This paper introduces a Monte Carlo simulation method for pricing multidimensional American options based on the computation of the optimal exercise frontier. We consider Bermudan options that can be exercised at a finite number of times and compute the optimal exercise frontier recursively. We show that for every date of possible exercise, any single point of the optimal exercise frontier is a fixed point of a simple algorithm. Once the frontier is computed, we use plain vanilla Monte Carlo simulation to price the option and obtain a low-biased estimator. We illustrate the method with applications to several types of options.

The finance literature documents a relation between labor income and the cross section of stock returns. One possible explanation for this is the hedging decisions of investors with relative wealth concerns. This implies a negative risk premium associated with stock returns correlated with local undiversifiable wealth because investors are willing to pay more for stocks that help their hedging goals. We find evidence that is consistent with these regularities. In addition, we show that the effect varies across geographic areas depending on the size and variability of undiversifiable wealth, proxied by labor income.

We conduct a controlled laboratory experiment in the spirit of Merton (1971), in which subjects dynamically choose their portfolio allocation between a risk-free and risky asset. Using the optimal allocation of an investor with hyperbolic absolute risk aversion (HARA) utility, we fit the experimental choices to characterize the risk profile of our participants. Despite substantial heterogeneity, decreasing absolute risk aversion and increasing relative risk aversion are the predominant types. We also find some evidence of increased risk taking after a gain. Finally, the session level risk attitudes show a different profile than the individual descriptions of risk attitudes.