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An Equilibrium Model of Rare Event Premia

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  • Liu, Jun
  • Pan, Jun
  • Wang, Tan
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    Abstract

    In this paper, we study the asset pricing implication of imprecise knowledge about rare events. Modeling rare events as jumps in the aggregate endowment, we explicitly solve the equilibrium asset prices in a pure-exchange economy with a representative agent who is averse not only to risk but also to model uncertainty with respect to rare events. Our results show that there are three components in the equity premium: the diffusive-risk premium, the jump-risk premium, and the "rare event premium." While the first two premia are generated by risk aversion, the last one is driven exclusively by uncertainty aversion. To dis-entangle the "rare event premium" from the standard risk-based premia, we examine the equilibrium prices of options with varying degree of moneyness. We consider models with different levels of uncertainty aversion -- including the one with zero uncertainty aversion, and calibrate all models to the same level of equity premium. Although observationally equivalent with respect to the equity market, these models provide distinctly different predictions on the option market. Without incorporating uncertainty aversion, the standard model cannot explain the extent of the premia implicit in options, particularly the prevalent "smirk" patterns documented in the index options market. In contrast, the models incorporating uncertainty aversion can generate significant premia for at-the-money option prices, as well as pronounced "smirk" patterns for options with different degrees of moneyness.

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    File URL: http://hdl.handle.net/1721.1/1575
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    Bibliographic Info

    Paper provided by Massachusetts Institute of Technology (MIT), Sloan School of Management in its series Working papers with number 4370-02.

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    Date of creation: 12 Aug 2002
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    Handle: RePEc:mit:sloanp:1575

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    Postal: MASSACHUSETTS INSTITUTE OF TECHNOLOGY (MIT), SLOAN SCHOOL OF MANAGEMENT, 50 MEMORIAL DRIVE CAMBRIDGE MASSACHUSETTS 02142 USA
    Phone: 617-253-2659
    Web page: http://mitsloan.mit.edu/
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    Postal: MASSACHUSETTS INSTITUTE OF TECHNOLOGY (MIT), SLOAN SCHOOL OF MANAGEMENT, 50 MEMORIAL DRIVE CAMBRIDGE MASSACHUSETTS 02142 USA

    Related research

    Keywords: Asset Prices; Event Premia; Equilibrium Model;

    References

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    1. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
    2. Bryan R. Routledge & Stanley E. Zin, 2001. "Model Uncertainty and Liquidity," NBER Working Papers 8683, National Bureau of Economic Research, Inc.
    3. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
    4. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
    5. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    6. Epstein, Larry G. & Miao, Jianjun, 2003. "A two-person dynamic equilibrium under ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1253-1288, May.
    7. Raman Uppal & Tan Wang, 2003. "Model Misspecification and Underdiversification," Journal of Finance, American Finance Association, vol. 58(6), pages 2465-2486, December.
    8. Mehra, Rajnish & Prescott, Edward C., 1988. "The equity risk premium: A solution?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 133-136, July.
    9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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    Cited by:
    1. Fidel Gonzalez & Arnulfo Rodriguez, 2013. "Monetary Policy Under Time-Varying Uncertainty Aversion," Computational Economics, Society for Computational Economics, vol. 41(1), pages 125-150, January.
    2. Sbuelz, A. & Trojani, F., 2002. "Equilibrium Asset Pricing with Time-Varying Pessimism," Discussion Paper 2002-102, Tilburg University, Center for Economic Research.

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