Extending pricing rules with general risk functions
AbstractThe paper addresses pricing issues in imperfect and/or incomplete markets if the risk level of the hedging strategy is measured by a general risk function. Convex Optimization Theory is used in order to extend pricing rules for a wide family of risk functions, including Deviation Measures, Expectation Bounded Risk Measures and Coherent Measures of Risk. Necessary and sufficient optimality conditions are provided in a very general setting. For imperfect markets the extended pricing rules reduce the bid-ask spread. The findings are particularized so as to study with more detail some concrete examples, including the Conditional Value at Risk and some properties of the Standard Deviation. Applications dealing with the valuation of volatility linked derivatives are discussed.
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Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 201 (2010)
Issue (Month): 1 (February)
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Web page: http://www.elsevier.com/locate/eor
Incomplete and imperfect market Risk measure and deviation measure Pricing rule Convex optimization Optimality conditions;
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- Alejandro Balbás & Iván Blanco & Eliseo Navarro, 2013. "Equity, commodity and interest rate volatility derivatives," Business Economics Working Papers id-13-02, Universidad Carlos III, Instituto sobre Desarrollo Empresarial "Carmen Vidal Ballester".
- Assa, Hirbod & Balbás, Alejandro, 2011. "Good Deals and compatible modification of risk and pricing rule: a regulatory treatment," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/12967, Universidad Carlos III de Madrid.
- Alejandro Balbás & Beatriz Balbás & Antonio Heras, 2010. "Stability of the optimal reinsurance with respect to the risk measure," Business Economics Working Papers wb100201, Universidad Carlos III, Departamento de Economía de la Empresa.
- Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2010. "CAPM and APT-like models with risk measures," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1166-1174, June.
- Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2010. "CAPM and APT-like models with risk measures," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/12945, Universidad Carlos III de Madrid.
- Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2011. "Stable solutions for optimal reinsurance problems involving risk measures," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/13079, Universidad Carlos III de Madrid.
- Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2011. "Stable solutions for optimal reinsurance problems involving risk measures," European Journal of Operational Research, Elsevier, vol. 214(3), pages 796-804, November.
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