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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 framework 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://arxiv.org/pdf/1301.4614
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Paper provided by arXiv.org in its series Papers with number 1301.4614.

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Date of creation: Jan 2013
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Handle: RePEc:arx:papers:1301.4614
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  1. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
  2. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," NBER Working Papers 16181, National Bureau of Economic Research, Inc.
  3. 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.
  4. 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.
  5. Fernández-Villaverde, Jesús & Guerron-Quintana, Pablo A. & Rubio-Ramírez, Juan Francisco & Uribe, Martín, 2009. "Risk Matters: The Real Effects of Volatility Shocks," CEPR Discussion Papers 7264, C.E.P.R. Discussion Papers.
  6. Cosmin Ilut & Martin Schneider, 2012. "Ambiguous Business Cycles," Working Papers 12-06, Duke University, Department of Economics.
  7. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
  8. 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.
  9. Peter Carr & Roger Lee, 2009. "Volatility Derivatives," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 319-339, November.
  10. 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.
  11. 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.
  12. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
  13. Andrew W. Lo & Mark T. Mueller, 2010. "WARNING: Physics Envy May Be Hazardous To Your Wealth!," Papers 1003.2688, arXiv.org, revised Mar 2010.
  14. Larry Epstein & Martin Schneider, 2005. "Ambiguity, Information Quality and Asset Pricing," RCER Working Papers 519, University of Rochester - Center for Economic Research (RCER).
  15. Jörg Vorbrink, 2010. "Financial markets with volatility uncertainty," Working Papers 441, Bielefeld University, Center for Mathematical Economics.
  16. 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.
  17. 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.
  18. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  19. Joerg Vorbrink, 2010. "Financial markets with volatility uncertainty," Papers 1012.1535, arXiv.org, revised Dec 2010.
  20. Philipp Karl Illeditsch, 2011. "Ambiguous Information, Portfolio Inertia, and Excess Volatility," Journal of Finance, American Finance Association, vol. 66(6), pages 2213-2247, December.
  21. 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.
  22. Bjørn Eraker & Ivan Shaliastovich, 2008. "An Equilibrium Guide To Designing Affine Pricing Models," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 519-543.
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