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Ambiguous Volatility and Asset Pricing in Continuous Time

  • Larry G. Epstein
  • Shaolin Ji

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.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2012s-29.

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Length: 60 pages
Date of creation: 01 Nov 2012
Date of revision:
Handle: RePEc:cir:cirwor:2012s-29
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  1. 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.
  2. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," NBER Working Papers 16181, National Bureau of Economic Research, Inc.
  3. Zengjing Chen & Larry G. Epstein, 2000. "Ambiguity, risk and asset returns in continuous time," RCER Working Papers 474, University of Rochester - Center for Economic Research (RCER).
  4. Larry Epstein & Martin Schneider, 2005. "Ambiguity, Information Quality and Asset Pricing," RCER Working Papers 519, University of Rochester - Center for Economic Research (RCER).
  5. Andrew W. Lo & Mark T. Mueller, 2010. "WARNING: Physics Envy May Be Hazardous To Your Wealth!," Papers 1003.2688,, revised Mar 2010.
  6. 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.
  7. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER).
  8. 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.
  9. Larry Epstein & Shaolin Ji, 2011. "Ambiguous Volatility, Possibility and Utility in Continuous Time," Papers 1103.1652,, revised Jan 2013.
  10. 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.
  11. 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.
  12. Cosmin Ilut & Martin Schneider, 2012. "Ambiguous Business Cycles," NBER Working Papers 17900, National Bureau of Economic Research, Inc.
  13. Pablo Guerron & Martin Uribe & Juan Rubio-Ramirez & Jesus Fernandez-Villaverde, 2010. "Risk Matters: The Real Effects of Volatility Shocks," 2010 Meeting Papers 281, Society for Economic Dynamics.
  14. 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.
  15. Philipp Karl Illeditsch, 2011. "Ambiguous Information, Portfolio Inertia, and Excess Volatility," Journal of Finance, American Finance Association, vol. 66(6), pages 2213-2247, December.
  16. Bjørn Eraker & Ivan Shaliastovich, 2008. "An Equilibrium Guide To Designing Affine Pricing Models," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 519-543.
  17. Joerg Vorbrink, 2010. "Financial markets with volatility uncertainty," Papers 1012.1535,, revised Dec 2010.
  18. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  19. Jörg Vorbrink, 2010. "Financial markets with volatility uncertainty," Center for Mathematical Economics Working Papers 441, Center for Mathematical Economics, Bielefeld University.
  20. 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.
  21. Peter Carr & Roger Lee, 2009. "Volatility Derivatives," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 319-339, November.
  22. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
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