'Institute of Electrical and Electronics Engineers (IEEE)'
Doi
Abstract
Broadie and Glasserman proposed a
simulation-based method they named {\em stochastic mesh} for pricing
high-dimensional American options. Based on simulated states of the
assets underlying the option at each exercise opportunity, the
method produces an estimator of the option value at each sampled state.
Under the mild assumption of the finiteness of certain moments,
we derive an asymptotic upper bound on the probability of error
of the mesh estimator, where both the error size and the probability bound
vanish as the sample size increases.
We include the empirical performance
for the test problems used by Broadie and Glasserman in a recent unpublished
manuscript. We find that the mesh estimator
has large bias that decays very slowly with the sample size, suggesting that
in applications it will most likely be necessary to employ bias and/or
variance reduction techniques