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RFS Advance Access originally published online on November 3, 2004
Review of Financial Studies 2005 18(1):131-164; doi:10.1093/rfs/hhi011
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The Review of Financial Studies Vol. 18, No. 1 © 2005 The Society for Financial Studies; all rights reserved.

An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks

Jun Liu
Anderson School at UCLA

Jun Pan
MIT Sloan School of Management, CCFR and NBER

Tan Wang
Sauder School of Business at UBC and CCFR

Address correspondence to: Jun Pan, MIT Sloan School of Management, Cambridge, MA 02142, or e-mail: junpan{at}mit.edu.

This article studies 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. The equilibrium equity premium has three components: the diffusive- and jump-risk premiums, both driven by risk aversion; and the "rare-event premium," driven exclusively by uncertainty aversion. To disentangle the rare-event premiums from the standard risk-based premiums, we examine the equilibrium prices of options across moneyness or, equivalently, across varying sensitivities to rare events. We find that uncertainty aversion toward rare events plays an important role in explaining the pricing differentials among options across moneyness, particularly the prevalent "smirk" patterns documented in the index options market.


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