Beyond arbitrage: Good-deal asset price bounds in incomplete markets

One often wants to value a risky payoff by reference to prices of other ass ets rather than by exploiting full-fledged economic models. However, this a pproach breaks down if one cannot find a perfect replicating portfolio. We impose weak economic restrictions to derive usefully tight bounds on asset prices in this situation. The bounds assume that investors would want to bu y assets with high Sharpe ratios-"good deals"-as well as pure arbitrage opp ortunities. We show how to calculate the price bounds in one-period, multip eriod, and continuous-time contexts. We show that the multiperiod problem c an be solved recursively as a sequence of one-period problems. We calculate bounds in option pricing examples including infrequent trading and an opti on written on a nontraded event, and we use the bounds to explore the econo mic significance of option pricing predictions. We find that much variation in S&P 500 index option prices over time and across strike prices fits wit hin the bounds.