The original Black-Scholes (BS) [2] European call option pricing model does not take account of divided payments on the underlying stock and does not allow for the possibility of early exercise that may be optimal when the stock pays dividends. Black [1] has suggested that the original BS model can be modified to take account of dividends and Sharpe [14] predicts that this modified or pseudo-American BS approach, “while not exact, is probably sufficient for many listed options.”

The Sharpe-Lintner Capital Asset Pricing Model (CAPM) has always contained an implicit question: what if all investors are single-period wealth maximizers but the length of the single period varies across investors? Gressis, Philappatos, and Hayya (GPH) [7] have pointed out that as the assumption of investment horizon length is changed, the Capital Market Line (CML) intersects the Efficient Frontier (EF) at different points causing different investors to hold different efficient portfolios. GPH assert that these different portfolio holdings will result in an inefficient market portfolio—and dire consequences for the capital market model.

Black and Scholes [1] derived the pricing equation for a European put when the stock price follows geometric Brownian motion. For this same case, Merton [5] derived the pricing equation for an American put with infinite time to maturity. Brennan and Schwartz [2], Rubinstein and Cox [7], and Parkinson [6] have developed numerical solutions for the price of an American put. Numerical solutions are expensive and do not provide much intuition. Naturally, an analytic solution would be much preferred; unfortunately, pricing the American put requires solving a formidable and presumably intractable boundary value problem.

Recently, the finance literature has included empirical analysis of consumption in asset pricing models based on the cross-equation restrictions implied by optimality of a representative agent's consumption and investment plan. These studies have required some specification of an aggregate utility function, and power (constant relative risk aversion) utility has been predominant. The present paper extends this body of research by including models with constant absolute, as well as constant relative, risk aversion.