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Market consistent valuations with financial imperfection

Author

Listed:
  • Hirbod Assa

    (University of Liverpool)

  • Nikolay Gospodinov

    (Federal Reserve Bank of Atlanta)

Abstract

In this paper, we study market consistent valuations in imperfect markets. In the first part of the paper, we observe that in an imperfect market one needs to distinguish two type of market consistencies, namely types I and II. We show that while market consistency of type I holds without very strong conditions, market consistency of type II (which in the literature is known as the usual definition of market consistency) is only well defined in perfect markets. This is important since the existing literature on market consistency considers perfect markets where the two market consistencies are equivalent. In the second part of the paper, by introducing a best estimator we find strong connections between hedging and market consistency of either type. We show under very general conditions, the type I and the type II market consistent evaluators are best estimators, and establish a two-step representation for the market consistent risk evaluators. In the third part of the paper, we present several families of market consistent evaluators in imperfect markets.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:decfin:v:41:y:2018:i:1:d:10.1007_s10203-018-0207-2
    DOI: 10.1007/s10203-018-0207-2
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    References listed on IDEAS

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    1. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    2. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    3. Elyès Jouini & Hédi Kallal, 1999. "Viability and Equilibrium in Securities Markets with Frictions," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 275-292, July.
    4. Balbás, Alejandro & Balbás, Raquel & Mayoral, Silvia, 2009. "Portfolio choice and optimal hedging with general risk functions: A simplex-like algorithm," European Journal of Operational Research, Elsevier, vol. 192(2), pages 603-620, January.
    5. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    6. repec:dau:papers:123456789/5630 is not listed on IDEAS
    7. Jeremy Staum, 2004. "Fundamental Theorems of Asset Pricing for Good Deal Bounds," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 141-161, April.
    8. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short‐Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232, July.
    9. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    10. Dhaene, Jan & Stassen, Ben & Barigou, Karim & Linders, Daniël & Chen, Ze, 2017. "Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 14-27.
    11. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
    12. Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
    13. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    14. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    15. Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Discussion Paper 2014-002, Tilburg University, Center for Economic Research.
    16. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
    17. 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.
    18. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    19. repec:dau:papers:123456789/5647 is not listed on IDEAS
    20. repec:dau:papers:123456789/5603 is not listed on IDEAS
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    More about this item

    Keywords

    Imperfect financial valuation; Risk evaluation; Hedging; Market consistent valuation;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

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