Compatibility between pricing rules and risk measures: The CCVaR
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.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Economía de la Empresa in its series Business Economics Working Papers with number wb090201.
Date of creation: Jan 2009
Date of revision:
Risk Measure; Pricing Rule; Compatibility; Compatible Conditional Value at Risk;
Find related papers by JEL classification:
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
- G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
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