Enhanced Tilley's bundling algorithm using memory reduction Monte Carlo method

When pricing American-style options by Tilley's bundling algorithm, one has to store the simulated asset prices at all time steps on all paths in order to determine when to exercise the options. If N time steps and M paths are used, then the storage requirement is M · N. In this paper, we improve Tilley's bundling algorithm [6] by applying our backward-path method, which requires only O(M) storage. The only additional computational cost is that we have to generate each random number twice instead of once. For machines with limited memory, we can now use larger values of M and N to improve the accuracy in pricing options.