We introduce a new Monte Carlo method for constructing the exercise boundary of an American option in a generalized Black-Scholes framework. Based on a known exercise boundary, it is shown how to price and hedge the American option by Monte Carlo simulation of suitable probabilistic...

For evaluating a hedging strategy we have to know at every instant the solution of the Cauchy problem for a parabolic equation (the value of the hedging portfolio) and its derivatives (the deltas). We suggest to find these magnitudes by Monte Carlo simulation of the corresponding system of...