Pricing multi-asset American-style options by memory reduction Monte Carlo methods

When pricing American-style options on d assets by Monte Carlo methods, one usually stores 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 d · M · N. In this paper, we give a simulation method to price multi-asset American-style options, where the storage requirement only grows like (d + 1)M + N. 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 the options.