Beyond Arbitrage: Good‐Deal Asset Price Bounds in Incomplete Markets

Abstract

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.