Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 29, No 3, (2003), 271p-290p
We consider the valuation of American options using Monte
Carlo simulation, and propose a new technique which involves approximating
the optimal exercise boundary. Our method involves splitting the boundary
into a linear term and a Fourier series and using stochastic optimization in
the form of a relaxation method to calculate the coefficients in the series.
The cost function used is the expected value of the option using the the
current estimate of the location of the boundary. We present some sample
results and compare our results to other methods.