Estimating State Price Densities Implied by American Options

We propose a new method to estimate state price densities implicit in American-style options. The method involves estimating the parameters of a Gauss-Hermite series expansion and solving a sequence of recursive equations for the early exercise premium. The resulting estimator can capture sudden shifts in density that may occur during financial crises or in response to significant policy events. It also provides an estimate of the early exercise premium that is of independent interest. We illustrate the proposed method using both calibrated simulations and empirical applications. Our findings indicate that the state price densities implied by S&P 500 ETF options can predict future returns up to a one-year horizon for the period 2009–2023. An application to individual stock options suggests that the state price densities have predictive power for future stock returns at both short (one month) and long (one year) horizons. The analysis also reveals a pattern of sign reversal when moving from short to longer horizon predictions.