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Compatibility between pricing rules and risk measures: the CCVaR

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dc.affiliation.dptoUC3M. Departamento de Economía de la Empresaes
dc.contributor.authorBalbás, Alejandro
dc.contributor.authorBalbás, Raquel
dc.date.accessioned2014-01-20T16:39:23Z
dc.date.available2014-01-20T16:39:23Z
dc.date.issued2009-06
dc.description.abstractThis paper has considered a risk measure? and a (maybe incomplete and/or imperfect) arbitrage-free market with pricing rule p. They are said to be compatible if there are no reachable strategies y such that p (y) remains bounded and ?(y) is close to - 8. We show that the lack of compatibility leads to meaningless situations in financial or actuarial applications. The presence of compatibility is characterized by properties connecting the Stochastic Discount Factor of p and the sub-gradient of ?. Consequently, several examples pointing out that the lack of compatibility may occur in very important pricing models are yielded. For instance the CVaR and the DPT are not compatible with the Black and Scholes model or the CAPM. We prove that for a given incompatible couple (p,?) we can construct a minimal risk measure ?p compatible with p and such that ?p = ? . This result is particularized for the CVaR and the CAPM and the Black and Scholes model. Therefore we construct the Compatible Conditional Value at Risk (CCVaR). It seems that the CCVaR preserves the good properties of the CVaR and overcomes its shortcomings.en
dc.description.sponsorshipResearch partially supported by “RD Sistemas SA”, “Comunidad Autónoma de Madrid” (Spain), Grant s-0505/tic/000230, and “MEyC” (Spain), Grant SEJ2006-15401-C04en
dc.description.statusPublicadoes
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas (RACSAM), 2009, v. 103, n. 2, pp. 251-264es
dc.identifier.issn1578-7303
dc.identifier.publicationfirstpage251
dc.identifier.publicationissue2
dc.identifier.publicationlastpage264
dc.identifier.publicationtitleRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas
dc.identifier.publicationvolume103
dc.identifier.urihttps://hdl.handle.net/10016/18153
dc.identifier.uxxiAR/0000006593
dc.language.isoenges
dc.relation.isversionofhttp://hdl.handle.net/10016/3422
dc.relation.publisherversionhttp://dx.doi.org/10.1007/BF03191906
dc.rights.accessRightsopen accessen
dc.subject.jel91B28
dc.subject.jel91B30
dc.subject.otherRisk measureen
dc.subject.otherPricing ruleen
dc.subject.otherUnbounded optimization problemen
dc.subject.otherCompatibilityen
dc.subject.otherCompatible conditional value at risken
dc.titleCompatibility between pricing rules and risk measures: the CCVaRen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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