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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. 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.
  2. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," NBER Working Papers 16181, National Bureau of Economic Research, Inc.
  3. Joerg Vorbrink, 2010. "Financial markets with volatility uncertainty," Papers 1012.1535, arXiv.org, revised Dec 2010.
  4. Andrew W. Lo & Mark T. Mueller, 2010. "WARNING: Physics Envy May Be Hazardous To Your Wealth!," Papers 1003.2688, arXiv.org, revised Mar 2010.
  5. 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.
  6. Cosmin Ilut & Martin Schneider, 2012. "Ambiguous Business Cycles," NBER Working Papers 17900, National Bureau of Economic Research, Inc.
  7. 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.
  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. Philipp Karl Illeditsch, 2011. "Ambiguous Information, Portfolio Inertia, and Excess Volatility," Journal of Finance, American Finance Association, vol. 66(6), pages 2213-2247, December.
  10. 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.
  11. Larry Epstein & Martin Schneider, 2005. "Ambiguity, Information Quality and Asset Pricing," RCER Working Papers 519, University of Rochester - Center for Economic Research (RCER).
  12. 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.
  13. Larry Epstein & Shaolin Ji, 2011. "Ambiguous Volatility, Possibility and Utility in Continuous Time," Papers 1103.1652, arXiv.org, revised Jan 2013.
  14. Jason Beeler & John Y. Campbell, 2009. "The Long-Run Risks Model and Aggregate Asset Prices: An Empirical Assessment," NBER Working Papers 14788, National Bureau of Economic Research, Inc.
  15. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER).
  16. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, 05.
  17. 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).
  18. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
  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. Jörg Vorbrink, 2010. "Financial markets with volatility uncertainty," Working Papers 441, Bielefeld University, Center for Mathematical Economics.
  21. Bjørn Eraker & Ivan Shaliastovich, 2008. "An Equilibrium Guide To Designing Affine Pricing Models," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 519-543.
  22. 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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