Forward Indifference Valuation of American Options

We analyze the valuation of American options under the forward performance criterion introduced by Musiela and Zariphopoulou (2008). In this framework, the performance criterion 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. We also study the marginal forward performance price, which is related to the classical marginal utility 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 pricing the claim under the minimal martingale measure.