MONTE CARLO VALUATION OF AMERICAN OPTIONS THROUGH COMPUTATION OF THE OPTIMAL EXERCISE FRONTIER

This paper introduces a Monte Carlo simulation method for pricing multidimensional American options. The method is based on the computation of the optimal exercise frontier. It is simple, efficient and flexible, suitable for multidimensional options. We consider options that can be exercised at a finite number of points, and compute the points of the exercise frontier recursively. We introduce an algorithm that converges very quickly to the value of the optimal exercise frontier.For multidimensional options, we fix the values of all the paramethers but one (usually the underlying security) and compute the value of the underlying at the optimal exercise frontier. Since the method converges very quickly, it is relatively fast (at least for low-dimensional options) to construct a grid for the frontier. One of the advantages of computing the optimal exercise frontier is that it can be used in subsequent computations that will only require application of plain vanilla Monte Carlo simulationThe method also allows a quick computation of the hedging portfolio. We present examples and we compare the numbers we get to other existing papers and show that at a low computational cost our results are as good as the best with the advantage that we simultaneously compute the optimal exercise frontier (which will simplify further any subsequent computations).