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An Equilibrium Model of Rare Event Premia

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

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.

Suggested Citation

  • Liu, Jun & Pan, Jun & Wang, Tan, 2002. "An Equilibrium Model of Rare Event Premia," Working papers 4370-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
  • Handle: RePEc:mit:sloanp:1575
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    File URL: http://hdl.handle.net/1721.1/1575
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    References listed on IDEAS

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    1. Raman Uppal & Tan Wang, 2003. "Model Misspecification and Underdiversification," Journal of Finance, American Finance Association, vol. 58(6), pages 2465-2486, December.
    2. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
    3. Bryan Routledge & Stanley Zin, 2009. "Model Uncertainty and Liquidity," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(4), pages 543-566, October.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    5. 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.
    6. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    7. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
    8. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    9. Mehra, Rajnish & Prescott, Edward C., 1988. "The equity risk premium: A solution?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 133-136, July.
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    Cited by:

    1. Fidel Gonzalez & Arnulfo Rodriguez, 2013. "Monetary Policy Under Time-Varying Uncertainty Aversion," Computational Economics, Springer;Society for Computational Economics, vol. 41(1), pages 125-150, January.

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    Keywords

    Asset Prices; Event Premia; Equilibrium Model;

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