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Extending pricing rules with general risk functions

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  • Balbás, Alejandro
  • Balbás, Raquel
  • Garrido, José

Abstract

The 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.

Suggested Citation

  • Balbás, Alejandro & Balbás, Raquel & Garrido, José, 2010. "Extending pricing rules with general risk functions," European Journal of Operational Research, Elsevier, vol. 201(1), pages 23-33, February.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:1:p:23-33
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Hirbod Assa & Nikolay Gospodinov, 2018. "Market consistent valuations with financial imperfection," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(1), pages 65-90, May.
    2. Hirbod Assa & Keivan Mallahi Karai, 2013. "Hedging, Pareto Optimality, and Good Deals," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 900-917, June.
    3. 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.
    4. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2010. "Stability of the optimal reinsurance with respect to the risk measure," DEE - Working Papers. Business Economics. WB wb100201, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    5. Balbás, Alejandro & Garrido, José & Okhrati, Ramin, 2016. "Good deal measurement in asset pricing: Actuarial and financial implications," INDEM - Working Paper Business Economic Series 23546, Instituto para el Desarrollo Empresarial (INDEM).
    6. 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.
    7. Alejandro Balbás & Iván Blanco & José Garrido, 2014. "Measuring Risk When Expected Losses Are Unbounded," Risks, MDPI, vol. 2(4), pages 1-14, September.
    8. Hirbod Assa & Nikolay Gospodinov, 2017. "A Robust Approach to Hedging and Pricing in Imperfect Markets," Risks, MDPI, vol. 5(3), pages 1-20, July.
    9. Balbás, Alejandro & Blanco, Iván & Navarro, Eliseo, 2013. "Equity, commodity and interest rate volatility derivatives," INDEM - Working Paper Business Economic Series id-13-02, Instituto para el Desarrollo Empresarial (INDEM).

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