Optimal exercise frontier of Bermudan options by simulation methods

In this paper, a novel algorithm for determining the free exercise boundary for high-dimensional Bermudan option problems is presented. First, a rough estimate of the boundary is constructed on a fine (daily) time grid. This rough estimate is used to generate a more accurate estimate on a coarse time grid (exercise opportunities). Antithetic branching is used to reduce the computational workload. The method is validated by comparing it with other methods of solving the standard Black-Scholes problem. Finally, the method is applied to two cases of Bermudan options with a second stochastic variable: a stochastic interest rate and a stochastic volatility.