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ABSTRACT
Monte Carlo Simulation of an American Option
We implement gradient estimation techniques for sensitivity analysis
of option pricing which can be efficiently employed in Monte Carlo
simulation. Using these techniques we can simultaneously obtain an
estimate of the option value together with the estimates of
sensitivities of the option value to various parameters of the model.
After deriving the gradient estimates we incorporate
them in an iterative stochastic approximation algorithm for pricing an
option with early exercise features. We illustrate the procedure using
an example of an American call option with a single dividend that is
analytically tractable. In particular we incorporate estimates for the
gradient with respect to the early exercise threshold level.
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