Efficient Complete Markets Are the Rule Rather than the Exception
Código: WPE – 352
José Heleno Faro
When the nancial market has frictions there must be multiple or ambiguous risk-neutral probabilities. By providing a complete characterization of pricing rules of nancial markets with a nite number of assets over a given state space, we are able to describe how we can recover an underlying nancial market structure related to any nitely generated pricing rule. We provide a novel characterization for the set of efcient securities (that is, chosen by at least one rational expected utility agent) revealed by any valuation rule, which allows us to propose two meaningful notions of completeness: while a unique underlying complete market means that it is possible to replicate any position by trading efcient securities, the case of an underlying efcient complete market means that all nancial positions are replicable and efcient. Our main result shows that efcient complete markets (with bid-ask spreads) is the prevalent case that emerges from the universe of all nitely generated pricing rules. Furthermore, any failure of efcient completeness requires valuation rules associate to sets of probabilities allowing disagreement about null events. In particular, the assumption of a Savagian state space almost precludes incompleteness. Journal of Economic Literature Classication Number: D52, D53. Key words: Efciency; pricing rules; risk-neutral probabilities; asset pricing; bid-ask spreads; complete markets; incompleteness.