Spanning the State Space with Options

In the Arrow-Debreu approach to uncertainty it has been recognized that an inadequate number of markets in contingent claims would be a source of inefficiency. Several researchers have studied the allocative inefficiencies resulting from incomplete markets, i.e., when the number of independent securities is less than the number of states and therefore the state-space cannot be “spanned” by those securities. In a situation where the number of primitive assets is inadequate to span the state-space, the new spanning opportunities opened up by derived assets written on the primitives is an interesting question.