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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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File URL: http://www.cirano.qc.ca/files/publications/2012s-29.pdf
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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. Bjørn Eraker & Ivan Shaliastovich, 2008. "An Equilibrium Guide To Designing Affine Pricing Models," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 519-543.
  2. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
  3. Campbell, John Y & Giglio, Stefano W & Polk, Christopher & Turley, Robert, 2015. "An Intertemporal CAPM with Stochastic Volatility," CEPR Discussion Papers 10681, C.E.P.R. Discussion Papers.
  4. 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.
  5. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 315-346, December.
  6. 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).
  7. Larry Epstein & Martin Schneider, 2005. "Ambiguity, Information Quality and Asset Pricing," RCER Working Papers 519, University of Rochester - Center for Economic Research (RCER).
  8. 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.
  9. Joerg Vorbrink, 2010. "Financial markets with volatility uncertainty," Papers 1012.1535, arXiv.org, revised Dec 2010.
  10. 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.
  11. Pablo A. Guerron-Quintana & Martin Uribe & Juan Rubio-Ramirez & Jesús Fernández-Villaverde, 2009. "Risk Matters: The Real E¤ects of Volatility Shocks," 2009 Meeting Papers 237, Society for Economic Dynamics.
  12. Philipp Karl Illeditsch, 2011. "Ambiguous Information, Portfolio Inertia, and Excess Volatility," Journal of Finance, American Finance Association, vol. 66(6), pages 2213-2247, December.
  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. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  15. Jörg Vorbrink, 2010. "Financial markets with volatility uncertainty," Center for Mathematical Economics Working Papers 441, Center for Mathematical Economics, Bielefeld University.
  16. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
  17. Andrew W. Lo & Mark T. Mueller, 2010. "WARNING: Physics Envy May Be Hazardous To Your Wealth!," Papers 1003.2688, arXiv.org, revised Mar 2010.
  18. 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.
  19. 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.
  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.
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