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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.

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Bibliographic Info

Article provided by Society for Financial Studies in its journal The Review of Financial Studies.

Volume (Year): 26 (2013)
Issue (Month): 7 ()
Pages: 1740-1786

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Handle: RePEc:oup:rfinst:v:26:y:2013:i:7:p:1740-1786

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  1. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
  2. Beeler, Jason & Campbell, John Y., 2012. "The Long-Run Risks Model and Aggregate Asset Prices: An Empirical Assessment," Critical Finance Review, now publishers, vol. 1(1), pages 141-182, January.
  3. Cosmin Ilut & Martin Schneider, 2012. "Ambiguous Business Cycles," Working Papers 12-06, Duke University, Department of Economics.
  4. Jesús Fernández-Villaverde & Pablo A. Guerrón-Quintana & Juan Rubio-Ramírez & Martín Uribe, 2009. "Risk Matters: The Real Effects of Volatility Shocks," NBER Working Papers 14875, National Bureau of Economic Research, Inc.
  5. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, 05.
  6. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
  7. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
  8. Joerg Vorbrink, 2010. "Financial markets with volatility uncertainty," Papers 1012.1535, arXiv.org, revised Dec 2010.
  9. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
  10. Larry Epstein & Martin Schneider, 2004. "Ambiguity, Information Quality and Asset Pricing," RCER Working Papers 507, University of Rochester - Center for Economic Research (RCER).
  11. Larry Epstein & Shaolin Ji, 2011. "Ambiguous Volatility, Possibility and Utility in Continuous Time," Papers 1103.1652, arXiv.org, revised Jan 2013.
  12. Andrew W. Lo & Mark T. Mueller, 2010. "WARNING: Physics Envy May Be Hazardous To Your Wealth!," Papers 1003.2688, arXiv.org, revised Mar 2010.
  13. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
  14. Beeler, Jason & Campbell, John Y., 2012. "The Long-Run Risks Model and Aggregate Asset Prices: An Empirical Assessment," Scholarly Articles 9887621, Harvard University Department of Economics.
  15. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
  16. Peter Carr & Roger Lee, 2009. "Volatility Derivatives," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 319-339, November.
  17. Jörg Vorbrink, 2010. "Financial markets with volatility uncertainty," Working Papers 441, Bielefeld University, Center for Mathematical Economics.
  18. Bjørn Eraker & Ivan Shaliastovich, 2008. "An Equilibrium Guide To Designing Affine Pricing Models," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 519-543.
  19. 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.
  20. John Y. Campbell & Stefano Giglio & Christopher Polk & Robert Turley, 2012. "An Intertemporal CAPM with Stochastic Volatility," NBER Working Papers 18411, National Bureau of Economic Research, Inc.
  21. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 315-346, December.
  22. Willard, Gregory A & Dybvig, Philip H, 1999. "Empty Promises and Arbitrage," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 807-34.
  23. Philipp Karl Illeditsch, 2011. "Ambiguous Information, Portfolio Inertia, and Excess Volatility," Journal of Finance, American Finance Association, vol. 66(6), pages 2213-2247, December.
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Cited by:
  1. Larry Epstein & Shaolin Ji, 2011. "Ambiguous Volatility, Possibility and Utility in Continuous Time," Papers 1103.1652, arXiv.org, revised Jan 2013.

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