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.

We study the incentive effects of granting levered or unlevered stock to a risk-averse manager. The stock is granted by risk-neutral shareholders who choose leverage and compensation level. The manager applies costly effort and selects the level of volatility, both of which affect expected return. The results are driven by the attempt of the risk-neutral shareholders to maximize the value of their claims net of the compensation package. We consider a dynamic setting and find that levered stock is optimal for high-type managers, firms with high momentum, large firms, and firms for which additional volatility only implies a modest increase in expected return.