundary. Here, we present the pricing problem for American passport option, as a sequence of linear complementarity problems, using the three-time level finite difference scheme, which typically is suitable for non-smooth payoffs and also applicable in case of large temporal grid size. The option price is obtained through this scheme for the non-symmetric case (when the risk-free rate is different from the cost of carry). It is observed that the numerical approach presented, results in solving the pricing problem using lesser number of grid points as compared to numerical approaches for this problem used previously while maintaining the accuracy of the prices obtained.