An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks∗ Jun Liu Anderson School at UCLA

This paper 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 diffusiveand jump-risk premia, both driven by risk aversion; and the “rare-event premium,” driven exclusively by uncertainty aversion. To disentangle the rare-event premium from the standard risk-based premia, 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.