American options with stochastic dividends and volatility: A nonparametricinvestigation

In this paper, we consider American option contracts when the underlying as set has stochastic dividends and stochastic volatility. We provide a full d iscussion of the theoretical foundations of American option valuation and e xercise boundaries. We show how they depend on the various sources of uncer tainty which drive dividend rates and volatility, and derive equilibrium as set prices, derivative prices and optimal exercise boundaries in a general equilibrium model. The theoretical models identify the relevant factors und erlying option prices but yield fairly complex expressions which are diffic ult to estimate. We therefore adopt a nonparametric approach in order to in vestigate the reduced forms suggested by the theory. Indeed, we use nonpara metric methods to estimate call prices and exercise boundaries conditional on dividends and volatility. Since the latter is a latent process, we propo se several approaches, notably using EGARCH filtered estimates, implied and historical volatilities. The nonparametric approach allows us to test whet her call prices and exercise decisions are primarily driven by dividends, a s has been advocated by Harvey and Whaley (1992a. Journal of Financial Econ omics 30, 33-73; 1992b. Journal of Futures Markets 12, 123-137) and Fleming and Whaley (1994. Journal of Finance 49, 215-236) for the OEX contract, or whether stochastic volatility complements dividend uncertainty. We find th at dividends alone do not account for all aspects of option pricing and exe rcise decisions, suggesting a need to include stochastic volatility. (C) 20 00 Elsevier Science S.A. All rights reserved. JEL classification: C14; C51; D52; G13.