Markets that don't replicate any option

It is well known from the work of S. Ross that a securities market is complete if and only if each call option can be replicated using available securities. The present short note announces the following surprising complementary result to Ross' important contribution: If the number of securities is less than half the number of states of the world, then (generically) not a single option can be replicated by traded securities. This provides further strong motivation for relaxing the assumption of a perfect market in the theory of option pricing and portfolio insurance. (C) 2002 Elsevier Science B.V. All rights reserved.