[This article proposes to price an American option by approximating its early exercise boundary as a multipiece exponential function. Closed form formulas are obtained in terms of the bases and exponents of the multipiece exponential function. It is demonstrated that a three-point extrapolation scheme has the accuracy of an 800-time-step binomial tree, but is about 130 times faster. An intuitive argument is given to indicate why this seemingly crude approximation works so well. Our method is very simple and easy to implement. Comparisons with other leading competing methods are also included.]

This article proposes to price an American option by approximating its early exercise boundary as a multipiece exponential function. Closed form formulas are obtained in terms of the bases and exponents of the multipiece exponential function. It is demonstrated that a three-point extrapolation scheme has the accuracy of an 800-time-step binomial tree, but is about 130 times faster. An intuitive argument is given to indicate why this seemingly crude approximation works so well. Our method is very simple and easy to implement. Comparisons with other leading competing methods are also included.

We propose a novel generalized recursive smooth ambiguity model which permits a three-way separation among risk aversion, ambiguity aversion, and intertemporal substitution. We apply this utility model to a consumption-based asset-pricing model in which consumption and dividends follow hidden Markov regime-switching processes. Our calibrated model can match the mean equity premium, the mean risk-free rate, and the volatility of the equity premium observed in the data. In addition, our model can generate a variety of dynamic asset-pricing phenomena, including the procyclical variation of price–dividend ratios, the countercyclical variation of equity premia and equity volatility, the leverage effect, and the mean reversion of excess returns. The key intuition is that an ambiguity-averse agent behaves pessimistically by attaching more weight to the pricing kernel in bad times when his continuation values are low.

While stock options are commonly used in managerial compensation to provide desirable incentives, they can create adverse incentives to distort the choice of investment risk. Relative to the risk level that maximizes firm value, call options in a compensation contract can induce too much or too little corporate risk-taking, depending on managerial risk aversion and the underlying investment technology. We show that inclusion of lookback call options in compensation packages has desirable countervailing effects on managerial choice of corporate risk policies and can induce risk policies that increase shareholder wealth. We argue that lookback call options are analogous to the observed practice of option repricing.

The treatment of this article renders closed-form density approximation feasible for univariate continuous-time models. Implementation methodology depends directly on the parametric-form of the drift and the diffusion of the primitive process and not on its transformation to a unit-variance process. Offering methodological convenience, the approximation method relies on numerically evaluating one-dimensional integrals and circumvents existing dependence on intractable multidimensional integrals. Density-based inferences can now be drawn for a broader set of models of equity volatility. Our empirical results provide insights on crucial outstanding issues related to the rank-ordering of continuous-time stochastic volatility models, the absence or presence of nonlinearities in the drift function, and the desirability of pursuing more flexible diffusion function specifications.

This paper examines optimal capital structure choice using a dynamic capital structure model that is calibrated to reflect actual firm characteristics. The model uses contingent claim methods to value interest tax shields, allows for reorganization in bankruptcy, and maintains a long-run target debt to total capital ratio by refinancing maturing debt. Using this model, we calculate optimal capital structures in a realistic representation of the traditional trade-off model. In contrast to previous research, the calculated optimal capital structures do not imply that firms tend to use too little leverage in practice. We also estimate the costs borne by a firm whose capital structure deviates from its optimal target debt to total capital ratio. The costs of moderate deviations are relatively small, suggesting that a policy of adjusting leverage infrequently is likely to be reasonable for many firms.