RESEARCH PAPER NO. 832

MARKETS THAT DON'T REPLICATE ANY OPTION

by

CHARALAMBOS D. ALIPRANTIS & RABEE TOURKY

JANUARY 2002

Department of Economics. University of Melbourne. Melbourne Victoria 3010 Australia

ABSTRACT

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 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.

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