Measurement of Market Integration and Arbitrage

Closely-integrated markets should assign to similar payoffs prices that are close. This is the idea on which a measurement theory of market integration is developed in this paper. Two markets are said to be perfectly integrated in the weak sense if there is at least one stochastic discount factor that is shared by both markets. Then, the weak integration measure is conveniently defined to be the minimum distance between the respective sets of admissible stochastic discount factors for two markets. This measure is zero if and only if the markets are perfectly integrated in the weak sense, i.e., they assign to similar payoffs prices that are arbitrarily close. The smaller the measure, the more closely-integrated the two markets. In addition, two markets are said to be perfectly integrated in the strong sense if no arbitrage opportunity exists across them. Correspondingly, the strong integration measure is defined to be the minimum distance between the respective sets of non-negative stochastic discount factors for the two markets, and it reflects the extent that arbitrage profits are possible between the markets. The measurement theory can be applied to test market integration without relying on any parametric asset pricing models