Maximal submarkets that replicate any option

Polyrakis, IA; Xanthos, F

dc.contributor.author	Polyrakis, IA	en
dc.contributor.author	Xanthos, F	en
dc.date.accessioned	2014-03-01T02:02:25Z
dc.date.available	2014-03-01T02:02:25Z
dc.date.issued	2011	en
dc.identifier.issn	16142446	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29318
dc.subject	Completion by options	en
dc.subject	Positive bases	en
dc.subject	Replication of options	en
dc.subject	Security markets	en
dc.subject	Sublattices	en
dc.title	Maximal submarkets that replicate any option	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s10436-009-0143-9	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s10436-009-0143-9	en
heal.publicationDate	2011	en
heal.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 ε X so that any option written on x is replicated. So we determine also the set of securities with replicated options. © 2009 Springer-Verlag.	en
heal.journalName	Annals of Finance	en
dc.identifier.doi	10.1007/s10436-009-0143-9	en
dc.identifier.volume	7	en
dc.identifier.issue	3	en
dc.identifier.spage	407	en
dc.identifier.epage	423	en