Abstract
We analyze the American option valuation problem with the forward performance criterion introduced by Musiela and Zariphopoulou (2008). In this framework, utility evolves forward in time without reference to a specific future time horizon. Moreover, risk preferences change with stochastic market conditions, which is natural as investors are clearly more risk averse in economic downtimes. We examine two applications: the valuation of American options with stochastic volatility and the modeling of early exercises of American-style employee stock options. Finally, we introduce the marginal forward performance price introduced by Davis (1997). Among others, we find that, for arbitrary preferences, the marginal forward indifference price is always independent of the investor's wealth and is represented as the claim's risk-neutral price under the minimal martingale measure.
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