Abstract
This paper develops a procedure for modeling the optimal exercise patterns and for determining the value of employee stock options. I develop an approximate dynamic programming (ADP) procedure and show how ADP can be used instead of traditional backward dynamic programming to solve the single stock option problem. I show how ADP can be extended to solve a high dimensional problem numerically that allows for a portfolio of heterogeneous options while using a CRRA utility function. I then demonstrate that the exercise of an option depends importantly on the payouts of the previous exercises.
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