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Ambiguous Volatility and Asset Pricing in Continuous Time

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  • Larry G. Epstein
  • Shaolin Ji

Abstract

This paper formulates a model of utility for a continuous time frame-work that captures the decision-maker's concern with 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. Ambiguous volatility implies market incompleteness that rules out perfect hedging. Consequently, hedging arguments determine prices only up to intervals. However, sharper predictions can be obtained by assuming preference maximization and equilibrium. Thus we apply the model of utility to a representative agent endowment economy to study equilibrium asset returns. A version of the C-CAPM is derived and the effects of ambiguous volatility are described.

Suggested Citation

  • Larry G. Epstein & Shaolin Ji, 2012. "Ambiguous Volatility and Asset Pricing in Continuous Time," CIRANO Working Papers 2012s-29, CIRANO.
  • Handle: RePEc:cir:cirwor:2012s-29
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    File URL: http://www.cirano.qc.ca/files/publications/2012s-29.pdf
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    References listed on IDEAS

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    1. Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March.
    2. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 315-346, December.
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    7. 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.
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    Citations

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    Cited by:

    1. Patrick Beissner & Frank Riedel, 2014. "Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty," Papers 1409.6940, arXiv.org.
    2. Tolulope Fadina & Ariel Neufeld & Thorsten Schmidt, 2018. "Affine processes under parameter uncertainty," Papers 1806.02912, arXiv.org.
    3. 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.
    4. 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.
    5. Marcel Nutz, 2014. "Superreplication under model uncertainty in discrete time," Finance and Stochastics, Springer, vol. 18(4), pages 791-803, October.
    6. repec:spr:joecth:v:64:y:2017:i:2:d:10.1007_s00199-016-0979-y is not listed on IDEAS
    7. Meglena Jeleva & Jean-Marc Tallon, 2016. "Ambiguïté, comportements et marchés financiers," Post-Print halshs-01109639, HAL.
    8. Amine Ismail & Huy^en Pham, 2016. "Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix ," Papers 1610.06805, arXiv.org, revised Mar 2017.
    9. repec:eee:jfinec:v:126:y:2017:i:3:p:668-688 is not listed on IDEAS
    10. Vorbrink, Jörg, 2014. "Financial markets with volatility uncertainty," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 64-78.
    11. 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.
    12. 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.
    13. repec:spr:finsto:v:22:y:2018:i:3:d:10.1007_s00780-018-0362-x is not listed on IDEAS
    14. Thibaut Mastrolia & Dylan Possamai, 2015. "Moral hazard under ambiguity," Papers 1511.03616, arXiv.org, revised Oct 2016.
    15. repec:kap:annfin:v:13:y:2017:i:1:d:10.1007_s10436-016-0291-7 is not listed on IDEAS
    16. Tian, Dejian & Tian, Weidong, 2014. "Optimal risk-sharing under mutually singular beliefs," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 41-49.
    17. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    18. Qian Lin, 2015. "Dynamic indifference pricing via the G-expectation," Papers 1503.08628, arXiv.org.
    19. 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.
    20. repec:bla:irvfin:v:17:y:2017:i:2:p:205-233 is not listed on IDEAS
    21. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.

    More about this item

    Keywords

    ambiguity; option pricing; recursive utility; G-Brownian motion; robust stochastic volatility; sentiment; overconfidence; optimism.;

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