On Trading American Options

Abstract

This paper proves that the optimal exercise time for the holder of an American option depends upon the physical drift of the underlying asset and the utility of the option holder. We illustrate our results by applying them to several families of utility functions, namely the CARA, the HARA, and the expected return. While the option holder maximises his utility, the issuer gains from the difference between the price maximising exercise boundary and the exercise boundary performed by the option holder. We provide the numerical results which describe the effect of the physical drift and the risk aversion on the issuer's expected profit.