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

Abstract

It is often useful to price a given asset by reference to observed prices of other assets rather than construct full-fledged economic models that can price any asset. 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 incomplete market 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 single period, multiperiod and continuous time contexts. We calculate bounds for option pricing examples including the Black-Scholes setup with infrequent trading, and a model with stochastic stock volatility and a varying riskfree rate.

JEL Classification: G12, G13