One often wants to value a risky payoff by reference to prices of other assets rather than by exploiting full‐fledged economic models. However, this approach breaks down if one cannot find a perfect replicating portfolio. We impose weak economic restriction to derive usefully tight bounds on asset prices in this situation. The bounds assume that investors would want to buy assets with high Sharpe ratios‐“good deals”‐as well as pure arbitrage opportunities. We show how to calculate the price bounds in one‐period, multiperiod, and continuous‐time contexts. We show that the multiperiod problem can be solved recursively as a sequence of one‐period problems. We calculate bounds in option pricing examples including infrequent trading and an option written on a nontraded event, and we use the bounds to explore the economic significance of option pricing predictions. We find that much variation in S&P 500, index option prices over time and across strike prices fits within the bounds.

We present a consumption‐based model that explains a wide variety of dynamic asset pricing phenomena, including the procyclical variation of stock prices, the long‐horizon predictability of excess stock returns, and the countercyclical variation of stock market volatility. The model captures much of the history of stock prices from consumption data. It explains the short‐and long‐run equity premium puzzles despite a low and constant risk‐free rate. The results are essentially the same whether we model stocks as a claim to the consumption stream or as a claim to volatile dividends poorly corelated with consumption. The model is driven by an independently and identically distributed consumption growth process and adds a slow ‐moving external habit to the standard power utility function. These features generate slow countercyclical variation in risk premia. The model posits a fundamentally novel description of risk premia. Investors fear stocks primarily because they do poorly in recessions unrelated to the risks of long‐run average consumption growth.

We solve a model with two i.i.d. Lucas trees. Although the corresponding one-tree model produces a constant price-dividend ratio and i.i.d. returns, the two-tree model produces interesting asset-pricing dynamics. Investors want to rebalance their portfolios after any change in value. Because the size of the trees is fixed, prices must adjust to offset this desire. As a result, expected returns, excess returns, and return volatility all vary through time. Returns display serial correlation and are predictable from price-dividend ratios. Return volatility differs from cash-flow volatility, and return shocks can occur without news about cash flows.