We develop a measurement theory of market integration, based on two notions of “integrated markets”. First, two markets cannot be perfectly integrated in any sense if one can construct two portfolios, one from each market, that have identical payoffs but different prices. In that case, the law of one price is violated across the markets. Second, they cannot be integrated in a stronger sense if there are cross-market arbitrage opportunities. Two measures of market integration are developed, respectively reflecting these notions. The smaller the measures, the more closely integrated (in the respective senses) the markets. Among other things, they are interpreted as measuring pricing discrepancy between markets.

Substantial progress has been made in developing more realistic option pricing models. Empirically, however, it is not known whether and by how much each generalization improves option pricing and hedging. We fill this gap by first deriving an option model that allows volatility, interest rates and jumps to be stochastic. Using S&P 500 options, we examine several alternative models from three perspectives: (1) internal consistency of implied parameters/volatility with relevant time‐series data, (2) out‐of‐sample pricing, and (3) hedging. Overall, incorporating stochastic volatility and jumps is important for pricing and internal consistency. But for hedging, modeling stochastic volatility alone yields the best performance.