Maximal submarkets that replicate any option |
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Authors: | Ioannis A Polyrakis Foivos Xanthos |
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Institution: | (1) Department of City and Regional Planning, University of North Carolina, Chapel Hill, NC 27599-3140, USA |
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Abstract: | In this article we study the replication of options in security markets X with a finite number of states. Specifically, we study the existence of maximal submarkets (subspaces) Y of X so that any option written on the elements of Y is replicated by a marketed asset x of X. So inside these subspaces the pricing problem is simple because any option is priced by the replicating portfolio. Using
the theory of lattice-subspaces and positive bases developed by Polyrakis (Trans Am Math Soc 348:2793–2810, 1996; 351:4183–4203,
1999), we identify the set of all maximal replicated subspaces. In particular, for any maximal replicated subspace we determine
a positive basis of the subspace. Moreover we show that the union of all maximal replicated subspaces is the set of all marketed
securities x ? X{x\in X} so that any option written on x is replicated. So we determine also the set of securities with replicated options. |
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