Copyright © 2010 Christos E. Kountzakis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We combine the theory of finite-dimensional lattice subspaces and the theory of regular values for maps between smooth manifolds in order to study the completion of real asset markets by options. The strike asset of the options is supposed to be a nominal asset. The main result of the paper is like in the case of the completion of a nominal asset market by options that if the strike asset of the options is the riskless asset, then the completion of a real asset market is generically equal to .