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

Abstract

One often wants to value a given asset or risky payoff by reference to observed 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 restrictions to derive usefully tight bounds on asset prices in this situation. The bounds basically rule out high Sharpe ratios - "good deals" - as well as arbitrage opportunities. We show how to calculate the price bounds in two-period, multiperiod and continuous time contexts. We show that the multiperiod problem can be solved recursively as a sequence of two-period problems. We calculate bounds in option pricing examples including infrequent trading, an option written on a nontraded event, and in an environment with stochastic stock volatility and a varying riskfree rate.

JEL Classification: G12, G13