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Ambiguous Volatility and Asset Pricing in Continuous Time

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  • Larry G. Epstein
  • Shaolin Ji

Abstract

We formulate a model of utility for a continuous-time framework that captures aversion to ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules based on hedging arguments. Because ambiguous volatility implies market incompleteness, hedging arguments determine prices only up to intervals. In order to obtain sharper predictions, we apply the model of utility to a representative agent endowment economy and study equilibrium asset returns. A version of the consumption capital asset pricing model is derived, and the effects of ambiguous volatility are described. The Author 2013. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

Suggested Citation

  • Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
  • Handle: RePEc:oup:rfinst:v:26:y:2013:i:7:p:1740-1786
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    References listed on IDEAS

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    1. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 315-346, December.
    2. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
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    4. Larry G. Epstein & Martin Schneider, 2008. "Ambiguity, Information Quality, and Asset Pricing," Journal of Finance, American Finance Association, vol. 63(1), pages 197-228, February.
    5. Epstein, Larry G. & Ji, Shaolin, 2014. "Ambiguous volatility, possibility and utility in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 269-282.
    6. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, May.
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    15. Vorbrink, Jörg, 2017. "Financial markets with volatility uncertainty," Center for Mathematical Economics Working Papers 441, Center for Mathematical Economics, Bielefeld University.
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    Citations

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    Cited by:

    1. Jeleva, Meglena & Tallon, Jean-Marc, 2016. "Ambiguïté, comportements et marchés financiers," L'Actualité Economique, Société Canadienne de Science Economique, vol. 92(1-2), pages 351-383, Mars-Juin.
    2. Meglena Jeleva & Jean-Marc Tallon, 2016. "Ambiguïté, comportements et marchés financiers," Post-Print halshs-01109639, HAL.
    3. Amine Ismail & Huy^en Pham, 2016. "Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix ," Papers 1610.06805, arXiv.org, revised Mar 2017.
    4. Hu, Mingshang & Ji, Shaolin, 2017. "Dynamic programming principle for stochastic recursive optimal control problem driven by a G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 107-134.
    5. Tian, Dejian & Tian, Weidong, 2014. "Optimal risk-sharing under mutually singular beliefs," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 41-49.
    6. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    7. Qian Lin, 2015. "Dynamic indifference pricing via the G-expectation," Papers 1503.08628, arXiv.org.
    8. Frank Riedel, 2015. "Financial economics without probabilistic prior assumptions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(1), pages 75-91, April.
    9. Epstein, Larry G. & Ji, Shaolin, 2014. "Ambiguous volatility, possibility and utility in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 269-282.
    10. Patrick Beissner & Frank Riedel, 2014. "Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty," Papers 1409.6940, arXiv.org.
    11. Marcel Nutz, 2014. "Superreplication under model uncertainty in discrete time," Finance and Stochastics, Springer, vol. 18(4), pages 791-803, October.
    12. repec:spr:joecth:v:64:y:2017:i:2:d:10.1007_s00199-016-0979-y is not listed on IDEAS
    13. repec:eee:jfinec:v:126:y:2017:i:3:p:668-688 is not listed on IDEAS
    14. Vorbrink, Jörg, 2014. "Financial markets with volatility uncertainty," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 64-78.
    15. Huang, Helen Hui & Zhang, Shunming & Zhu, Wei, 2017. "Limited participation under ambiguity of correlation," Journal of Financial Markets, Elsevier, vol. 32(C), pages 97-143.
    16. Thibaut Mastrolia & Dylan Possamai, 2015. "Moral hazard under ambiguity," Papers 1511.03616, arXiv.org, revised Oct 2016.
    17. repec:kap:annfin:v:13:y:2017:i:1:d:10.1007_s10436-016-0291-7 is not listed on IDEAS
    18. repec:bla:irvfin:v:17:y:2017:i:2:p:205-233 is not listed on IDEAS
    19. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.

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